Scalable Management of Enterprise and Data-Center Networks

Scalable Management of Enterprise and Data-Center Networks
Scalable Management of Enterprise and
Data-Center Networks
Minlan Yu
A Dissertation
Presented to the Faculty
of Princeton University
in Candidacy for the Degree
of Doctor of Philosophy
Recommended for Acceptance
By the Department of
Computer Science
Adviser: Jennifer Rexford
September 2011
c Copyright by Minlan Yu, 2011. All rights reserved.
Abstract
The networks in campuses, companies, and data centers are growing larger and becoming more
complicated to manage. Today, network operators devote tremendous time and effort to three key
management tasks — routing, access control, and troubleshooting. Rather than trying to make
today’s brittle networks easier to manage, we focus on new network designs that are inherently
easier to manage and scale to many hosts, switches, and applications.
We design and develop a new management system that scales the routing, access control, and
performance diagnosis in enterprise and data center networks. The key challenges are the large
number of hosts, switches, and applications in these networks and the need for flexible policies,
while faced with strict memory and power constraints in the switches. To address these challenges,
we propose three key ideas: (1) designing new data structures and algorithms that make effective
use of limited memory in switches; (2) redirecting traffic when simple switches do not have enough
memory to handle packets; (3) rethinking the division of labor among switches, hosts, and a
centralized management system to make the network both flexible and scalable.
Based on the key ideas, we propose a new management system that addresses the scalability challenges of routing, supporting flexible policies, and performance diagnosis with three key
components:
(i) BUFFALO: A scalable packet forwarding architecture that reduces the switch memory
usage for storing the forwarding table using Bloom filters — a compact way of representing a set
of elements. To gracefully handle the false positives caused by Bloom filters, BUFFALO sends
packets through a slightly longer path.
(ii) DIFANE: A scalable way to enforce flexible management policies from the centralized
management system to the switches. DIFANE rethinks the division of labor between the centralized management system and the switches, by pulling some rule processing functions back to the
switches, to achieve better scalability.
(iii) SNAP: A scalable network performance diagnosis architecture that exposes the interactions
between the network and applications in data centers. SNAP passively logs traffic statistics in the
end-host network stack and pinpoints problems that occur at the network device, network stack
and the application software.
iii
Our systems can be easily implemented with small modifications in today’s switches and end
hosts, as demonstrated by our prototypes built using the OpenFlow switches and Microsoft Windows servers, and our evaluation using configuration data from AT&T networks and a deployment
in a production data center.
iv
Acknowledgments
I would like to thank my advisor Jennifer Rexford for bringing me into the field of data networking,
for her guidance and constant encouragement. She has taught me how to find research problems
from practice, conduct solid research with real world impact, and present research results to
different audiences. Being a student of hers is one of the luckiest experiences in my life.
I’ve been very lucky to get a chance to work with and learn from Albert Greenberg. He keeps
reminding me to find real problems from engineers and to provide practical tools that can solve
these real problems. I also learnt that good research projects should not only be intellectually
exciting, but also be practical and useful. This will be a goal for my future research.
Mike J. Freedman has been another awesome colleague and mentor. His good taste of research
problems, his diligence on systems research, and passion on building real systems served as a good
model for me.
I also benefited a lot from collaborations with many people that led to this thesis. I especially
thank Alex Fabrikant for contributing to the theoretical proofs in Chapter 2; Michael J. Freedman
and Jia Wang for insightful discussions on the distributed system solutions and rule partitioning
and caching algorithms in Chapter 3; Albert Greenberg, Dave Maltz, Lihua Yuan, Srikanth Kandula, and Changhoon Kim for the great help on the motivations of designing the SNAP tool and
evaluating SNAP in the production data centers in Chapter 4. I also thank Ed Felten and Vivek
Pai for being part of my committee and giving great feedback.
I would also like to thank my collaborators on various finished and ongoing projects including
Matthew Caesar, Mung Chiang, Nick Feamster, Lavanya Jose, Eric Keller, Steven Ko, Li Erran
Li, Lucian Popa, Sanjay Rao, Sylvia Ratnasamy, Michael Schapira, Ion Stoica, Peng Sun, Xin
Sun, Marina Thottan, Yung Yi for sharing your expertise and ideas with me. It is an exciting
experience to collaborate with you!
I thank previous and current cabernet group members Nate Foster, Sharon Goldberg, Rob
Harrison, Wenjie Jiang, Elliot Karpilovsky, Changhoon Kim, Haakon Ringberg, Martin Suchara,
Yi Wang, Rui Zhang-Shen, Yaping Zhu for their inspiring discussions and many thoughtful comments on papers and practice talks. I also thank Kai Li for giving me great advice on how to be
a good researcher over the years.
v
I benefited a lot from my three summer internships. Many thanks to Marina Thottan at Bell
Labs; Angela Chiu, Robert Doverspike, Guangzhi Li, and Dahai Xu at AT&T Labs - Research;
Chuanxiong Guo, Randy Kern, Varugis Kurien, Saby Mahajan, Jitendra Padhye, Murari Sridharan, and Ming Zhang at Microsoft for giving me great industrial internship experiences and letting
me appreciate the importance of solving practically challenging problems.
I would like to thank my parents Gang and Yuli for their love and support; I would like to
thank Zhiwei for sharing his life with me; I would also like to thank my friends, both inside and
outside Princeton University, for bringing happiness and wisdom to my life. Finally, I would like
to thank Princeton University for giving me wonderful memory as a graduate student.
This dissertation work was supported by DARPA Coronet PO S000004001, NSF grants CNS
05-09447, 08-31646, and 09-04729.
vi
Contents
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1 Introduction
1.1
iii
1
Edge Networks and Their Scalability Challenges . . . . . . . . . . . . . . . . . . .
1
1.1.1
Edge Networks Are Large . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2
1.1.2
Edge Networks Need Fine-grained Policies . . . . . . . . . . . . . . . . . . .
2
1.1.3
Simple, Cheap Switches Have Limited Memory . . . . . . . . . . . . . . . .
3
Management of Today’s Edge Networks . . . . . . . . . . . . . . . . . . . . . . . .
4
1.2.1
Hybrids of Ethernet Islands Connected by IP Routers . . . . . . . . . . . .
5
1.2.2
Policy Support with Access Control Lists Between Virtual LANs . . . . . .
6
1.2.3
Ad-hoc Troubleshooting with Application and Network Logs . . . . . . . .
6
1.2.4
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7
Emerging Trends of Redesigning for Manageability . . . . . . . . . . . . . . . . . .
7
1.3.1
Flat Addresses to Support Zero Configuration and Host Mobility . . . . . .
8
1.3.2
Shortest Path Routing to Improve Performance . . . . . . . . . . . . . . . .
9
1.3.3
Centralized Control to Make Policy Configuration Easier . . . . . . . . . .
9
1.3.4
Flow-based Switches to Enable Fine-grained Policies . . . . . . . . . . . . .
9
1.4
Key Design Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10
1.5
A Scalable Management System for Edge Networks . . . . . . . . . . . . . . . . . .
11
1.2
1.3
2 BUFFALO: Scaling Packet Forwarding on Switches
2.1
14
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
15
2.1.1
15
Memory Problems in the Data Plane . . . . . . . . . . . . . . . . . . . . . .
vii
2.1.2
. . . . . . . . . . . . . . . . . . .
16
2.2
Shortest Paths & Flat Addresses . . . . . . . . . . . . . . . . . . . . . . . . . . . .
18
2.3
Packet Forwarding in BUFFALO . . . . . . . . . . . . . . . . . . . . . . . . . . . .
19
2.3.1
One Bloom Filter Per Next Hop . . . . . . . . . . . . . . . . . . . . . . . .
20
2.3.2
Handling False Positives in Fast Memory . . . . . . . . . . . . . . . . . . .
21
2.3.3
CBFs for Handling Routing Changes . . . . . . . . . . . . . . . . . . . . . .
22
Handling False Positives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
23
2.4.1
Handling One False Positive by Avoiding Incoming Interface . . . . . . . .
23
2.4.2
Handling Multiple False Positives with Random Selection . . . . . . . . . .
25
2.4.3
Stretch in Realistic Networks . . . . . . . . . . . . . . . . . . . . . . . . . .
42
2.4
2.5
The BUFFALO Forwarding Architecture
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
44
2.5.1
Optimizing Bloom-Filter Sizes . . . . . . . . . . . . . . . . . . . . . . . . .
44
2.5.2
Analytical Results of False Positives . . . . . . . . . . . . . . . . . . . . . .
46
Handling Routing Changes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
49
2.6.1
Update BF Based on CBF . . . . . . . . . . . . . . . . . . . . . . . . . . . .
49
2.6.2
Adjust BF Size Without Reconstructing CBF . . . . . . . . . . . . . . . . .
50
2.7
Implementation and Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
51
2.8
Extensions to BUFFALO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
53
2.9
Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
54
2.10 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
56
2.6
Optimizing Memory Usage
3 DIFANE: Scaling Flexible Policy Support on Switches
3.1
3.2
3.3
57
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
57
3.1.1
DIFANE: Doing It Fast ANd Easy . . . . . . . . . . . . . . . . . . . . . . .
58
3.1.2
Comparison to Related Work . . . . . . . . . . . . . . . . . . . . . . . . . .
60
DIFANE Design Decisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
60
3.2.1
Reducing Overhead of Cache Misses . . . . . . . . . . . . . . . . . . . . . .
61
3.2.2
Scaling to Large Networks and Many Rules . . . . . . . . . . . . . . . . . .
62
DIFANE Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
63
3.3.1
63
Rule Partition and Allocation . . . . . . . . . . . . . . . . . . . . . . . . . .
viii
3.3.2
Packet Redirection and Rule Caching . . . . . . . . . . . . . . . . . . . . .
67
3.3.3
Implement DIFANE with Wildcard Rules . . . . . . . . . . . . . . . . . . .
67
Handling Network Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
68
3.4.1
Changes to the Rules
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
68
3.4.2
Topology Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
69
3.4.3
Host Mobility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
70
Handling Wildcard Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
71
3.5.1
Caching Wildcard Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
71
3.5.2
Partitioning Wildcard Rules . . . . . . . . . . . . . . . . . . . . . . . . . . .
73
Design and Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
77
3.6.1
Managing Multiple Sets of Rules . . . . . . . . . . . . . . . . . . . . . . . .
77
3.6.2
DIFANE Switch Prototype . . . . . . . . . . . . . . . . . . . . . . . . . . .
78
Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
80
3.7.1
Performance of the DIFANE Prototype . . . . . . . . . . . . . . . . . . . .
80
3.7.2
Evaluation of Partitioning and Caching . . . . . . . . . . . . . . . . . . . .
84
3.8
DIFANE Deployment Scenarios . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
88
3.9
Flexible Management Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
89
3.10 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
91
3.4
3.5
3.6
3.7
4 SNAP: Scaling Performance Diagnosis on Hosts
4.1
4.2
4.3
92
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
93
4.1.1
Troubleshooting Network Performance . . . . . . . . . . . . . . . . . . . . .
93
4.1.2
Lightweight, Continuous Profiling . . . . . . . . . . . . . . . . . . . . . . . .
94
4.1.3
SNAP Research Contributions . . . . . . . . . . . . . . . . . . . . . . . . .
95
Design of the SNAP Profiler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
96
4.2.1
Socket-Level Monitoring of TCP . . . . . . . . . . . . . . . . . . . . . . . .
97
4.2.2
Classifying Single-Socket Performance . . . . . . . . . . . . . . . . . . . . . 100
4.2.3
Correlation Across TCP Connections . . . . . . . . . . . . . . . . . . . . . . 101
Production Data Center Deployment . . . . . . . . . . . . . . . . . . . . . . . . . . 103
4.3.1
Data Center Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
ix
4.3.2
4.4
4.5
4.6
SNAP Configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
SNAP Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
4.4.1
Validation by Injecting Known Bugs . . . . . . . . . . . . . . . . . . . . . . 105
4.4.2
Validation Against Packet Traces . . . . . . . . . . . . . . . . . . . . . . . . 107
Profiling Data Center Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
4.5.1
Frequency of Performance Problems . . . . . . . . . . . . . . . . . . . . . . 110
4.5.2
Packet Loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
4.5.3
Send Buffer and Receiver Window . . . . . . . . . . . . . . . . . . . . . . . 112
Performance Problems Caught by SNAP . . . . . . . . . . . . . . . . . . . . . . . . 113
4.6.1
Sending Pattern/Packet Loss Issues . . . . . . . . . . . . . . . . . . . . . . 113
4.6.2
Buffer Management and Delayed ACK . . . . . . . . . . . . . . . . . . . . . 115
4.6.3
Other Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
4.7
Reducing SNAP CPU Overhead . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
4.8
Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
4.9
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
5 Conclusion
123
5.1
The Overall Picture of the New Management Systems . . . . . . . . . . . . . . . . 123
5.2
Deployments in Enterprises and Data Centers Differ . . . . . . . . . . . . . . . . . 125
5.2.1
Differences Between Enterprise and Data Center Networks . . . . . . . . . . 125
5.2.2
Customizing the Management System for Enterprises and for Data Centers
126
5.3
Summary of Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
5.4
Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
x
List of Figures
1.1
Three layers in today’s management systems. . . . . . . . . . . . . . . . . . . . . .
4
1.2
Emerging techniques for better network management. . . . . . . . . . . . . . . . .
8
1.3
A Scalable Management System for Edge Networks. . . . . . . . . . . . . . . . . .
11
2.1
BUFFALO Switch Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
20
2.2
Loops caused by false positives (99K false positive link, −→ shortest path link) . .
24
2.3
BUFFALO forwarding graph (99K false positive link, −→ shortest path tree)
26
2.4
Coupling for the expected stretch proof: all nodes at the same hop distance from
. . .
dst are collapsed into 1 node. Forward false positive links, like D to B, are dropped.
The number of backward edges on the line graph is the maximum over all nodes at
that distance of the number of backward and same-depth false-positive links (B’s
edges at d = 1, D’s edges at d = 2). A random walk on the line graph converges no
faster than a random walk on the original. The line graph itself is a valid network,
thus allowing for tight bounds. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
27
2.5
Coupling the depth process in B and L . . . . . . . . . . . . . . . . . . . . . . . .
30
2.6
Exponential stretch with k false positives and no multiple edges: an i + 1-row network like the one on the left has 9i false positives, with worst-case stretch equivalent
to the line graph on the right: S(k) = Θ(3i ) = Θ(3k/9 ) . . . . . . . . . . . . . . . .
40
2.7
Expected stretch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
43
2.8
Stretch with real traces in campus network . . . . . . . . . . . . . . . . . . . . . .
43
2.9
Effect of memory size (T = 10, N = 200K) . . . . . . . . . . . . . . . . . . . . . . .
47
2.10 Effect of number of next hops (M = 600KB, N = 200K) . . . . . . . . . . . . . . .
47
xi
2.11 Effect of number of entries (T = 10, kmax = 8) . . . . . . . . . . . . . . . . . . . . .
48
2.12 Comparison of hash table and Bloom filters (T = 10, kmax = 8) . . . . . . . . . . .
48
2.13 Adjust BF size from m to 2m based on CBF . . . . . . . . . . . . . . . . . . . . .
50
3.1
DIFANE flow management architecture. (Dashed lines are control messages. Straight
lines are data traffic.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
59
3.2
Rule operations in the controller. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
64
3.3
Wildcard rules in DIFANE (A-D are authority switches). . . . . . . . . . . . . . .
65
3.4
An illustration of wildcard rules. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
72
3.5
Construct decision tree for a group of rules. . . . . . . . . . . . . . . . . . . . . . .
74
3.6
Rules for various management modules. . . . . . . . . . . . . . . . . . . . . . . . .
78
3.7
DIFANE prototype implementation. (Cache manager and authority rules (shaded
boxes) only exist in authority switches.) . . . . . . . . . . . . . . . . . . . . . . . .
79
3.8
Experiment setup. (Dashed lines are control messages; straight lines are data traffic.) 81
3.9
Delay comparison of DIFANE and NOX. . . . . . . . . . . . . . . . . . . . . . . . .
82
3.10 Throughput comparison of DIFANE and NOX. . . . . . . . . . . . . . . . . . . . .
82
3.11 Authority switch failure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
84
3.12 Comparison of overlapping and non-overlapping rules. . . . . . . . . . . . . . . . .
85
3.13 Evaluation on number of authority switches. . . . . . . . . . . . . . . . . . . . . . .
85
3.14 The overhead of rule partition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
86
3.15 Cache miss rate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
87
3.16 The stretch of campus network. (We place 1,3,10 authority switches for each set of
the authority rules using k-median and random algorithms respectively.) . . . . . .
87
4.1
SNAP socket-level monitoring and analysis . . . . . . . . . . . . . . . . . . . . . . . .
96
4.2
PDF of #Machines with different average correlation coefficient. . . . . . . . . . . 107
4.3
SNAP estimation error of identifying delayed ACK problems. . . . . . . . . . . . . 109
4.4
# of fast retransmissions and timeouts over time. . . . . . . . . . . . . . . . . . . . 111
4.5
Comparing #FastRetrans and #Timeouts of flows with different throughput. . . . 111
4.6
Delayed ACK after a retransmission timeout. . . . . . . . . . . . . . . . . . . . . . 115
4.7
Performance problem in pipeline communication. . . . . . . . . . . . . . . . . . . . 117
xii
4.8
The CPU overhead of polling TCP statistics (poll) and reading TCP table (rt) with
different number of connections (10, 100, 1K, 5K) and different intervals (from 50
ms to 10 sec). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
4.9
Number of connections per machine. . . . . . . . . . . . . . . . . . . . . . . . . . . 119
4.10 Adjust CPU overhead by dynamically tuning TCP polling rate on a machine with
500 connections (ǫ = 1, r = 2). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
5.1
Combining BUFFALO and DIFANE functions in the same data plane. . . . . . . . 124
xiii
List of Tables
2.1
Notations for the false-positive handler . . . . . . . . . . . . . . . . . . . . . . . . .
23
2.2
Optimal sequences for 1 ≤ k ≤ 17, obtained by brute-force search. . . . . . . . . .
39
3.1
Network characteristics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
84
4.1
Key TCP-level statistics for each socket [1] . . . . . . . . . . . . . . . . . . . . . .
98
4.2
Classes of network performance for a socket . . . . . . . . . . . . . . . . . . . . . .
98
4.3
Characteristics in the production data center. . . . . . . . . . . . . . . . . . . . . . 103
4.4
Percentage of connections and number of applications that have different TCP performance limitations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
xiv
Chapter 1
Introduction
Many networks at the edge of the Internet—in campuses, companies, data centers, and homes—
are growing larger in recent years and are becoming the important components of the Internet. To
manage these networks, campuses, companies, and data centers usually need a huge army of people
to perform daily management tasks such as registering new devices, assigning network addresses,
configuring routing policies, setting up firewalls, troubleshooting, and maintaining efficient and
reliable network connectivity. According to a Yankee group report [2], in most enterprises, network
management is responsible for 80% of the IT budget and 62% of the outages.
The key question that this thesis answers is how to build a management system that both
flexibly supports various management tasks and scales with the growth of these edge networks.
1.1
Edge Networks and Their Scalability Challenges
Edge networks are those networks that are located at the edge of the Internet, such as enterprise
networks (i.e., networks in campuses and corporations) and data center networks. These networks
have grown dramatically in the number of hosts, switches, and applications. The management of
these networks is getting more complex because operators have to assign network addresses for each
device, configure routing policies for each host and application, set up firewalls, and troubleshoot.
It is a challenging problem to scale the management of these networks because the networks are
growing large with complex management tasks, but only have cheap, simple switches.
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1.1.1
Edge Networks Are Large
Large enterprises can easily have tens to hundreds of thousands of heterogeneous hosts such as
laptops, mobile phones, desktops and computing clusters [3]. Some hosts can move around to
different locations in the enterprise. There are thousands of switches and routers connecting these
hosts together. There are also hundreds of applications running on these hosts with different traffic
patterns and performance requirements.
Data center networks can easily have hundreds of thousands of servers with tens of virtual
machines on each server. These virtual machines can migrate to different servers. There are
multiple layers of switches connecting these servers. Data center applications include many mapreduce jobs, search applications, and cloud storage applications and have stricter performance
requirements than enterprise applications.
1.1.2
Edge Networks Need Fine-grained Policies
Operators of the enterprise and data center networks have many considerations for network management such as security, mobility, application performance, energy consumption, cost saving,
debugging and maintenance, etc. To express these management considerations, operators need
to specify fine-grained policies for different types of traffic. Here are some example types of finegrained policies:
Routing: Different applications have different requirements for routing. For example, a banking
application may require secure paths that malicious users do not have access to; a video streaming
application may need high-bandwidth paths; the financial applications that exchange real-time
stock information may need low-latency paths.
Access control: Operators use access control rules to block the traffic from malicious users, in
order to improve the security of their networks. For example, in a medical company, operators
should make sure that attackers should not have access to the server which stores patients’ private
information. These access control rules should be fine-grained enough to capture various types of
malicious traffic without affecting the normal traffic.
Measurement: Operators need to measure the behaviors in the network for accounting, anomaly
detection, troubleshooting, and traffic engineering. For example, cloud providers need to accurately
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count the traffic from different users and applications in order to charge the users for the bandwidth
they use. Operators in data centers may need to identify the large flows in the network to better
configure their routing for traffic engineering (A flow is a sequence of packets that share the same
packet header properties such as source address/port, destination address/port, and/or protocol).
1.1.3
Simple, Cheap Switches Have Limited Memory
Unfortunately, to support ever growing networks with more complicated policies, there are only
simple and cheap switches in today’s enterprise and data center networks. This is because these
switches must process each packet within hundreds of nanoseconds to support high link speeds
(e.g., 10 Gbps, 40 Gbps and more). To store the state needed to process these packets, the switches
must use expensive, power-hungry on-chip memory. Due to cost and power constraints, the switch
memory is limited in size.
There are two types of memory in switches — SRAM (Static Random-Access Memory) and
TCAM (Ternary Content-Addressable Memory): The SRAM is used for direct lookup of key-value
pairs. For example, the SRAM in switches is used to store forwarding tables which match the
destination MAC addresses to the outgoing interfaces. In contrast, the TCAM is used for wildcard
matching where the keys can contain not only 0s and 1s, but also “don’t care” bits. For example,
the TCAM is used to store ACLs (Access Control Lists) at switches, which permit, block, or
rate-limit the flows whose packet headers match the patterns defined in the ACLs. The SRAM is
much cheaper and consume less power than the TCAM.
While the switch memory is very small due to its cost and energy constraints1, operators hope
to store a lot of state in the switch. For example, just to perform the simple forwarding action,
each switch may need to store 10K entries for an enterprise network with 10K hosts, because one
entry is needed for each host destination. Furthermore, switches may need to provide different
access control policies and quality of service (QoS) to different users and applications — requiring
even more memory. Switches may also need to maintain counters for specific flows for accounting
and diagnosis.
1 The
study [4] shows that a 48-port switch takes about 100-200 Watts power.
3
Figure 1.1: Three layers in today’s management systems.
1.2
Management of Today’s Edge Networks
To address the scalability challenges of enterprise and data center networks, most research focuses
on making them faster and more efficient. However, the management of these edge networks is an
important yet under-explored area in networking research.
There are three key scalability challenges of managing enterprise and data center networks:
How to make the basic function of routing scale with many hosts and switches? How to scalably
enforce fine-grained polices at switches? How to diagnose performance problems with many hosts
and complicated applications?
Today, all these management tasks are performed with a three-layer architecture as shown in
Figure 1.1. The first layer is the data plane—the fast path of these networks that actually processes
packets. The data plane usually has fast on-chip memory such as SRAM and TCAM to store the
network state and packet processing rules. The second layer is the control plane—the brains of the
networks that run protocols to decide how to handle traffic. The third layer is the management
plane—the place where operators configure policies. Switches and routers from different vendors
typically have different data plane implementations, all of which only support limited policies. In
addition, the control plane is tightly bundled with the data plane. Therefore, different switches
and routers may have different control plane APIs and different levels of protocol support, making
management even harder. As a result, operators have to configure individual network devices
separately in an offline fashion, sometimes even manually. For example, to prevent attackers from
accessing the web server, operators have to identify the IP or MAC addresses of all the attackers’
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machines, locate the routers that direct traffic to the web server, and then install ACLs at these
routers.
Now, we will describe how the key management tasks — routing, access control, and diagnosis — are done in today’s networks with the three layer architecture. We will also discuss the
scalability limitations in this architecture.
1.2.1
Hybrids of Ethernet Islands Connected by IP Routers
In an Ethernet network, hosts are allocated with MAC addresses and the switches forward Ethernet
frames based on their destination MAC addresses. The MAC address is tied to the device and
is independent of the hosts’ locations. Thus, MAC addresses are a good choice for the enterprise
networks where laptops and mobile devices are moving frequently and data center networks where
virtual machine migration is common.
To deliver traffic, the switches cooperate to construct a spanning tree in the control plane to
provide loop-free routing paths. In the data plane, each switch maintains a forwarding table which
records how to reach different destinations. When a switch receives a frame and it contains no
forwarding-table entry for the frame’s destination MAC address, the switch floods each frame over
the entire spanning tree. The switch learns how to reach a MAC address by remembering the
incoming link for frames with a particular source MAC addresses and saving the mapping.
However, these Ethernet protocols do not scale to large networks: MAC addresses cannot be
aggregated, so we need one entry for each destination at each switch. Flooding requires large
amounts of state and control messages that grow with the size of the network [5]. Since spanning
tree networks can leave some links completely unused, they fail to take advantage of multiple
paths for higher bisectional bandwidth. Two nodes near each other may have to reach each other
through much longer paths if the shorter paths are not in the spanning tree. Sometimes, operators
must configure the switches carefully so that the switches can construct a spanning tree with low
latency for most pairs of nodes [6]. When a link or node fails, operators have to reconfigure the
entire network to construct a new spanning tree with low latency for most nodes.
To address the scalability and efficiency problems of the Ethernet, most enterprise and data
center networks today use small Ethernet islands interconnected by routers. The network is divided
into many Ethernet islands, each with only a limited number of hosts. Within each Ethernet island,
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MAC addresses are used to support host mobility and run spanning tree protocols to route packets.
Each Ethernet island is allocated with an IP subnet (i.e., the list of IP addresses that belongs to the
same IP prefix). A few IP routers deliver traffic based on the IP subnet a destination host belong
to. IP routers make Ethernet more scalable at the expense of configuration complexity. Since IP
addresses represent the locations of hosts, it is very hard to support host mobility. When hosts
move between Ethernet islands, these hosts must get new IP addresses or the routing configuration
at routers should change.
1.2.2
Policy Support with Access Control Lists Between Virtual LANs
In order to support flexible policies (e.g., customized routing, access control, and measurement),
operators group hosts sharing the same networking requirements using Virtual Local Area Networks (VLANs), instead of grouping hosts based on their locations. Each VLAN is usually allocated an IP subnet, and hosts within the VLAN communicate using Ethernet protocols. Between
VLANs, there are some routers where operators can specify policies such as configuring different
queues with different quality of service (QoS), installing access control lists that block malicious
flows, or counting the amount of traffic from different applications.
VLANs can only support limited granularity of policy because operators can only express
their management policies at a few routers located in these networks and have limited control
and measurement of the traffic. VLANs are not scalable because a network can have only a
limited number of VLANs and each VLAN can have only a limited number of hosts [6]. VLAN
configuration is complex and error-prone because operators must ensure that each host’s IP address
belongs to the IP subnet of its VLAN, and that each VLAN has an efficient spanning tree that
remains connected under common failure scenarios [6].
1.2.3
Ad-hoc Troubleshooting with Application and Network Logs
To troubleshoot for reachability and performance problems, today’s enterprise and data center
networks often collect application logs on the servers about the liveness, correctness, and performance of applications. At switches, these networks collect SNMP (Simple Network Management
Protocol) logs about the number of bytes/packets transferred through each switch. In addition,
operators maintain trouble ticket systems where users can report their problems. For example,
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operators usually pick out the trouble ticket with the most significant problems, manually investigate the problem description in the ticket, and then look into the application logs to identify
the problem. If they find that the problem is related to the network, they will study the network
logs, or run a few tools to identify the problems (e.g., ping to test reachability, traceroute to verify
routing).
Although these logs can reveal the significant problems in these networks, it is still a challenging
job to infer the causal relations between these problems and identify the root causes. Worse still,
for large enterprises and data centers, there are application and network teams each in charge
of different components in the system. It is challenging to identify which team is responsible for
performance problems or failures. It is even more challenging to automatically report problems
when they happen, quickly point out the root causes, and fix or get around these problems in real
time before the problems start to affect application performance.
1.2.4
Summary
In summary, today’s enterprise and data center networks lack the scalability and flexibility to
support various management tasks. Often, in order to keep the networks manageable, operators
impose a lot of restrictions on the growth of the networks and the kind of applications that can run.
Therefore, to realize the full power of the enterprise and data center networks, we should make
the network easier and less expensive to manage. Future networks should be totally transparent
to applications, so that they can use the network freely without worrying about the network
configurations and resource constraints. However, today’s networks are far from that goal.
1.3
Emerging Trends of Redesigning for Manageability
Most of these problems of managing today’s brittle networks arise from the fact that these networks
were not designed with management in mind. Yet it is challenging to simplify the management of
today’s networks. Instead, we focus on how to design future networks to make them inherently
easier to manage.
There have been several recent directions arising from the research community with the goal
of making management easier: flat addresses, shortest path routing, logically centralized control,
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Figure 1.2: Emerging techniques for better network management.
and flow-based switches (as shown in Figure 1.2). While all these trends enable more scalable and
flexible management of these edge networks, they introduce new scalability challenges in the data
plane. We will discuss the benefits of these new trends and their scalability challenges below.
1.3.1
Flat Addresses to Support Zero Configuration and Host Mobility
To avoid complex configuration and better support host mobility, new protocols with flat addresses
such as SEATTLE [5], RBridges/TRILL [7, 8] and SPBM (Shortest-Path Bridging MAC) [9] have
been proposed. Each host has a fixed identifier that does not change when the host moves around,
so the host can be plugged into the network and start using the network immediately without
any extra configuration. Even when the network topology changes, administrators do not need
to reassign addresses. Furthermore, with flat addresses for routing, we can assign IP addresses to
express policies in a more aggregatable way. For example, for a campus network, we can assign
one IP prefix to the students’ machines although these machines may be located at different places
on campus. As a result, we only need a single IP prefix to express the policies for the student
group.
However, with all the hosts using MAC addresses that cannot be easily combined, we have too
many forwarding-table entries at each switch to reach a large amount of hosts.
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1.3.2
Shortest Path Routing to Improve Performance
Recent advances in Ethernet such as Rbridges/TRILL [7, 8] and SEATTLE [5] compute shortest
paths based on link weights between all pairs of hosts. We can also tune the link weights to control
the flow of traffic to minimize the delay and network congestion. Since shortest path routing uses
all the links in the network, it provides more efficient connectivity than spanning tree protocols.
We can also split traffic across multiple shortest paths, which is common in data center networks.
In addition, these shortest path routing protocols can quickly propagate link and node failure
events in the network, and automatically recalculate the new shortest paths.
1.3.3
Centralized Control to Make Policy Configuration Easier
Instead of configuring each switch and router separately, recent works propose to replace the
control-plane software at individual switches with a logically-centralized controller in the management plane [10, 11, 12, 13]. With the centralized controller, operators only need to configure
policies at a single place without worrying about reconfiguring the network when network topology
or traffic changes. The centralized controller is responsible for keeping information about the address assignment, network topology, and routing. With this information, the centralized controller
can automatically configure the data plane of network devices to express the management policies.
The logically centralized controller imposes new scalability and reliability challenges. Instead of
making decisions on their own, the switches send the packets to the controller if they do not know
how to handle those packets, which significantly increases the load on the centralized controller [13].
The centralized controller can also be a single point of failure.
1.3.4
Flow-based Switches to Enable Fine-grained Policies
Traditional switches in enterprise and data center networks do not have much support for policies
such as customized routing, access control, and measurement. Flow-based switches [14, 15] are
proposed to support the policies. These flow-based switches perform simple actions based on rules.
The rules match on bits in the packet header (e.g., source address/port, protocol, etc.). Possible
actions include dropping packets from malicious users, forwarding packets to a specific outgoing
interface, and counting packets that belong to the web traffic. These flow-based switches are
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already available from several switch vendors (e.g., HP, NEC, etc.), and have been deployed in
several enterprises and backbones (e.g., National LambdaRail and Internet2).
With flow-based switches enabling fine-grained policies, operators can now specify new policies
that can have fine-grained control of their networks. As a result, operators may be tempted to
deploy many policies, which in turn introduce further scalability challenge of fitting these policies
into the small switch memory.
1.4
Key Design Principles
This thesis describes the design, implementation, and evaluation of new architectures that address
these key challenges: improving scalability and handling flexible policies with simple switches for
enterprise and data center networks. There are three key design principles that guide the design
of these new systems:
Traffic indirection that minimizes the state required at each switch.
Switches need
to store various network state such as forwarding tables and ACLs. To minimize the state at
each switch, we propose to compress the state information or only store part of the state. As a
result, one switch may not be able to make decisions on its own. Instead, we redirect the traffic
to other switches that have stored the required state to make the decisions. In general, we reduce
switch memory usage by sending a small fraction of packets on a slightly longer path. Since most
enterprise and data center networks are local area networks with low end-to-end delay, the slightly
longer path would not introduce significant performance problems.
New data structures that work with today’s commodity switches. We design and build
new data structures for the data plane to reduce the memory usage at the switches and to support
traffic indirection. These new designs can be implemented with today’s commodity switches
without much hardware changes, because our data structures match the hardware features such as
hashing support at switches and wildcard rule support in TCAM. By leveraging the key features
in the enterprise and data center network settings (e.g., all the nodes are in a single domain,
managed by a centralized controller, and are well connected via shortest path routing), we can
guarantee the reachability, reduce the extra delay of traffic indirection, and quickly adapt to the
dynamics of these edge networks such as host mobility, traffic changes, and topology changes.
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Figure 1.3: A Scalable Management System for Edge Networks.
Rethinking the division of labor among hosts, switches and the centralized management system.
Hosts, switches, and the centralized controller are the three key components in
enterprises and data centers. It is important to place the right function at the right component to
achieve the scalability and flexibility at the same time. For example, we should place the function
of configuring high-level policies in the centralized controller to make management easier, and
process all the packets in the data plane at the switches to achieve the best performance. We also
rethink the division of labor between the network and the end hosts. For example, we place the
performance monitoring function at end hosts to leverage the computing and storage resources at
millions of end hosts.
1.5
A Scalable Management System for Edge Networks
Following the key design principles, we propose a scalable management system which consists of
three parts to scale packet forwarding, policy enforcement, and performance diagnosis as shown in
Figure 1.3. In this management system, operators can configure high-level policies at a centralized
controller. The controller enforces the high-level policies at the switches in the network, and collects
measurement data from both the switches and the end hosts to understand network behavior. To
improve the scalability of the system, we build three components: BUFFALO — a scalable packet
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forwarding data plane that provides basic network connectivity, DIFANE — a system that scalably
enforces fine-grained policies at the switches, and SNAP — a scalable performance diagnosis system
for data centers. We have built prototypes for all three parts and evaluated them with industrial
configuration data and real-world deployment.
BUFFALO [16]: A scalable packet forwarding architecture using Bloom filters and
random walks. As the link speed and the number of hosts and switches grow, simply building
switches with larger amounts of faster memory is not appealing, since high-speed memory is both
expensive and power-hungry. Given the fixed size of fast on-chip memory SRAM in switches,
BUFFALO uses a compact data structure, called a Bloom filter, to store the set of addresses
associated with each outgoing link. Bloom filters reduce SRAM usage at the expense of false
positives.If a Bloom filter reports that an address is in the set of addresses, it may not be the case.
In contrast, a Bloom filter does not have any false negatives. That is, if a Bloom filter indicates
that an address is not in the set, it must be the case. We propose a new way to gracefully
handle false positives without reducing the packet-forwarding rate, by redirecting those packets
which experience false positives through a slightly longer path. To reduce the extra delay of
packet redirection, we leverage the shortest-path routing features in enterprises and data centers.
Using random walk theory, we proved a bound of the average delay that packets could experience.
Our extensive analysis, simulation, and prototype implementation in Click (a kernel-level software
router) show that BUFFALO significantly reduces memory cost, increases the scalability of the
data plane, and improves packet-forwarding performance.
DIFANE [17]: A distributed flow-based architecture built on OpenFlow switches.
Emerging flow-based networking and commercially available OpenFlow switches [18] use a centralized controller software. With the centralized controller, enterprise administrators can easily
specify fine-grain policies to control how the underlying switches forward, drop, and measure
traffic. However, existing techniques rely too heavily on the controller to install rules based on
fine-grained policies, leading to poor scalability and high latency. DIFANE relegates the controller
to the simpler task of translating high-level policies to low-level rules, and decentralizes rule installation and all the packet processing in the underlying switches. To reduce the memory usage
of storing rules at switches, DIFANE builds a distributed rule directory service among the switches
by partitioning the rules among several switches, and selectively redirecting packets through these
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switches. DIFANE can be easily implemented with small software modifications to commercial
OpenFlow switches, as demonstrated by our prototypes built using the Click modular router. We
evaluated DIFANE on a 40-node testbed and conducted simulations of realistic topologies consisting of thousands of nodes and millions of access-control rules extracted from real corporate and
campus networks.
SNAP [19]: A scalable network-application diagnosis system for data center applications. Network performance problems are notoriously difficult to diagnose, and this difficulty is
magnified when applications are often split into multiple tiers of application components spread
across thousands of servers in a data center. We observe that performance problems often arise
in the communication between the tiers, where either the application or the network (or both!)
could be to blame. Therefore, we designed and built SNAP, a scalable network-application profiler
that guides developers in identifying and fixing performance problems. SNAP passively collects
network stack information (e.g., congestion window size, send buffer size, number of packet loss,
etc.) with low computation and storage overhead. Then SNAP leverages statistical techniques to
correlate connections across shared resources (e.g., host, link, switch) to pinpoint the locations of
the performance problem. Our one-week deployment of SNAP in a production data center (with
over 8,000 servers and over 700 application components) has already helped developers uncover
15 major performance problems in application software, the network stack on the server, and the
underlying network.
The remainder of this thesis is organized as follows: Chapter 2 presents BUFFALO, the scalable
forwarding layer. Chapter 3 describes DIFANE, the scalable way to enforce flexible polices at
switches. Chapter 4 shows SNAP, the scalable diagnosis system for data center applications.
Chapter 5 discusses how the three systems work together and concludes the thesis.
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Chapter 2
BUFFALO: Scaling Packet
Forwarding on Switches
This chapter focuses on the scalability challenges for providing basic packet forwarding under flat
addressing. Simply building switches with larger amounts of faster memory is not appealing, since
high-speed memory is both expensive and power hungry. Implementing hash tables in SRAM is
not appealing either because it requires significant overprovisioning to ensure that all forwarding
table entries fit. Instead, we propose the BUFFALO architecture that provides a scalable packet
forwarding layer on switches.
BUFFALO uses a small SRAM to store one Bloom filter of the addresses associated with each
outgoing link. We provide a practical switch design leveraging flat addresses and shortest-path
routing. BUFFALO gracefully handles false positives without reducing the packet-forwarding
rate, while guaranteeing that packets reach their destinations with bounded stretch with high
probability. We tune the sizes of Bloom filters to minimize false positives for a given memory
size. We also handle routing changes and dynamically adjust Bloom filter sizes using counting
Bloom filters in slow memory. Our extensive analysis, simulation, and prototype implementation in
kernel-level Click show that BUFFALO significantly reduces memory cost, increases the scalability
of the data plane, and improves packet-forwarding performance.
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2.1
Introduction
The Ethernet switches used in today’s enterprise and data-center networks do not scale well with
increasing forwarding-table size and link speed. Rather than continuing to build switches with
ever larger and faster memory in the data plane, we believe future switches should leverage Bloom
filters for a more scalable and cost-effective solution.
2.1.1
Memory Problems in the Data Plane
Enterprises and data centers would be much easier to design and manage if the network offered
the simple abstraction of a virtual layer-two switch. End hosts could be identified directly by
their hard-coded MAC addresses, and retain these addresses as they change locations (e.g., due to
physical mobility or virtual-machine migration). The hosts could be assigned IP addresses out of
a large pool, without the artificial constraints imposed by dividing a network into many small IP
subnets. However, traditional Ethernet can only support this abstraction in small network topologies, due to a heavy reliance on network-wide flooding and spanning tree. Recent advances [7, 8, 5]
have made it possible to build much larger layer-2 networks, while still identifying hosts by their
MAC addresses. These new architectures focus primarily on improving the control plane, enabling
the use of shortest-path routing protocols (instead of spanning tree) and efficient protocols for
disseminating end-host information (instead of flooding data packets).
As these new technologies enable the construction of ever larger “flat” networks, the scalability of the data plane becomes an increasingly serious problem. In today’s Ethernet and in
proposed solutions like TRILL [7, 8], each switch maintains a forwarding-table entry for each active MAC address. Other solutions [5] cache a smaller number of end-host MAC addresses, but
still require a relatively large amount of data-plane state to reach every switch in the network.
Large networks can easily have tens or hundreds of thousands of end-host MAC addresses, due
to the proliferation of PDAs (in enterprises) and virtual machines (in data centers). In addition,
link speeds are increasing rapidly, forcing the use of ever-faster—and, hence, more expensive and
power-hungry—memory for the forwarding tables. This motivates us to explore new ways to
represent the forwarding table that require less memory and (perhaps more importantly) do not
require memory upgrades when the number of end hosts inevitably grows.
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To store the forwarding table, one simple solution is to use a hash table in SRAM to map MAC
addresses to outgoing interfaces. However, this approach requires significant overprovisioning the
fast memory for three reasons: First, when switches are out of memory, the network will either
drop packets in some architectures [7, 8] or crash in others [5]. Second, it is difficult and expensive
to upgrade the memory for all the switches in the networks. Third, collisions in hash tables (i.e.,
different destination addresses mapped to the same place in the hash table) require extra memory
overhead to handle them, and affect the throughput of the switch.
Given these memory problems in the data plane, our goal is to make efficient use of a small,
fast memory to perform packet forwarding. Such small fast memory can be the L1 or L2 cache
on commodity PCs serving as software switches, or dedicated SRAM on the line cards. When
the memory becomes limited with the growth of forwarding table, we ensure that all packetforwarding decisions are still handled within the SRAM, and thus allow the switches last longer
with the increase of forwarding table size.
2.1.2
The BUFFALO Forwarding Architecture
Most enterprise and data center networks are “SPAF networks”, which uses Shortest Path routing
on Addresses that are Flat (including conventional link-state, distance-vector, and spanning tree
protocols). Leveraging the unique properties in SPAF networks, we propose BUFFALO, a Bloom
Filter Forwarding Architecture for Large Organizations. BUFFALO performs the entire address
lookup for all the packets in a small, fast memory while occasionally sending the packets through
a slightly longer path.
To make all packet-forwarding decisions with a small fast memory, we use a Bloom filter [20],
a hash-based compact data structure for storing a set of elements, to perform the flat address
lookup.
Similar to previous work on resource routing [20, 21]1 , we construct one Bloom filter
for each next hop (i.e., outgoing link), and store all the addresses that are forwarded to that next
hop. By checking which Bloom filter the addresses match, we perform the entire address lookup
within the fast memory for all the packets. In contrast, previous work [22] uses Bloom filters to
assist packet lookup and every address lookup still has to access the slow memory at least once.
1 These studies design the algorithms of locating resources by using one Bloom filter to store a list of resources
that can be accessed through each neighboring node.
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To apply our Bloom filter based solution in practice, we provide techniques to resolve three
issues:
Handling false positives: False positives are one key problem for Bloom filters. We propose a
simple mechanism to forward packets experiencing false positives without any memory overhead.
This scheme works by randomly selecting the next hop from all the matching next hops, excluding
the interface where the packet arrived. We prove that in SPAF networks the packet experiencing
one false positive (which is the most common case for the packet) is guaranteed to reach the destination with constant bounded stretch. We also prove that in general the packets are guaranteed
to reach the destination with probability 1. BUFFALO gracefully degrades under higher memory
loads by gradually increasing stretch rather than crashing or resorting to excessive flooding. In
fact, in enterprise and data center networks with limited propagation delay and high-speed links,
a small increase in stretch would not run the risk of introducing network congestion. Our evaluation with real enterprise and data center network topologies and traffic shows that the expected
stretch of BUFFALO is only 0.05% of the length of the shortest path when each Bloom filter has
a false-positive rate of 0.1%.
Optimizing memory and CPU usage:
To make efficient use of limited fast memory, we
optimize the sizes and number of hash functions of the Bloom filters to minimize the overall falsepositive rate. To reduce the packet lookup time, we let the Bloom filters share the same group
of hash functions and reduce the memory access times for these Bloom filters. Through extensive
analysis and simulation, we show that BUFFALO reduces the memory usage by 65% compared to
hash tables.
Handling routing dynamics: Since routing changes happen on a much longer time scale than
packet forwarding, we separate the handling of routing changes from the packet forwarding and
use counting Bloom filters in the large, slow memory to assist the update of the Bloom filters. To
reduce the false-positive rate under routing changes, we dynamically adjust the sizes and number
of hash functions of Bloom filters in fast memory based on the large fixed-size counting Bloom
filters in slow memory.
We implement a prototype in the Click modular router [23] running in the Linux kernel. By
evaluating the prototype under real enterprise and data center network topologies and traffic,
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we show that in addition to reducing memory size, BUFFALO forwards packets 10% faster than
traditional hash table based implementation. BUFFALO also reacts quickly to routing changes
with the support of counting Bloom filters.
The rest of the chapter is organized as follows: Section 2.2 describes the underlying SPAF
networks we focus on in this chapter. Section 3.2 presents an overview of the BUFFALO architecture. Section 2.4 describes how to handle false positives and proves the packet reachability. In
Section 2.5, we adjust the sizes of Bloom filters to make the most efficient use of limited fast memory. In Section 2.6, we show how to dynamically adjust the sizes of Bloom filters using counting
Bloom filters. Section 3.6 presents our prototype implementation and the evaluation. Section 2.8
discusses several extensions of BUFFALO. Section 2.9 and 4.9 discuss related work and conclude
the chapter.
2.2
Shortest Paths & Flat Addresses
This chapter focuses on SPAF networks, the class of networks that perform Shortest-Path routing
on Addresses that are Flat. In fact, most enterprise and data center networks are SPAF networks.
Flat addresses:
Flat addresses are used widely in enterprise and data center networks. For
example, MAC addresses in Ethernet are flat addresses. New protocols with flat address spaces
(e.g., SEATTLE [5], ROFL [24], AIP [25]) have been proposed to facilitate network configuration and management, because they simplify the handling of topology changes and host mobility
without requiring administrators to reassign addresses. Even IP routing can be done based on
flat addresses, by converting variable-length IP prefixes into multiple non-overlapping fixed-length
(i.e., /24) sub-prefixes.
Shortest path routing: We also assume shortest-path routing on the network topology, based
on link-state protocols, distance-vector protocols, or spanning-tree protocols.2 Recent advances
in Ethernet such as Rbridges [7, 8] and SEATTLE [5] all run link-state protocols that compute
shortest paths.
Based on the above two properties, we define the SPAF network as a graph G = (V, E), where
V denotes the set of switches in the network, and E denotes all the links viewed in the data
2 In today’s Ethernet the control plane constructs a spanning tree and the data plane forwards packets along
shortest paths within this tree.
18
plane. In the SPAF network we assume all the links in E are actively used, i.e., the weight on link
e(A, B) is smaller than that on any other paths connecting A and B. This is because if a link is
not actively used, it should not be seen in the data plane. Let P (A, B) denote the set of all paths
from A to B. Let l(A, B) denote the length of the shortest path from A to B, i.e., the length of
P
e(A, B), and the length of a path p is l(p) = e∈p l(e). We have:
∀A, B ∈ V, p ∈ P (A, B), l(A, B) ≤ l(p).
In this chapter, we propose an efficient data plane that supports any-to-any reachability between flat addresses over (near) shortest paths. We do not consider data-plane support for Virtual
LAN (VLANs) and access-control lists (ACLs), for three main reasons. First, the new generation
of layer-two networks [7, 8, 5] do not perform any flooding of data packets, obviating the need to
use VLANs simply to limit the scope of flooding. Second, in these new architectures, IP addresses
are opaque identifiers that can be assigned freely, allowing them to be assigned in ways that make
ACLs more concise. For example, a data center could use a single block of IP addresses for all
servers providing a particular service; similarly, an enterprise could devote a small block of IP
addresses to each distinct set of users (e.g., faculty vs. students). This makes ACLs much more
concise, making it easier to enforce them with minimal hardware support at the switches. Third,
ACLs are increasingly being moved out of the network and on to end hosts for easier management
and better scalability. In corporate enterprises, distributed firewalls [26, 27], managed by Active
Directory [28] or LDAP (Lightweight Directory Access Protocol), are often used to enforce accesscontrol policies. In data-center networks, access control is even easier since the operators have
complete control of end hosts. Therefore, the design of BUFFALO focuses simply on providing
any-to-any reachability, though we briefly discuss possible ways to support VLAN in Section 2.8.
2.3
Packet Forwarding in BUFFALO
In this section, we describe the BUFFALO switch architecture in three aspects: First, we use one
Bloom filter for each next hop to perform the entire packet lookup in the fast SRAM. Second,
we leverage shortest-path routing to forward packets experiencing false positives through slightly
longer paths without additional memory overhead. Finally, we leverage counting Bloom filters
19
Control Plane
routing
updates
FIB updates
Slow memory:
Counting
Bloom Filters
routing
updates
Nexthop0
Nexthop1
... ...
NexthopT-1
BF updates
packets
Fast memory:
Bloom Filters
matching
next hop set
Nexthop0
Nexthop1
... ...
packets
False Positive
Handler
NexthopT-1
Figure 2.1: BUFFALO Switch Architecture
in slow memory to enable fast updates to the Bloom filters after routing changes. Figure 3.7
summarizes the BUFFALO design.
2.3.1
One Bloom Filter Per Next Hop
One way to use a small, fast memory is route caching. The basic idea is to store the most frequently
used entries of the forwarding table (FIB) in the fast memory, but store the full table in the slow
memory. However, during cache misses, the switch experiences low throughput and high packet
loss. Malicious traffic with a wide range of destination addresses may significantly increase the
cache miss rate. In addition, when routing changes or link failures happen, many of the cached
routes are simultaneously invalidated. Due to its bad performance under worst-case workloads,
route caching is hardly used today.
To provide predictable behavior under various workloads, we perform the entire packet lookup
for all the packets in the fast memory by leveraging Bloom filters, a hash-based compact data
structure to store a set of elements. We set one Bloom filter BF (h) for each next hop h (or
outgoing link), and use it to store all the addresses that are forwarded to that next hop. For a
switch with T next hops, we need T Bloom filters. A Bloom filter consists of an array of bits.
To insert an address into Bloom filter BF (h), we compute k hash values of the address, each
20
denoting a position in the array. All the k positions are set to 1 in the array. By repeating the
same procedure for all the addresses with next hop h, Bloom filter BF (h) is constructed.
It is easy to check if an address belongs to the set with Bloom filter BF (h). Given an address,
we calculate the same k hash functions and check the bits in the corresponding k positions of the
array. If all the bits are 1, we say that the element is in the set; otherwise it is not. To perform
address lookup for an address addr, we check which BF (h) contains addr, and forward the packet
to the corresponding next hop h.
Note that there are different number of addresses associated with each next hop. Therefore we
should use different size for each Bloom filter according to the number of addresses stored in it,
in order to minimize the overall false-positive rate with a fixed size of fast memory. We formulate
and solve the false-positive rate optimization problem in Section 2.5.
2.3.2
Handling False Positives in Fast Memory
One key problem with Bloom filters is the false positive — an element can be absent from the set
even if all k positions are marked as 1, since each position could be marked by the other elements
in the set. Because all the addresses belong to one of the Bloom filters we construct, we can easily
detect packets that experience false positives if they match in multiple Bloom filters.3
One way to handle packets experiencing false positives is to perform a full packet lookup in the
forwarding table stored in the slow memory. However, the lookup time for packets experiencing
false positives will be much longer than others, leading to the throughput decrease. Attackers may
detect those packets with longer latency and send a burst of them. Therefore, we must handle
false positives in fast memory by picking one of the matching next hops.
For the packets that experience false positives, if we do not send them through the next hop
on the shortest path, they may experience stretch and even loops. One way to prevent loops is
to use a deterministic solution by storing the false positive information in the packets (similar to
FCP [29]). When a packet is detected to have false positives in a switch, we store the switch and
the next hop it chooses in the packet. So next time the packet travels to the same switch, the
3 The handling of addresses that should have multiple matches (e.g., Equal-Cost Multi-Path) are discussed in
Section 2.8. Addresses that have no match in the FIB should be dropped. Yet these packets may hit one Bloom
filter due to false positives. We cannot detect these addresses, but they will eventually get dropped when they hit
a downstream switch that has no false positives. In addition, an adversary cannot easily launch an attack because
it is hard to guess which MAC addresses would trigger this behavior.
21
switch will choose a different next hop for the packet. However, this method requires modifying
the packets and has extra payload overhead.
Instead, we use a probabilistic solution without any modification of the packets. We observe
that if a switch sends the packet back to the interface where it comes from, it will form a loop.
Therefore, we avoid sending the packet to the incoming interface. To finally get out the possible
loops, we randomly pick one from all the remaining matching next hops. In Section 2.4, we prove
that in SPAF networks, the packet experiencing one false positive (which is the most common case
for the packet) is guaranteed to reach the destination with constant bounded stretch. In general,
packets are guaranteed to reach the destination with probability 1. This approach does not require
any help from the other switches in the network and thus is incrementally deployable.
2.3.3
CBFs for Handling Routing Changes
When routing changes occur, the switch must update the Bloom filters with a new set of addresses.
However, with a standard Bloom filter (BF) we cannot delete elements from the set. A counting
Bloom filter (CBF) is an extension of the Bloom filter that allows adding and deleting elements [30].
A counting Bloom filter stores a counter rather than a bit in each slot of the array. To add an
element to the counting Bloom filter, we increment the counters at the positions calculated by the
hash functions; to delete an element, we decrement the counters.
A simple way to handle routing changes is to use CBFs instead of BFs for packet forwarding.
However, CBFs require much more space than BFs. In addition, under routing changes the number
of addresses associated with each next hop may change significantly. It is difficult to dynamically
increase/decrease the sizes of CBFs to make the most efficient use of fast memory according to
routing changes.
Fortunately, since routing changes do not happen very often, we can store CBFs in slow
memory, and update the BFs in small fast memory based on the CBFs. We store CBF in slow
memory rather than a normal FIB because it is easier and faster to update BFs from CBFs under
routing changes. With a CBF layer between BFs and control plane, we can even change the sizes
of BFs to the optimal values with low overhead. By using both CBFs and BFs, we make an
efficient use of small fast memory without losing the flexibility to support changes in the FIB. The
details of using CBFs are discussed in Section 2.6.
22
As shown in Figure 3.7, there are three layers in our switch architecture. The control plane can
be either today’s Ethernet or new Ethernet techniques such as Rbridges [7, 8] and SEATTLE [5].
CBFs are stored in slow memory and learn about routing changes from the control plane. BFs
are stored in the fast memory for packet lookup. During routing changes, the related BFs will be
updated according to the corresponding CBFs. If the number of addresses associated with a BF
changes significantly, BFs are reconstructed with new optimal sizes from CBFs.
2.4
Handling False Positives
When BUFFALO detects packets that experience false positives, it randomly selects a next hop
from the candidates that are different from the incoming interface, as discussed in Section 2.3.2.
In the case of a single false positive, which is the most common, avoiding sending the packet to
the incoming interface guarantees that packets reach destination with tightly bounded stretch. In
the improbable case of multiple false positives, this randomization guarantees packet reachability
with probability 1, with a good bounds on expected stretch.
Notation
N Hsp (A)
N Hf p (A)
l(A, B)
P (A, B)
Definition
The next hop for shortest path at switch A
The matching next hop due to a sole false
positive at switch A
The length of the shortest path from
switch A to B
All the paths from switch A to B
Table 2.1: Notations for the false-positive handler
2.4.1
Handling One False Positive by Avoiding Incoming Interface
We first investigate the case that a packet only experiences one false positive at one switch, i.e.,
at switch A, the packet has two matching next hops. Let N Hsp (A) denote the next hop A should
forward the packet to on the shortest path, and N Hf p (A) denote the additional next hop matched
by a Bloom filter false positive. (The notations are summarized in Table 2.4.) Note that this single
false positive case is the most common case, because with reasonable Bloom filter parameters the
probability of multiple false positives is much lower than one false positive. Since switch A connects
23
A
(ii)
B
A
B
dst
(i)
dst
D
C
(b) Multiple false positives
(a) One false positive
Figure 2.2: Loops caused by false positives (99K false positive link, −→ shortest path link)
to each end host through one switch port, there is no false positives for the ports that connect to
end hosts. Therefore, N Hf p (A) must be a switch rather than an end host.
The one false positive case is shown in Figure 2.2(a). (We hereafter use 99K to denote false
positive link, and → for shortest path link.) Switch A has a false positive, and randomly picks
a next hop B (N Hf p (A) = B). Switch B receives the packet, and may (i) send it to a next hop
different from A, which leads to the destination or (ii) send it back to A. For (i), we will prove
that there are not any loops. For (ii), when A receives the packet, it will not pick B since the
packet comes from B.
In general, we have the following theorem:
Theorem 1. In SPAF networks, if a packet only experiences one false positive in one switch, it
is guaranteed to reach the destination with no loops except a possible single transient 2-hop one.
Proof. Suppose the packet matches two next hops at switch A: N Hsp (A) and some B = N Hf p (A).
If A picks N Hsp (A), there is no loop. If B is selected, it will have a path B → . . . → dst to forward
the packet to the destination, since the network is connected. With a single false positive, a packet
will follow the correct shortest-path hops at all nodes other than A. Thus, the only case that can
cause a loop is the packet going through A again (A 99K B → . . . → A → . . . → dst). However,
in SPAF networks, we assume the link e(B, A) is actively used (This assumption is introduced in
Sec. 2.2), i.e.,
l(N Hf p (A), A) ≤ l(p), ∀p ∈ P (N Hf p (A), A).
Thus, on a shortest path from B to dst, if the packet visits A at all, it would be immediately after
B. If the packet is sent back to A, A will avoid sending it to the incoming interface N Hf p (A),
and thus send the packet to N Hsp (A), and the shortest path from there to dst can’t go through
24
A. Thus, the packet can only loop by following A 99K N Hf p (A) → A → . . . → dst. So the path
contains at most one 2-hop loop.
Now we analyze the stretch (i.e., latency penalty) the packets will experience. For two switches
A and B, let l(A, B) denote the length of the shortest path from A to B. Let l′ (A, B) denote the
latency the packet experiences on the path in BUFFALO. We define the stretch as:
S = l′ (A, B) − l(A, B)
.
Theorem 2. In SPAF networks, if a packet experiences just one false positive at switch A, the
packet will experience a stretch of at most l(A, N Hf p (A)) + l(N Hf p (A), A).
Proof. Since there is one false positive in A, A will choose either N Hsp (A) or N Hf p (A). If A picks
N Hsp (A), there is no stretch. If A picks N Hf p (A), there are two cases: (i) If N Hf p (A) sends
the packet to the destination without going through A, the shortest path from N Hf p (A) to the
destination is followed. Based on the triangle inequality, we have:
l(N Hf p (A), dst) ≤ l(N Hf p (A), A) + l(A, dst)
l′ (A, dst) − l(A, dst) ≤ l(A, N Hf p (A)) + l(N Hf p (A), A)
(ii) If N Hf p (A) sends the packet back to A, the stretch is l(A, N Hf p (A)) + l(N Hf p (A), A).
Therefore, we prove that in the one false positive case, packets are guaranteed to reach the
destination with bounded stretch in SPAF networks.
2.4.2
Handling Multiple False Positives with Random Selection
Now we consider the case where all the switches in the network apply our Bloom filter mechanism.
We choose different hash functions for different switches so that the false positives are independent
among the switches. (We can choose different keys for key-based hash functions to generate a group
of hash functions.) Thus it is rare for a packet to experience false positives at multiple switches.
25
F
G
C
D
E
B
A
dst
Figure 2.3: BUFFALO forwarding graph (99K false positive link, −→ shortest path tree)
Let us fix a destination dst, and condition the rest of this section on the fixed forwarding table
and memory size (which, per Section 2.5, means the Bloom filter parameters are fixed, too). Let
f (h) be the probability of Bloom filter h erroneously matching dst (a priori independent of dst
if dst shouldn’t be matched). Then, k, the number of Bloom filters mistakenly matching d is, in
P
expectation, F = h f (h). If all values of f are comparable and small, F is roughly binomial,
with Pr[k > x] decays exponentially for x ≫ 2f |E|.
There may exist loops even when we avoid picking the incoming interface. For example, in
Figure 2.2(b), A may choose the false-positive hop to B at first, and B may choose the falsepositive next hop C. However, the packet can eventually get out of the loop if each switch chooses
the next hop randomly: any loop must contain a false-positive edge, and the source node of that
edge will with some probability choose its correct hop instead. For example, A will eventually
choose the next hop D to get out of the loop. Such random selection may also cause out-of-order
packets. This may not be a problem for some applications. For the applications that require
in-order packet forwarding, we can still reorder packets in the end hosts.
In general, in SPAF networks there is a shortest path tree for each destination dst, with each
packet to dst following this tree. In BUFFALO, packets destined to dst are forwarded in the
directed graph consisting of a shortest path tree for dst and a few false positive links. We call this
graph BUFFALO forwarding graph. An example is shown in Figure 2.3, where two false positives
occur at A and B. Note that, if the shortest-path links are of the same length (e.g., in terms of
latency), the link from A to F cannot be less than about twice that length: otherwise F ’s shortest
26
G
F
C
D
A
d=3
E
B
d=2
d=1
d=0
dst
Figure 2.4: Coupling for the expected stretch proof: all nodes at the same hop distance from dst
are collapsed into 1 node. Forward false positive links, like D to B, are dropped. The number of
backward edges on the line graph is the maximum over all nodes at that distance of the number of
backward and same-depth false-positive links (B’s edges at d = 1, D’s edges at d = 2). A random
walk on the line graph converges no faster than a random walk on the original. The line graph
itself is a valid network, thus allowing for tight bounds.
path would go through A. If all links are the same length , no false positive edge can take more
than one “step” away from the destination.
If a packet arrives at the switch that has multiple outgoing links in BUFFALO forwarding graph
due to false positives, we will randomly select a next hop from the candidates. Thus, the packet
actually takes a random walk on the BUFFALO forwarding graph, usually following shortest-path
links with occasional “setbacks”.
Theorem 3. With an adversarially designed BUFFALO network with uniform edge latencies, and
even worst-case placement of false positives, the expected stretch of a packet going to a destination
√
529
√
< 6.8.
associated with k false positives is at most S(k) = ρ · ( 3 3)k , where ρ = 54·
3
3
To prove this theorem, we first present the model used in our proof:
Step 1: Model.
We make the following two assumptions:
1. We assume the underlying SPAF computation is based on “hop count” only, or, equivalently,
equal edge weights on all edges. We expect that the bounds we derive under this assumption
27
will not differ qualitatively from the typical case of edge weights that are diverse but roughly
on the same order of magnitude.
2. BUFFALO implements a “no-bounce” rule: if a node detects a false positive, it randomly
selects a next hop out of the several candidates that the Bloom filters then offer, but excludes
from consideration the hop that the packet arrived from. We allow the selection of the latter,
as well, ignoring the “no-bounce” optimization in BUFFALO. This simplifies the analysis,
and we expect that the upper bounds should not get any worse in the presence of this feature.
We represent the underlying network with an undirected graph G = (V, E), with n nodes, each
representing a switch or an end host. Consider forwarding to a particular destination dst ∈ V with
some, possibly all, switches in the network implementing BUFFALO. The underlying protocol
builds a shortest-path tree (V, T ⊂ E), directed toward dst.
After any given FIB update, some BUFFALO-using routers may have false positives for destination dst. A false positive at node v for next hop v ′ will cause BUFFALO to possibly forward
from v to v ′ — but this can only happen if the edge {v, v ′ } exists in G. Let (V, B) be the directed
”BUFFALO graph,” containing all the edges along which BUFFALO switches might forward, given
the current false positives. That is, B consists of T , and, for each false positive at node v that
matches next hop v ′ for destination dst, an additional (directed) edge (v, v ′ ). We use P to denote
the false-positive edges alone (P = B \ T ).
Observation 2.4.1. Without the “no-bounce” rule, if some or all routers use BUFFALO, a packet
to dst performs an unbiased random walk on (V, B) until reaching dst.
For background on random walks, we refer the reader to any of a number of standard books,
such as [31, 32, 33].
We denote by dT (v, w) the hop distance from v to w in T , and use d(v) as shorthand for
dT (v, dst), the distance from v to the destination in T , which we call the depth of v.
Observation 2.4.2. d(v) = dE (v, dst) = dB (v, dst), since T is a shortest-path tree, and is contained in B and E. The shortest-path property also ensures that, for any edge {v, w} ∈ E,
|d(v) − d(w)| ≤ 1.
28
We say a packet traveling from v to dst experiences stretch S if it traverses d(v)+ S hops before
reaching dst. The expected stretch of a packet starting at v is directly connected to the random
walk’s expected hitting time from v to dst: Tv,dst = d(v) + E[S].
Now, Let’s prove Theorem 3.
Step 2: Calculate expected stretch.
First, “project” the whole graph (the shortest path tree and the “noise” false positive edges)
onto a line (multi)graph L where node li corresponds to all nodes in the real network at depth i
away from dst, as shown in Figure 2.4. Let’s say l0 , corresponding to the destination, is on the
“right” while lx , where x is the equivalent of “diameter” (the length of the longest shortest path
to d), is on the left.
li has 1 edge pointing to the right, and ki edges pointing to the left, where ki is the max, over
all nodes v at depth i in the original graph, of the number of false positives at v that point to
nodes of depth i or i + 1.
Lemma 2.4.3. The expected stretch of an unbiased random walk on B starting at v is at most
the expected stretch of an unbiased random walk on L starting at ld(v) .
Proof. The lemma follows from a conventional coupling argument, between the random walk’s
depth in B and the random walk’s depth in L.
Consider the next hop from some node v in B, at depth d, which has i ≥ 1 edges to nodes of
depth d − 1, j edges to nodes of depth d, and k edges to nodes of depth d + 1. By construction,
the corresponding node ld has at least k + j edges to ld+1 and one edge to ld−1 . The probability
of the walk moving to depth d − 1 in L at most 1/(k + j + 1), while the walk in B moves to depth
d − 1 with probability i/(i + k + j) ≥ 1/(k + j + 1). This allows a natural coupling for depth of
the next hop in B and in L:
If the L walk takes a deeper next hop than the B walk, we can “suspend” the B walk, and
let the L walk continue until the next time it reaches a node at the same depth as the B walk —
this is guaranteed to happen, since depth never changes by more than 1 hop. After that point,
proceed with the next hop on both random walks. Since L and B random walks start at the same
depth, this coupling guarantees that L will never move to a lower depth than B, and thus that L
will take at least as many hops as B.
29
Figure 2.5: Coupling the depth process in B and L
We now analyze the worst-case expected hitting time for an unweighted random walk on L.
For any i > j, the hitting time from li to l0 must include at least one visit to lj , guaranteeing that
the expected hitting time to l0 is maximized at lx . The transition probability matrix (where Pi,j
is the probability, when at li , of going to lj on the next step) is:

0

 kx−1

 kx−1 +1

 0


 .
P =  ..


 0



 0

0
1
0
···
0
1
kx−1 +1
0
···
kx−2
kx−2 +1
0
1
kx−2 +1
..
..
0
..
.
.
0
···
.
0
k2
k2 +1
0
1
k2 +1
···
0
k1
k1 +1
0
···
0
0
···



0 


0 


.. 
. 


0 


1 
k1 +1 

1
(2.1)
Following the expected hitting time analysis detailed in, e.g., [34], which cites [35], we let Q
be the matrix P with the last row and last column removed. The expected hitting time from vx
to v0 is then:
T =
X
(I − Q)−1
0,j
j
30
(2.2)
Inversion of (I − Q) via Gaussian elimination on the augmented matrix yields:
1
−1
0
···
−kx−1
kx−1 +1
1
−1
kx−1 +1
0
···
0
Rx−2 :
..
.
0
..
.
−kx−2
kx−2 +1
1
..
.
−1
kx−2 +1
···
..
.
0
..
.
R2 :
0
···
0
−k2
k2 +1
1
−1
k2 +1
R1 :
0
···
0
−k1
k1 +1
1
Rx :
Rx−1 :
Rx′ :
′
Rx−1
1
−1
0
..
···
0
.
0
1
!
1
1
..
.
1
′
′
← Rx−2
= (kx−2 + 1)Rx−2 + kx−2 Rx−1
..
.
← R2′ = (k2 + 1)R2 + k2 R3′
← R1′ = (k1 + 1)R1 + k1 R2′
1
1
′
← Rx−1
= (kx−1 + 1)Rx−1 + kx−1 Rx′
0
···
:
0
1
−1
0
···
0
kx−1
(kx−1 + 1)
0
···
′
Rx−2
:
..
.
0
..
.
0
1
−1
..
.
···
..
.
0
..
.
kx−1 kx−2
(kx−1 + 1)kx−2
(kx−2 + 1)
0
..
.
R2′ :
0
···
R1′ :
0
..
.
···
0
0
1
−1
kx−1 kx−2 · · · k2
(kx−1 + 1)kx−2 · · · k2
···
(k2 + 1)
0
···
0
0
1
kx−1 kx−2 · · · k2 k1
(kx−1 + 1)kx−2 · · · k2 k1
···
(k2 + 1)k1
(k1 + 1)
!
← Rx′′ =
P
i
Ri′
(2.3)
The expecting hitting time, the sum of the top row of the inverse matrix, is thus the sum
of all the entries on the right side. We split the sum of each column c except the first into
Px−c+1 Qx−c+1
Px−c Qx−c
kj + i=1 j=i kj + 1, and then group the first term with the previous column,
i=1
j=i
c − 1. This yields:
T =x+2
x x−c
X
X x−c
Y
kj
(2.4)
c=1 i=1 j=i
X
=x+2
b
Y
ki
(2.5)
1≤a≤b≤x i=a
Since, with no false positives, a packet may take up to x hops to get to d, the stretch S is thus
P
Q
upper bounded by S ≤ T − x = 2 1≤a≤b≤x bi=a ki .
P
Q
We’ll use the symbol Sqp for p≤a≤b≤q bi=a ki , i.e. the sum of products over each possible
substring of integer sequence {ki }.
The Sqp notation, as well as the Lq and Rp notations introduced below, leave implicit their
dependence on the sequence {ki }. When discussing proposed changes to the sequence, these
symbols are to always be interpreted in terms of the sequence before the change in question.
Step 3: Exact patterns for maximizing Sx1 .
31
The remainder of the proof of Theorem 3 is a detailed combinatorial treatment of maximizing
P
Sx1 over all sequences whose sum, i.e. the total number of false positives i ki , is fixed at some k.
We proceed by listing a series of transformations of any candidate maximizing sequence that never
change the sum, never decrease the sum of substring products, and converge to a very specific
family of maximum sequences that allows S to be explicitly computed.
We forewarn the reader that this subsection is relatively technical and is unlikely to be of
broader interest outside this proof.
In all the statements below, we implicitly require that
P
i
ki = k.
Observation 2.4.4. To upper-bound stretch, we can assume, WLOG, that ki > 0 for all i.
Otherwise, removing that ki and thus shrinking x by 1 cannot decrease S: the walk before the edge
is removed can never return to the part of L above this edge, so contracting the edge only adds
possible extra upward traversals, which would still have to return to this node before continuing to
dst.
Lemma 2.4.5. There is a sequence {ki } maximizing Sx1 that has ki ≤ 3 for all i.
Proof. Suppose there is a ki ≥ 4 in some sequence {ki } maximizing Sx1 . Then, split ki into two
adjacent sequence elements, 2 and ki − 2. Since 2(ki − 2) ≥ ki , each substring of the original
sequence that contained ki will have a corresponding substring including both 2 and ki − 2 in the
new sequence, with a product at least as big as the original substring. Any substring that didn’t
include ki originally will still exist as-is. Also, the new sum of substring products will also include
the substring containing just the new 2 element, which does not correspond to any of the original
substrings, thus guaranteeing a strictly greater substring product sum.
Lemma 2.4.6. There is a sequence {ki } that maximizes S that has 1 ≤ ki ≤ 3 and is dip-free: if
a < b < c, and ka > kb , then kb ≥ kc ; and if a < b < c and kb < kc , then ka ≤ kb . That is, {ki }
matches the regular expression 1∗ 2∗ 3∗ 2∗ 1∗ .
Proof. Consider a sequence {ki } maximizing S. We will see that it is dip-free by considering
transpositions of two adjacent sequence elements.
P
Qp
Let Lp denote 1≤a≤p i=a ki , the partial sum of substring products covering all substrings
P
Qb
ending exactly at p. Similarly, let Rq denote q≤b≤x i=q ki , the partial sum of substring products
covering all substrings starting exactly at q. We define L0 = Rx+1 = 0.
32
Note that, since ki ≥ 1, Lp = kp Lp−1 + kp monotonically strictly increases with p, and Rq =
kq Rq+1 + kq monotonically strictly decreases with q.
For any 1 ≤ i ≤ x − 1, we can now split the full sum of Sx1 into several categories, based on
where the substring lies in relation to ki and ki+1 :
Sx1 =Si−1
+ Sxi+2 + ki ki+1 + ki + ki+1 + ki ki+1 Li−1 + Ri+2 + Li−1 Ri+2
1
+ ki Li−1 + ki+1 Ri+2
All except the last two of the terms add up to an expression that is symmetric with respect to
transposing ki and ki+1 . Now, suppose ki < ki+1 . Then, since the sequence is maximizing, its Sx1
is greater than it would be if ki and ki+1 were transposed, requiring:
ki Li−1 + ki+1 Ri+2 ≥ ki+1 Li−1 + ki Ri+2
(ki+1 − ki )(Ri+2 − Li−1 ) ≥ 0
Ri+2 − Li−1 ≥ 0
′
Then, for any i′ < i, strict monotonicity gives us Ri′ +2 − Li −1 > 0. If ki′ > ki′ +1 , we would
′
have (ki′ +1 − ki′ ) Ri′ +2 − Li < 0, contradicting maximality of {ki }, since that would allow us to
raise Sx1 by transposing ki′ and ki′ +1 . Inductively applying this argument shows that, if a > b > c
and kb < kc , then ka ≤ kb . The other side follows by symmetry.
Lemma 2.4.7. There exists a maximizing sequence obeying the constraints of Lemma 2.4.6 that
starts and ends with a 1, i.e., it matches the regular expression 11∗ 2∗ 3∗ 2∗ 1∗ 1.
Proof. If k1 > 1 in a maximizing sequence, consider splitting it into adjacent elements 1 and k1 −1.
This transforms the original sum of substring products from k1 + k1 R2 + Sx2 into 1 + k1 − 1 + 1(k1 −
1) + (k1 − 1)R2 + 1(k1 − 1)R2 + Sx2 = 1 + 2(k1 − 1) + 2(k1 − 1)R2 + Sx2 . Since k1 ≤ 2(k1 − 1), this
increases the total sum of substring products by 1. The same argument holds for kx .
33
Observation 2.4.8. An adjacent (1, 3) pair can always be replaced with a (2, 2) pair, strictly
increasing Sx1 . It changes from Si−2
+ Sxi+1 + (1 + 3)Li−2 + (3 + 3)Ri+1 + 3Li−2 Ri+1 + 1 + 3 + 3 to
1
Si−2
+ Sxi+1 + (2 + 4)Li−2 + (2 + 4)Ri+1 + 4Li−2 Ri+1 + 2 + 2 + 4, an increase by 2Li−2 + Li−2 Ri+1 + 1,
1
which is always positive.
Lemma 2.4.9. For k ≥ 7, there is an maximizing sequence satisfying 2.4.2 that has at most two
1’s on each side.
Proof. Consider a sequence satisfying 2.4.2 with at least three 1’s at the start. If the first non-1
element is some ki = 3, Observation allows us to replace it and the preceding 1 with (2,2).
If the first non-1 element is some ki = 2, consider replacing (1, 2) with a 3. Sx1 changes from
Si−2
+ Sxi+1 + (1 + 2)Li−2 + (2 + 2)Ri+1 + 2Li−2 Ri+1 + 1 + 2 + 2 to Si−2
+ Sxi+1 + 3Li−2 + 3Ri+1 +
1
1
3Li−2 Ri+1 + 3. The increment is Li−2 Ri+1 − Ri+1 − 2, non-negative if (Li−2 − 1)Ri+1 ≥ 2.
For k ≥ 7, this is satisfied, since either:
1. There are four or more ones before ki . Then, Li−2 − 1 ≥ 2. By 2.4.2, there is at least one
element after ki , guaranteeing Ri+1 ≥ 1;
2. Or
Px
j=i+1
kj ≥ 2, guaranteeing Ri+1 ≥ 2. Since the sequence starts with three or more
ones, Li−2 − 1 ≥ 1.
A symmetrical argument applies to the other end of the sequence.
Lemma 2.4.10. For k ≥ 18, any maximizing sequence satisfying 2.4.9 has at least one 3.
Proof. With k ≥ 18 no 3’s, and at most two 1’s at each end, the sequence must then have at least
seven 2’s. Let ki−2 be the first 2. We consider replacing the third, fourth, and fifth 2’s (ki , ki+1 ,
and ki+2 )) with two 3’s.
Before the change, Sx1 is Si−1
+ Sxi+3 + (2 + 4 + 8)Li−1 + (2 + 4 + 8)Ri+3 + 8Li−1 Ri+3 + 2 + 2 +
1
2 + 4 + 4 + 8 = Si−1
+ Sxi+3 + 14(Li−1 + Ri+3 ) + 8Li−1 Ri+3 + 22. After the change, it becomes
1
Si−1
+ Sxi+3 + (3 + 9)Li−1 + (3 + 9)Ri+3 + 9Li−1 Ri+3 + 3 + 3 + 9 = Si−1
+ Sxi+3 + 12(Li−1 + Ri+3 ) +
1
1
9Li−1 Ri+3 + 15. This is an increase of Li−1 Ri+3 − 2(Li−1 + Ri+3 ) − 7 = (Li−1 − 2)(Ri+3 − 2) − 11.
With ki−2 = ki−1 = ki+3 = ki+4 = 2, we are guaranteed that both Li−1 and Ri+3 are at least 6,
making the increase positive.
34
Lemma 2.4.11. For k ≥ 18, any maximizing sequence satisfying 2.4.10 has exactly one 1 on each
side.
Proof. Suppose, WLOG, there are exactly two 1’s in the beginning (Lemmas 2.4.2 and 2.4.9 allow
us to reach such a maximizing sequence from any other). Use b for the number of 2’s between the
last 1 and the first 3 (b = i − 3). Consider replacing k2 = 1 and the first 3, ki = 3 (which Lemma
2.4.10 guarantees to exist) with k2 = ki = 2. The increment in Sx1 is:


Sxi+1 + Si−1
+ Ri+1 1 · 2 · 2b · 2 + 2 · 2b · 2 + 2
3

+2·
b
X
j=0

b
X
j=0
2j 

2j  + 2 · 2b · 2 + 2 · 2b · 2 · 1 + 2 · 



b
X
j=0



b
X
2j  + 1 −
2j  + 1 · 2 · 

Sxi+1 + Si−1
+ Ri+1 1 · 1 · 2b · 3 + 1 · 2b · 3 + 3
3
j=0
b
X
j=0

2j 







b
b
b
X
X
X
2j  + 1
2j  + 1 · 1 · 
+3·
2j  + 3 · 2b · 1 + 3 · 2b · 1 · 1 + 1 · 
j=0
j=0
= Ri+1
j=0
(12 · 2b − 2) − (12 · 2b − 3) + (20 · 2b − 5) − (16 · 2b − 4)
= Ri+1 + 2b+2 − 1 (2.6)
Since b ≥ 1, the increment is strictly positive, violating maximality. A symmetric argument
applies for two 1’s at the end.
Lemma 2.4.12. For k ≥ 18, any maximizing sequence satisfying 2.4.11 has at most three 2’s on
each side of the 3’s.
Proof. Consider a maximizing sequence with at least four 2’s before the 3’s. First, apply to ensure
that we’re considering a maximizing sequence starting and ending with a 1.
By Observation 2.4.2, in a maximizing sequence, there must be at least one 2 after the 3’s —
else the total is strictly increased by replacing a (3, 1) pair with (2, 2).
Like in Lemma 2.4.10 above, we consider replacing the last three 2’s before the 3’s with two new
3’s, which will increase the total if (Li−1 − 2)(Ri+3 − 2) > 11. But the existence of at least one 3, at
35
least one 2, and a 1 after the triple we’re replacing guarantees that Ri+3 − 2 ≥ 3 + 6 + 6 − 2 = 13.
Since there must be at least one extra 2 before the triple, and at least one 1, we have Li−1 ≥ 4,
guaranteeing the strict inequality.
We are now guaranteed, for k ≥ 18, the existence of a maximizing sequence of form 12b 3c 2d 1
where 1 ≤ b, d ≤ 3 and c ≥ 1. We can now obtain a convenient closed form for Sx1 for such
sequences. First note that the substring products of a homogeneous sequence z n add up to:
b
Y
X
m(z, n) =
ki
1≤a≤b≤n i=a
n X
n
X
b−a
=z
=z
z
a=1 b=a
n
(n−a+1)
X
z
z−1
a=1
=
z
z−1
−1
n
X
i=1
(z i − 1)
n+1
z
z
−1
=
·
−1−n
z−1
z−1
n+2
z
− (n + 1)z 2 + nz
=
(z − 1)2
Using this, we can split up the computation of Sx1 based on which part of the sequence the
substring starts and ends in:
36
Sx1 = 1 + m(2, b) + m(3, c) + m(2, d) + 1
+1·
+
b
X
i=1
b
X
2i + 1 · 2b ·
2i
!
3i
!
i
!
i=1
+
c
X
i=1
+
d
X
i=1
2
c
X
i=1
i=1
3i
!
2i
!
i=1
d
X
c
X
3i + 1 · 2b · 3c ·
+
b
X
+
i=1
i=1
2i
!
· 3c ·
3i
!
· 2d · 1
i=1
c
X
d
X
2i + 1 · 2b · 3c · 2d · 1
d
X
i=1
2i
!
+
b
X
i=1
2i
!
· 3c · 2d · 1
(2.7)
·1
9
9
9 3
= 4 · 2b − 2b − 4 + 4 · 2d − 2d − 4 + 3c − c − + c
4
4
4 4
3
3
b
d
+ (2 − 2 + 3) + (2 − − 3)2 + (2 − − 3)2 + (−3 + 4 − 3)3c
2
2
3
3
b c
+ ( − 2 + 3 − 4)2 3 + ( − 2 + 3 − 4)3c 2d + (2 + 1 + 4 + 2)2b 3c 2d
2
2
= 9 · 2b 3c 2d − 1.5 · 3c (2b + 2d ) + 0.25 · 3c + 1.5(2b + 2d ) − 2(b + d) − 1.5c − 6.25
Lemma 2.4.13. For k ≥ 18, any maximizing sequence satisfying 2.4.12 cannot contain three
consecutive 2’s.
Proof. Suppose, WLOG, b = 3. We consider two cases for d:
Suppose d = 1. Consider “balancing” the sequence, by setting b = d = 2, and leaving c fixed.
In equation 2.7, this preserves the value of b + d and 2b 2d . Thus, the only change to Sx1 is in the
terms involving (2b + 2d ), which goes from 9 to 8. Since c ≥ 1 by Lemma 2.4.10, this guarantees
a strict increase in Sx1 , by 1.5 · 3c − 1.5 ≥ 3.
Suppose 2 ≤ d ≤ 3. Consider replacing k3 and k4 , the second and third 2 at the beginning,
and kx−2 , the first 2 at the end, with two 3’s. This changes b from 3 to 1, d to d − 1, and c to
c + 2. Thus, Sx1 is incremented by:
37
9 · 3c (2 · 2d−1 · 9 − 8 · 2d ) − 1.5 · 3c (9(2 + 2d−1 ) − (8 + 2d )) + 0.25 · 3c (9 − 1)
+ 1.5(2 + 2d−1 − 8 − 2d ) − 2(1 + (d − 1) − (3 + d)) − 1.5 · 2 =
= 7.5 · 3c 2d−1 − 13 · 3c − 1.5 · 2d−1 − 6
≥ 15 · 3c − 13 · 3c − 1.5 · 4 − 6
= 2 · 3c − 12
Since there are at most three 2’s and exactly one 1 on each side of the sequence, k ≥ 18 requires
c ≥ 2, which renders the increment strictly positive.
We now know that 1 ≤ b, d ≤ 2 in a maximizing sequence. But, at this point, if k mod 3 = 0,
this only allows b = d = 1; if k mod 3 = 1, this only allows b = d = 2; and if k mod 3 = 2 this only
allows b = 2 and d = 1 or vice versa — and since the formula for Sx1 is symmetric with respect
to reversing the sequence, in all three cases, this specifies the exact sequence maximizing Sx1 , and
hence the expected stretch.
For k ≥ 18, Theorem 3 follows from substituting each of the three possibilities into equation
2.7:




(9 · 4 − 6 + 0.25)3(k−6)/3 − 1.5 k−6
(k mod 3 = 0)

3 + 6 − 4 − 6.25



S(k) ≤ 2 max (9 · 16 − 12 + 0.25)3(k−10)/3 − 1.5 k−10 + 12 − 8 − 6.25 (k mod 3 = 1)
3






(9 · 8 − 9 + 0.25)3(k−8)/3 − 1.5 k−8 + 9 − 6 − 6.25
(k mod 3 = 2)
3




121/36
(k mod 3 = 0)




√
< 2 · 3k/3 max 529/(108 3 3) (k mod 3 = 1)




√


253/(36 3 9)
(k mod 3 = 2)
=
529
√ · 3k/3
54 3 3
38
k
max S(k)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
2
6
12
20
32
52
76
120
170
260
370
544
786
1126
1622
2370
3400
j
529
√ 3k/3
54 3 3
9
14
20
29
42
61
88
127
183
264
381
550
793
1144
1650
2380
3433
k
Maximum stretch at:
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
2
2
2
2
2
2
2
2
1
1
2
2
2
2
3
2
2
2
2
2
2
2
2
1
1
1
2
2
2
2
3
2
3
3
2
3
3
1
1
1
2
2
2
2
3
3
3
3
1
1
2
2
2
2
2
3
1
1
1
21
21
21
Table 2.2: Optimal sequences for 1 ≤ k ≤ 17, obtained by brute-force search.
For 1 ≤ k ≤ 17, brute force search among sequences adding up to k and obeying Lemma 2.4.6
shows that the sequences in Table 2.2 maximize stretch, which obeys the bound of Theorem 3, as
well, concluding the proof of the latter.
Step 4: Tight lower bound.
Observation 2.4.14. Assuming that there can be multiple (a, b) edges from a particular node a to
a particular node b, the line graph L itself is then a valid “tree and false positives” configuration,
which means the sequence defined by Lemma 2.4.13 corresponds to a concrete, valid example that
makes the above bound exactly tight for k mod 3 = 1.
Observation 2.4.15. If multiple edges between the same pair of nodes are not allowed, we expect
that the worst-case stretch will be somewhat better, but can still be exponential under worst-case
false positive placements. An example of such an arrangement is in Figure 2.6.
Though the expected stretch is exponential, this is counterbalanced by the exponentially low
probability of k false positives. Tuning the Bloom filter parameters to optimize memory usage
will allow us to bound F , yielding at least a superlinear tail bound on the probability of large
stretches, assuming f values are comparable to 1/2m or smaller, yielding F = O(1):
39
Figure 2.6: Exponential stretch with k false positives and no multiple edges: an i + 1-row network
like the one on the left has 9i false positives, with worst-case stretch equivalent to the line graph
on the right: S(k) = Θ(3i ) = Θ(3k/9 )
Theorem 2.4.16. For any z ≥ 60.3 · 7.3221F , the probability of stretch exceeding z is bounded by
2/z. Asymptotically, the tail will decay as Õ(1/z 1.54), to within polylog factors.
Proof. Assume the worst-case arrangement of false positive locations. Consider packets starting
at the source with the worst expected stretch to the destination. With k false positives, by the
Markov bound, the stretch will be at most 2S(k) with probability at least 1/2. After every 2S(k)
steps, any such packet not at the destination can be “reset” to the worst possible starting location
without shortening its current expected arrival time. Thus, for any integer α, the probability of
the stretch being more than 2αS(k) is at most 1/2α .
We can bound the overall stretch by setting k, with foresight, to the solution of k3k/3 =
z
ρ(2−1/e)
(here and below, e is Euler’s constant), which is a unique positive value, by monotonicity4 .
4 We
forgo the details of dealing with rounding and integrality.
40
This value of k will allow us to productively apply the following union bound:
Pr[stretch > z] ≤ Pr[stretch > z| ≤ k false pos] +
+ Pr[> k false pos]
(2.8)
(2.9)
The above iterated Markov bound covers the first term, which is then bounded by 1/2z/2S(k) =
1/2k(1−1/2e) .
For the second term, let F =
P
f (h) be the expected number of false positives anywhere in
the system for any fixed destination, i.e. the sum of the probabilities of false positives along each
possible edge. If k > 2eF (where e is Euler’s constant), we can use the fact that the hashes for
each Bloom filter are chosen independently and apply the following form of the Chernoff bound
[32]: Pr[X > (1 + δ) E[X]] < 2−δ E[X] , for any δ > 2e − 1. With X as the random variable counting
the false positives for our destination, we set δ = k/F − 1 yielding Pr[X > k] < 2−(k/F −1)F =
2−k+F < 1/2k(1−1/2e) , bounding the overall probability by 2/(21−1/2e )k ≤ 2/1.76k .
To satisfy the k > 2eF requirement of the Chernoff bound, we need z = (2 − 1/e)ρk3k/3 ≥
60.3 · 7.3221F . The same constraint, since F > 0, guarantees z ≥ 29, ensuring that 2/1.76k ≤
2/((2 − 1/e)ρk3k/3 ) = 2/z.
With z = 3k/3+O(log(k)) , the tail asymptotically decays as Õ(1/z log 3 3 1.76 ), to within polylog
√
factors, yielding the second part of the theorem.
This bound characterizes the worst-case configuration the network may end up in after any
particular control-plane event. As a description of the typical behavior, on the other hand, this
bound is quite crude. We expect that an average-case analysis over false positive locations, corresponding to the typical behavior of BUFFALO, will yield polynomial expected stretch for fixed
k: the exponential worst-case behavior relies on all the false-positives carefully “conspiring” to
point away from the destination, and randomly placed false positives, as with real Bloom filters,
will make the random walk behave similarly to a random walk on an undirected graph, producing
polynomial hitting times. This will allow z = poly(k) and hence an exponentially decaying stretch
distribution.
While our scheme works with any underlying network structure, it works particularly well with
a tree topology. Tree topologies are common in the edges of enterprise and data center networks.
41
A logical tree is usually constructed with the spanning tree protocols in today’s Ethernet. Roughly
speaking, in a tree, a lot of distinct false positives are needed at each distance from the destination
in order to keep “pushing” the packet away from the destination.
Claim 4. If the underlying network is a tree, with no multiple links between any one pair of
routers, the expected stretch with k false positives, even if they are adversarially placed, is at most
2(k − 1)2 .
Proof. Consider any configuration of the shortest path tree and the extra false positive edges.
Since there are no multiedges, each edge of the shortest path tree has 1 or 0 antiparallel false
positive edges. Contracting all the tree edges without a corresponding false positive edge will
not decrease the expected stretch, by an argument similar to Observation 2.4.4: Any such edge
renders the subtree behind it unreachable after it’s traversed. Shrinking this edge only adds the
possibility of an extra detour back into the subtree, which would have to pass through this node
again before proceeding — at that point, the expected remaining time until destination will be
the same as when this node was first visited in the original graph.
The resulting graph is effectively undirected, with each edge having a corresponding antiparallel
edge. A random walk is thus identical to a random walk on an undirected tree, shown in, e.g.,
Sec. 5.3 of [31] to have the expected hitting time of at most 2(k − 1)2 .
We believe that similar results should apply when we allow heterogeneous latencies, especially
when the per-link latencies are within a small constant factor of each other, as is likely in many
geographically-local networks.
2.4.3
Stretch in Realistic Networks
We evaluate the stretch in three representative topologies: Campus is the campus network of a
large (roughly 40,000 students) university, consisting of 1600 switches [36]. AS 1239 is a large
ISP network with 315 routers [37]. (The routers are viewed as switches in our simulation.) We
also constructed a model topology similar to the one used in [5], which represents a typical data
center network composed of four full-meshed core routers each of which is connected to a mesh of
twenty one aggregation switches. This roughly characterizes a commonly-used topology in data
centers [38].
42
Expected Stretch Normalized
by Shortest Path Length
0.01
0.001
0.0001
1e-05
1e-06
Data Center, Campus
ISP
1e-07
1e-06
1e-05
0.0001
0.001
False Positives [fraction]
0.01
CCDF
Figure 2.7: Expected stretch
1
0.1
0.01
0.001
0.0001
1e-05
1e-06
1e-07
1e-08
fp=0.5%
fp=0.1%
fp=1e-4
fp=1e-5
fp=1e-6
0
1
2
3
4
5
6
Stretch Normalized by Shortest Path Length
Figure 2.8: Stretch with real traces in campus network
In the three topologies, we first analyze the expected stretch given the false-positive rate. We
then use simulation to study the stretch with real packet traces.
Analysis of expected stretch:
We pick the false-positive rate of Bloom filters and calculate
the expected stretch for each pair of source and destination in the network by analyzing all the
cases with different numbers and locations of false positives and all the possible random selections.
The expected stretch is normalized by the length of the shortest path. We take the average stretch
among all source-destination pairs. We can see that the expected stretch increases linearly with
the increase of the false-positive rate. This is because the expected stretch is dominated by the
one false-positive case. Since we provide a constant stretch bound for the one false-positive case in
BUFFALO, the expected stretch is very small. Even with a false-positive rate of 1%, the expected
stretch is only 0.5% of the length of the shortest path (Figure 3.16).
43
Simulation on stretch distribution:
We also study the stretch of BUFFALO with packet
traces collected from the Lawrence Berkeley National Lab campus network by Pang et. al. [39].
There are four sets of traces, each collected over a period of 10 to 60 minutes, containing traffic to
and from roughly 9,000 end hosts distributed over 22 different subnets. Since we cannot get the
network topology where the trace is collected, we take the same approach in [5] to map the trace
to the above campus network while preserving the distribution of source-destination popularity of
the original trace. Figure 2.8 shows the distribution of stretch normalized by shortest path length.
When the false-positive rate is 0.01%, 99% of the packets do not have any stretch and 0.01% of
the packets have a stretch that is twice as long as the length of the shortest path. Even when the
false-positive rate is 0.5%, only 0.0001% of the packets have a stretch of 6 times of the length of
the shortest path. Note that in an enterprise or data center, the propagation delays are small, so
the stretch caused by false positives is tolerable.
2.5
Optimizing Memory Usage
In this section, we consider a switch with M -bit fast memory (i.e., SRAM) and a fixed routing
table. We formulate the problem of minimizing the overall false-positive rate through tuning the
sizes in the Bloom filters. This optimization is done by a Bloom filter manager implemented in a
BUFFALO switch. We then show numerical results of false positives with various sizes of memory
and forwarding tables.
2.5.1
Optimizing Bloom-Filter Sizes
Our goal is to minimize the overall false-positive rate. If any one of the T Bloom filters has a false
positive, an address will hit in multiple Bloom filters. In this case, we send the packets through a
slightly longer path as described in Section 2.4. To reduce the stretch, we must minimize the false
positives in each switch. We define the overall false-positive rate for a switch as the probability
that any one of the T Bloom filters has a false positive. As above, let f (h) denote the false-positive
rate of Bloom filter BF (h). Since Bloom filters for different next hops store independent sets of
addresses, and thus are independent of each other, the overall false-positive rate of T Bloom filters
44
is
F =1−
T
Y
(1 − f (h)) ≈
h=1
T
X
f (h)
h=1
(when f (h) ≪ 1/T, ∀h = 1..T )
Optimizing the sum approximation for F also directly optimizes the applicability threshold for
Theorem 2.4.16, expressed in terms of the sum as such.
Since there are different numbers of addresses per next hop, we should use different sizes for
the Bloom filters according to the number of addresses stored in them, in order to minimize the
overall false-positive rate with the M-bit fast memory.
In addition to constraining the fast memory size, we should also avoid overloading the CPU.
We bound the packet lookup time, which consists of hash computation time and memory access
time. To reduce the computational overhead of address lookup, we apply the same group of hash
functions to all T Bloom filters. Since we use the same hash functions for all the Bloom filters,
we need to check the same positions in all the Bloom filters for an address lookup. Therefore, we
put the same positions of the Bloom filters in one memory unit (e.g., a byte or a word), so that
they can be accessed by one memory access. In this scheme, the packet lookup time is determined
by the maximum number of hash functions in T Bloom filters (kmax = maxTh=1 (k(h)), where k(h)
denotes the number of hash functions used in BF (h)). Let uhash denote the number of hash
functions that can be calculated in a second. We need kmax /uhash time for hash computation.
Let tf mem denote the access time on small, fast memory. Assume there are b bits in a memory
unit which can be read by one memory access. We need ⌈(T kmax /b)tf mem ⌉ memory access time.
Since both hash computation and memory access time are linear in the maximum number of hash
functions kmax , we only need to bound kmax in order to bound the packet lookup time.5
We minimize the lookup time for each packet by choosing m(h) (the number of bits in BF (h))
and k(h) (i.e., the number of hash functions used in BF (h)), with the constraint that Bloom filters
must not take more space than the size of the fast memory and must have a bounded number of
hash functions.
5 In switch hardware, the 4-8 hash functions can be calculated in parallel. We also assert that fabrication of 6 to
8 read ports for an on-chip Random Access Memory is attainable with today’s embedded memory technology [40].
The cache line size on a Intel Xeon machine is about 32 bytes to 64 bytes, which is enough to put all the positions
of T Bloom filters in one cache line.
45
Let n(h) denote the number of addresses in Bloom filter BF (h). The optimization problem is
formulated as:
M in
F =
T
X
f (h)
(2.10)
h=1
s.t.
f (h) = (1 − e−k(h)n(h)/m(h) )k(h)
T
X
m(h) = M
(2.11)
(2.12)
h=1
k(h) ≤ kmax , ∀h ∈ [1..T ]
given
(2.13)
T, M, kmax , and n(h)(∀h ∈ [1..H])
Equation (2.10) is the overall false-positive rate we need to minimize. Equation (2.11) shows the
false-positive rate for a standard Bloom filter. Equation (2.12) is the size constraint of the fast
memory. Equation (2.13) is the bound on the number of hash functions. We have proved that
this problem is a convex optimization problem.6 Thus there exists an optimal solution for this
problem, which can be found by the IPOPT [41] (Interior Point OPTimizer) solver. Most of our
experiments converge within 30 iterations, which take less than 50 ms. Note that the optimization
is executed only when the forwarding table has significant changes such as a severe link failure
leading to lots of routing changes. The optimization can also be executed in the background
without affecting the packet forwarding.
2.5.2
Analytical Results of False Positives
We study in a switch the effect of forwarding table size, number of next hops, the amount of fast
memory, and number of hash functions on the overall false-positive rate.7 We choose to analyze the
false positives with synthetic data to study various sizes of forwarding tables and different memory
and CPU settings. We have also tested BUFFALO with real packet traces and forwarding tables.
The results are similar to the analytical results and thus omitted in the thesis. We studied a
forwarding table with 20K to 2000K entries (denoted by N ), where the number of next hops (T )
varies from 10 to 200. The maximum number of hash functions in the Bloom filters (kmax ) varies
6 The
proof is omitted due to lack of space.
Section 2.4, the false-positive rate is defined for each Bloom filter. Here the overall false-positive rate is
defined for the switch because different Bloom filters have different false-positive rates. The overall false-positive
rate can be one or two orders of magnitude larger than individual Bloom-filter false-positive rate.
7 In
46
Overall False-Positive
Rate (fraction)
0.1
0.01
0.001
0.0001
1e-05
kmax=4
kmax=6
kmax=8
1e-06
200
400
600
800
Memory Size M (KB)
1000
Overall False-Positive
Rate (fraction)
Figure 2.9: Effect of memory size (T = 10, N = 200K)
0.04
0.035
0.03
0.025
0.02
0.015
0.01
0.005
0
kmax=4
kmax=6
kmax=8
0
50
100
# Next Hop (T)
150
200
Figure 2.10: Effect of number of next hops (M = 600KB, N = 200K)
from 4 to 8. Since next hops have different popularity, Pareto distribution is used to generate the
number of addresses for each next hop. We have the following observations:
(1) A small increase in memory size can reduce the overall false-positive rate significantly. As shown in Figure 2.9, to reach the overall false-positive rate of 0.1%, we need 600 KB
fast memory and 4-8 hash functions to store a FIB with 200K entries and 10 next hops. If we
have 1 MB fast memory, the false-positive rate can be reduced to the order of 10−6 .
(2) The overall false-positive rate increases almost linearly with the increase of T .
With the increase of T and thus more Bloom filters, we will have larger overall false-positive
rate. However, as shown in Figure 2.10, even for a switch that has 200 next hops and a 200Kentry forwarding table, we can still reach a false-positive rate of 1% with 600KB fast memory
(kmax = 6). This is because if we fix the total number of entries N , with the increase of T , the
number of addresses for each next hop drops correspondingly.
47
Overall False-Positive
Rate (fraction)
1
0.1
0.01
0.001
0.0001
1e-05
1e-06
M=0.5MB
1e-07
M=1MB
1e-08
M=2MB
1e-09
20K 200K 500K
1000K
# Forwarding Table Entries (N)
2000K
Fast Memory Size (KB)
Figure 2.11: Effect of number of entries (T = 10, kmax = 8)
14000
hashtable
12000
fp=0.01%
10000
fp=0.1%
fp=1%
8000
6000
4000
2000
0
20K 200K 500K
1000K
# Forwarding Table Entries (N)
2000K
Figure 2.12: Comparison of hash table and Bloom filters (T = 10, kmax = 8)
(3) BUFFALO switch with fixed memory size scales well with the growth of forwarding
table size. For example, as shown in Figure 2.11, if a switch has a 1MB fast memory, as the
forwarding table grows from 20K to 1000K entries, the false-positive rate grows from 10−9 to 5%.
Since packets experiencing false positives are handled in fast memory, BUFFALO scales well with
the growth of forwarding table size.
(4) BUFFALO reduces fast memory requirement by at least 65% compared with hash
tables at the expense of a false-positive rate of 0.1%. We assume a perfect hash table that
has no collision. Each entry needs to store the MAC address (48 bits) and an index of the next hop
(log(T ) bits). Therefore the size of a hash table for an N-entry forwarding table is (log(T ) + 48)N
bits. Figure 2.12 shows that BUFFALO can reduce fast memory requirements by 65% compared
with hash tables for the same number of FIB entries at the expense of a false-positive rate of
0.1%. With the increase of forwarding table size, BUFFALO can save more memory. However
48
in practice, handling collisions in hash tables requires much more memory space and affects the
throughput. In contrast, BUFFALO can handle false positives without any memory overhead.
Moreover, the packet forwarding performance of BUFFALO is independent of the workload.
2.6
Handling Routing Changes
In this section, we first describe the use of CBFs in slow memory to keep track of changes in the
forwarding table. We then discuss how to update the BF from the CBF and how to change the
size of the BF without reconstructing the CBF.
2.6.1
Update BF Based on CBF
In a switch, the control plane maintains the RIB (Routing Information Base) and updates the FIB
(Forwarding Information Base) in the data plane. When FIB updates are received, the Bloom
filters should be updated accordingly. We use CBFs in slow memory to assist the update of Bloom
filters. We implement a group of T CBFs, each containing the addresses associated with one
next hop. To add a new route of address addr with next hop h, we will insert addr to CBF (h).
Similarly, to delete a route, we remove addr in CBF (h). The insertion and deletion operations
on the CBF are described in Section 2.2. Since CBFs are maintained in slow memory, we set
the sizes of CBFs large enough, so that even when the number of addresses in one CBF increases
significantly due to routing changes, the false-positive rates on CBFs are kept low.
After the CBF (h) is updated, we update the corresponding BF (h) based on the new CBF (h).
We only need to modify a few BFs that are affected by the routing changes without interrupting
the packet forwarding with the rest BFs. To minimize the interruption of packet forwarding with
the modified BFs, we implement a pointer for each BF in SRAM. We first generate new snapshots
of BFs with CBFs and then change the BF pointers to the new snapshots. The extra fast memory
for snapshots is small because we only need to modify a few BFs at a time.
If the CBF and BF have the same number of positions, we can easily update the BF by checking
if each position in the CBF is 0 or not. The update from CBF to BF becomes more challenging
when we have to dynamically adjust the size of the BF to reduce the overall false-positive rate.
49
BF*
1
(2m bits)
2
...
m
...
...
2m
... ...
CBF 1
(S bits)
2
...
m m+1 m+2 ...
2m
...
... ...
3m ...
... ...
BF
(m bits)
1
2
...
4m ...
S
... ...
m
Figure 2.13: Adjust BF size from m to 2m based on CBF
2.6.2
Adjust BF Size Without Reconstructing CBF
When the forwarding table changes over time, the number of addresses in the BF changes, so the
size of the BF and the number of hash functions to achieve the optimal false-positive rate also
change. We leverage the nice property that to halve the size of a Bloom filter, we just OR the first
and second halves together [20]. In general, the same trick applies to reducing the size of a Bloom
filter by a constant c. This works well in reducing the BF size when the number of addresses in
the BF decreases. However, when the number of addresses increases, it is hard to expand the BF.
Fortunately, we maintain a large, fixed size CBF in the slow memory. we can dynamically
increase or decrease the size of the BF by mapping multiple positions in the CBF to one position
in the BF. For example in Figure 2.13, we can easily expand the BF with size m to BF ∗ with size
2m by collapsing the same CBF.
To minimize the overall false-positive rate under routing changes, we monitor the number of
addresses in each CBF, and periodically reconstruct BFs to be of the optimal sizes and number
of hash functions. Since resizing a BF based on a CBF requires the BF and CBF to use the same
number of hash functions. We need to adjust the number of hash functions in the CBF before
resizing the BF. The procedure of reconstructing a BF with an optimal size from the corresponding
CBF is described in three steps:
Step 1: Calculate the optimal BF size and the number of hash functions. Solving the optimization
problem in Section 2.5, we first get the optimal size of each BF and denote it by m∗ . Then we
50
round m∗ to m′ , which is a factor of S,
m′ = S/c, where c = ⌈S/m∗ ⌉.
Finally we calculate the optimal number of hash functions to minimize false positives with size
m′ and the number of addresses n in the BF, which is m′ ln 2/n based on standard Bloom filter
analysis [20]. We also need to bound the number of hash functions by kmax . Thus the number of
hash functions is k ′ = min(kmax , m′ ln 2/n).
Step 2: If k 6= k ′ , change the number of hash functions in the CBF from k to k ′ .
The number
of hash functions does not always change because routing changes are sometimes not significant
and we have the kmax bound. When we must change k, there are two ways with either more
computation or more space: (i) If k ′ > k, we obtain all the addresses currently in the forwarding
table from the control plane, calculate the hash values with the k ′ −k new hash functions on all the
addresses currently in the BF, and update the CBF by incrementing the counters in corresponding
positions. If k ′ < k, we also calculate k − k ′ hash values, and decrementing the corresponding
counters. (ii) Instead of doing the calculation on the fly, we can pre-calculate the values of these
hash functions with all the elements and store them in the slow memory.
Step 3: Construct the BF of size m′ = S/c based on the CBF of size S. As shown in Figure 2.13,
the value of the BF at position x (x ∈ [1..m′ ]) is updated by c positions in CBF x, 2x, ... cx. If
all the counters in the c positions of CBF are 0, we set the position x in BF to 0; otherwise, we
set it to 1. During routing changes, the BFs can be updated based on CBFs in the same way.
2.7
Implementation and Evaluation
To verify the performance and practicality of our mechanism through a real deployment, we built
a prototype BuffaloSwitch in kernel-level Click [23]. The overall structure of our implementation
is shown in Figure 3.7. BuffaloSwitch consists of four modules:
Counting Bloom filters: The counting Bloom filter module is used to receive routing changes
from the control plane and increment/decrement the counters in the related CBFs correspondingly.
51
Bloom filters: The Bloom filter module maintains one Bloom filter for each next hop. It also
performs the packet lookup by hash calculation and checking all the Bloom filters. When it finds
out the multiple next hop candidates due to false positives, it will call the false positive handler.
Bloom filter manager: The Bloom filter manager monitors the number of addresses in each BF.
If the number of addresses in one BF changes significantly (above threshold T H), we recalculate
the optimal size of the BF and reconstruct it based on the CBF.
False positive handler:
The false positive handler module is responsible for selecting a next
hop for the packets that experience false positives.
To evaluate our prototype, we need a forwarding table and real packet traces. We map the
Lawrence Berkeley National Lab Campus network traces [39] to the campus network topology [36]
as described in Section 2.4.3. We then calculate shortest paths in the network and construct the
forwarding table accordingly. The forwarding table consists of 200K entries.
We run BuffaloSwitch on a 3.0 GHz 64-bit Intel Xeon machine with a 8 KB L1 and 2 MB L2
data cache. The main memory is a 2 GB 400 Mhz DDR2 RAM. We take the fast memory size
M as 1.5MB to make sure Bloom filters fit in the L2 cache. The Bloom filter manager optimizes
sizes of Bloom filters given the forwarding table and M . To avoid the potential bottleneck at the
Ethernet interfaces, we run the Click packet generator on the same machine with BuffaloSwitch.
We send the packet with constant rate and measure the peak forwarding rate of BuffaloSwitch.
The packet size is set as 64 bytes, which is the minimum Ethernet packet size, so that the packet
payload does not pollute the cache much. For comparison, we also run EtherSwitch — a standard
Click element which performs Ethernet packet forwarding using hash tables.
Our experiment shows that BuffaloSwitch achieves a peak forwarding rate of 365 Kpps, 10%
faster than EtherSwitch which has 330 Kpps peak forwarding rate. This is because all the Bloom
filters in BuffaloSwitch fit in the L2 cache, but the hash table in EtherSwitch does not and thus
takes longer time to access memory. The forwarding rate with BuffaloSwitch can be further
improved by parallelizing the hash calculations on multiple cores.
To measure the performance of BuffaloSwitch under routing changes, we generate a group of
routing updates which randomly change FIB entries and replay these updates. It takes 10.7 µsec
for BuffaloSwitch to update the Bloom filters for one route change. Under significant routing
changes, it takes an additional 0.47 seconds to adjust the Bloom filter sizes based on counting
52
Bloom filters. This is because CBFs are very large and takes longer time to scan through them.
However, it is much faster than recalculating hash functions for all FIB entries to reconstruct
Bloom filters.
2.8
Extensions to BUFFALO
In this section we discuss the extensions of BUFFALO to support ECMP, VLAN, broadcast and
multicast packets, and backup routes.
Supporting ECMP: In shortest-path routing protocols like OSPF and IS-IS, ECMP (EqualCost Multi-Path) is used to split traffic among shortest paths with equal cost. When a destination
address has multiple shortest paths, the switch inserts the destination address into the Bloom
filter of each of the next hops. Since packets with this address match multiple next hops, the
BUFFALO false-positive handler will randomly choose one next hop from them, achieving even
splitting among these equal-cost multiple paths.
Supporting virtual LANs: VLAN is used in Ethernet to allow administrators to group multiple
hosts into a single broadcast domain. A switch port can be configured with one or more VLANs.
We can no longer use just a single Bloom filter for each port because due to false positives a
packet in VLAN A may be sent to a switch which does not know how to reach VLAN A and thus
get dropped. To support VLANs in BUFFALO, we use one Bloom filter for each (VLAN, next
hop) pair. For a packet lookup, we simply check those Bloom filters that have the same VLAN
as the packet. However, this does not scale well with a large number of VLANs in the network.
For future architectures that have simpler network configuration and management methods rather
than VLAN, we do not have this problem.
Broadcast and multicast: In this chapter, we have focused on packet forwarding for unicast
traffic. To support Ethernet broadcast, the switch can identify the broadcast MAC address and
forward broadcast packets directly without checking the Bloom filters. Supporting multicast in
the layer-2 network is more complex. One way is to broadcast all the multicast packets and let the
NIC on the hosts decide whether to accept or drop the packets. Another way is to allow switches
to check whether the destination IP address of the packet is a multicast-group packet, and leverage
IP multicast solutions such as storing the multicast forwarding information in packets [42, 43].
53
Fast failover to backup routes: When a significant failure happens such as one of the switch’s
own links fail, many routes change in a short time. In order to quickly recover from significant
failures, we provide an optional optimization of BUFFALO. The control plane calculates backup
routes for every link/node failure case in advance, and notifies the data plane about the failure
event. In addition to the original routes stored in CBF (h) (h ∈ [1..T ]), we pre-calculate backup
counting Bloom filters CBF (h1 , h2 ) (for all h1 ∈ [1..T ], h2 ∈ [1..T ]), which denotes the set of
addresses that are originally forwarded to next hop h1 , but if h1 is not accessible, they should
be forwarded to next hop h2 . When the failure happens and thus h1 is not accessible, we simply
need to update the Bloom filters based on the original Bloom filters and backup counting Bloom
filters. For example, we update BF (h2 ) based on the old BF (h2 ) and CBF (h1 , h2 ). This is fast
because merging two Bloom filters is just OR operations.
2.9
Related Work
Bloom filters have been used for IP packet forwarding, and particularly the longest-prefix match
operation [22]. The authors use Bloom filters to determine the length of the longest matching
prefix for an address and then perform a direct lookup in a large hash table in slow memory. The
authors in [44] design a d-left scheme using d hash functions for IP lookups. To perform an IP
lookup, they still need to access the slow memory at least d times. The paper [45] stores Bloom
filter in the fast memory, and stores the values in a linked structure in the slow memory such
that the value can be accessed via one access on the slow memory most of the times. Different
from these works, we focus on flat addresses and perform the entire lookup in fast memory at
the expense of a few false positives. We also propose a simple scheme that handles false positives
within fast memory, and proves its reachability and stretch bound.
Bloom filters have also been used in resource routing [20, 21], which applies Bloom filters to
probabilistic algorithms for locating resources. Our “one Bloom filter per next hop” scheme is
similar to their general idea of using one Bloom filter to store the list of resources that can be
accessed through each neighboring node. To keep up with link speed in packet forwarding with a
strict fast memory size constraint, we dynamically tune the optimal size and the number of hash
functions of Bloom filters by keeping large fixed-size counting Bloom filters in slow memory. We
54
also handle false positives without any memory overhead. BUFFALO is also similar to Bloomier
filters [46] in that we both use a group of Bloom filters, one for each value of a function that maps
the key to the value. However, Bloomier filters only work for a static element set.
Bloom filters are also been used for multicast forwarding. LIPSIN [43] uses Bloom filters to
encode the multicast forwarding information in packets. False positives in Bloom filters may cause
loops in its design. LIPSIN caches packets that may experience loops and send the packets to a
different link when a loop is detected. However, they do not show how well they can prevent loops
and the cache size they need. In contrast, our loop prevention mechanism is simple and effective,
and does not have any memory overhead.
To handle routing changes, the paper [45] store counting Bloom filters (CBFs) in fast memory,
which uses more memory space than the Bloom filters (BFs). Both our paper and the paper [22]
and leverage the fact that routing changes happen on a much longer time scale than address
lookup, and thus store only the BF in fast memory, and use the CBF in slow memory to handle
routing changes. The idea of maintaining both the CBF and BF is similar to the work in [30],
which uses BFs for sharing caches among Web proxies. Since cache contents change frequently,
the authors suggest that caches use a CBF to track their own cache contents, and broadcast the
corresponding BF to the other proxies. The CBF is used to avoid the cost of reconstructing the
BF from scratch when an update is sent; the BF rather than the CBF is sent to the other proxies
to reduce the size of broadcast messages. Different from previous work, we dynamically adjust
the size of the BF without reconstructing the corresponding CBF, which may be useful for other
Bloom filter applications.
Our idea of using one Bloom filter per port is similar to SPSwitch [47] which forward packets
on flat identifiers in content-centric networks. Our workshop paper [48] applies Bloom filters for
enterprise edge routers by leveraging the fact that edge routers typically have a small number of
next hops. However, it does not deal with loops caused by false positives. The paper uses one
Bloom filter for each (next hop, prefix length) pair and discusses its effect on false positives. It
also proposes the idea of using CBF to assist the BF update and resizing. We consider flat address
lookup in SPAF networks in this paper, and thus eliminate the effect of various prefix lengths.
We also propose a mechanism to handle false positives in the network without extra memory. We
perform extensive analysis, simulation, and prototype implementation to evaluate our scheme.
55
2.10
Summary
With recent advances in improving control plane scalability, it is possible now to build large
layer-2 networks. The scalability problem in the data plane becomes challenging with increasing
forwarding table sizes and link speed. Leveraging flat addresses and shortest path routing in SPAF
networks, we proposed BUFFALO, a practical switch design based on Bloom filters. BUFFALO
performs the entire packet forwarding in small, fast memory including those packets experiencing
false positives. BUFFALO gracefully degrades under higher memory loads by gradually increasing
stretch rather than crashing or resorting to excessive flooding. Our analysis, simulation and
prototype demonstrate that BUFFALO works well in reducing memory cost and improving the
scalability of packet forwarding in enterprise and data center networks.
56
Chapter 3
DIFANE: Scaling Flexible Policy
Support on Switches
This chapter focuses on the scalability challenges of supporting flexible policies. Ideally, enterprise
administrators could specify fine-grain policies that drive how the underlying switches forward,
drop, and measure traffic. However, existing techniques for flow-based networking rely too heavily
on centralized controller software that installs rules reactively, based on the first packet of each
flow. In this chapter, we propose DIFANE, a scalable and efficient solution for enforcing flexible
policies at switches.
DIFANE keeps all traffic in the data plane by selectively directing packets through intermediate
switches that store the necessary rules. DIFANE relegates the controller to the simpler task of
partitioning these rules over the switches. DIFANE can be readily implemented with commodity
switch hardware, since all data-plane functions can be expressed in terms of wildcard rules that
perform simple actions on matching packets. Experiments with our prototype on Click-based
OpenFlow switches show that DIFANE scales to larger networks with richer policies.
3.1
Introduction
The emergence of flow-based switches [14, 15] has enabled enterprise networks that support flexible
policies. These switches perform simple actions, such as dropping or forwarding packets, based
57
on rules that match on bits in the packet header. Installing all of the rules in advance is not
attractive, because the rules change over time (due to policy changes and host mobility) and the
switches have relatively limited high-speed memory (such as TCAMs). Instead, current solutions
rely on directing the first packet of each “microflow” to a centralized controller that reactively
installs the appropriate rules in the switches [13, 10]. In this thesis, we argue that the switches
themselves should collectively perform this function, both to avoid a bottleneck at the controller
and to keep all traffic in the data plane for better performance and scalability.
3.1.1
DIFANE: Doing It Fast ANd Easy
Our key challenge, then, is to determine the appropriate “division of labor” between the controller
and the underlying switches, to support high-level policies in a scalable way. Previous work has
demonstrated that a logically-centralized controller can track changes in user locations/addresses
and compute rules the switches can apply to enforce a high-level policy [10, 11, 12]. For example, an access-control policy may deny the engineering group access to the human-resources
database, leading to low-level rules based on the MAC or IP addresses of the current members
of the engineering team, the IP addresses of the HR servers, and the TCP port number of the
database service. Similar policies could direct packets on customized paths, or collect detailed
traffic statistics. The controller can generate the appropriate switch rules simply by substituting
high-level names with network addresses. The policies are represented with 30K - 8M rules in the
four different networks we studied. This separation of concerns between rules (in the switches)
and policies (in the controller) is the basis of several promising new approaches to network management [13, 49, 50, 51, 52].
While we agree the controller should generate the rules, we do not think the controller should
(or needs to) be involved in the real-time handling of data packets. Our DIFANE (DIstributed Flow
Architecture for Networked Enterprises) architecture, illustrated in Figure 3.1, has the following
two main ideas:
• The controller distributes the rules across (a subset of) the switches, called “authority
switches,” to scale to large topologies with many rules. The controller runs a partitioning
algorithm that divides the rules evenly and minimizes fragmentation of the rules across
multiple authority switches.
58
Controller
Distribute
partition
information
Install
authority
rules
e
First
Packet
h
Cac
Ingress
Switch
Subsequent
Packets
s
rule
Authority
Switch
t
irec
d
e
R
...
Authority
Switch
Forward
Egress
Switch
Hit cached rules and forward
Figure 3.1: DIFANE flow management architecture. (Dashed lines are control messages. Straight
lines are data traffic.)
• The switches handle all packets in the data plane (i.e., TCAM), diverting packets through
authority switches as needed to access the appropriate rules. The “rules” for diverting
packets are themselves naturally expressed as TCAM entries.
All data-plane functionality in DIFANE is expressible in terms of wildcard rules with simple
actions, exactly the capabilities of commodity flow switches. As such, a DIFANE implementation
requires only modifications to the control-plane software of the authority switches, and no dataplane changes in any of the switches. Experiments with our prototype, built on top of the Clickbased OpenFlow switch [53], illustrate that distributed rule management in the data plane provides
lower delay, higher throughput, and better scalability than directing packets through a separate
controller.
Section 3.2 presents our main design decisions, followed by our DIFANE architecture in Section 3.3. Next, Section 3.4 describes how we handle network dynamics, and Section 3.5 presents
our algorithms for caching and partitioning wildcard rules. Section 3.6 presents our switch implementation, followed by the performance evaluation in Section 4.5. Section 3.8 describes different
deployment scenarios of DIFANE. The chapter concludes in Section 4.9.
59
3.1.2
Comparison to Related Work
Recent work shows how to support policy-based management using flow switches [14, 15] and
centralized controllers [10, 11, 12, 13]. The most closely related work is the Ethane controller
that reactively installs flow-level rules based on the first packet of each TCP/UDP flow [13]. The
Ethane controller can be duplicated [13] or distributed [54] to improve its performance. In contrast,
DIFANE distributes wildcard rules amongst the switches, and handles all data packets in the data
plane. Other recent work capitalizes on OpenFlow to rethink network management in enterprises
and data centers [49, 50, 51, 52]; these systems could easily run as applications on top of DIFANE.
These research efforts, and ours, depart from traditional enterprise designs that use IP routers
to interconnect smaller layer-two subnets, and rely heavily on inflexible mechanisms like VLANs.
Today, network operators must configure Virtual LANs (VLANs) to scope broadcast traffic and
direct traffic on longer paths through routers that perform access control on IP and TCP/UDP
header fields. In addition, an individual MAC address or wall jack is typically associated with
just one VLAN, making it difficult to support more fine-grained policies that treat different traffic
from the same user or office differently.
Other research designs more scalable networks by selectively directing traffic through intermediate nodes to reduce routing-table size [5, 55, 56]. However, hash-based redirection techniques [5, 55], while useful for flat keys like IP or MAC addresses, are not appropriate for look-ups
on rules with wildcards in arbitrary bit positions. ViAggre [56] subdivides the IP prefix space,
and forces some traffic to always traverse an intermediate node, and does not consider on-demand
cache or multi-dimensional, overlapping rules.
3.2
DIFANE Design Decisions
On the surface, the simplest approach to flow-based management is to install all of the low-level
rules in the switches in advance. However, preinstalling the rules does not scale well in networks
with mobile hosts, since the same rules would need to be installed in multiple locations (e.g., any
place a user might plug in his laptop). In addition, the controller would need to update many
switches whenever rules change. Even in the absence of mobile devices, a network with many
rules might not have enough table space in the switches to store all the rules, particularly as the
60
network grows or its policies become more complex. Instead, the system should install rules on
demand [13].
To build a flow-processing system that has high performance and scales to large networks,
DIFANE makes four high-level design decisions that reduce the overhead of handling cache misses
and allow the system to scale to a large number of hosts, rules, and switches.
3.2.1
Reducing Overhead of Cache Misses
Reactively caching rules in the switches could easily cause problems such as packet delay, larger
buffers, and switch complexity when cache misses happen. More importantly, misbehaving hosts
could easily trigger excessive cache misses simply by scanning a wide range of addresses or port
numbers — overloading TCAM and introducing extra packet-processing overhead. DIFANE handles “miss” packets efficiently by keeping them in the data plane and reduces the number of “miss”
packets by caching wildcard rules.
Process all packets in the data plane: Some flow management architectures direct the first
packet (or first packet header) of each microflow to the controller and have the switch buffer the
packet awaiting further instructions [13].1 In a network with many short flows , a controller that
handles “miss” packets can easily become a bottleneck. In addition, UDP flows introduce extra
overhead, since multiple (potentially large) packets in the same flow may be in flight (and need to
visit the controller) at the same time. The switches need a more complex and expensive buffering
mechanism, because they must temporarily store the “miss” packets while continuing to serve
other traffic, and then retrieve them upon receiving the rule. Instead, DIFANE makes it cheap
and easy for switches to forward all data packets in the data plane (i.e., hardware), by directing
“miss” packets through an intermediate switch. Transferring packets in the data plane through a
slightly longer path is much faster than handling packets in the control plane.
Efficient rule caching with wildcards: Caching a separate low-level rule for each TCP or UDP
microflow [13], while conceptually simple, has several disadvantages compared to wildcard rules.
For example, a wildcard rule that matches on all destinations in the 123.132.8.0/22 subnet would
require up to 1024 microflow rules. In addition to consuming more data-plane memory on the
1 Another solution to handle cache miss is for the switch to encapsulate and forward the entire packet to the
controller. This is also problematic because it significantly increases controller load.
61
switches, fine-grained rules require special handling for more packets (i.e., the first packet of each
microflow), leading to longer delays and higher overhead, and more vulnerability to misbehaving
hosts. Instead, DIFANE supports wildcard rules, to have fewer rules (and fewer cache “misses”)
and capitalize on TCAMs in the switches. Caching wildcard rules introduces several interesting
technical challenges that we address in our design and implementation.
3.2.2
Scaling to Large Networks and Many Rules
To scale to large networks with richer policies, DIFANE divides the rules across the switches
and handles them in a distributed fashion. We also keep consistent topology information among
switches by leveraging link-state protocols.
Partition and distribute the flow rules: Replicating the controller seems like a natural way
to scale the system and avoid a single point of failure. However, this requires each controller
to maintain all the rules, and coordinate with the other replicas to maintain consistency when
rules change. (Rules may change relatively often, not only because the policy changes, but also
because host mobility triggers changes in the mapping of policies to rules.) Instead, we partition
the space of rules to reduce the number of rules each component must handle and enable simpler
techniques for maintaining consistency. As such, DIFANE has one primary controller (perhaps
with backups) that manages policies, computes the corresponding rules, and divides these rules
across the switches; each switch handles a portion of the rule space and receives updates only
when those rules change. That is, while the switches reactively cache rules in response to the data
traffic, the DIFANE controller proactively partitions the rules across different switches.
Consistent topology information distribution with the link-state protocol: Flow-based
management relies on the switches having a way to communicate with the controller and adapt
to topology changes. Relying on rules for this communication introduces circularity, where the
controller cannot communicate with the switches until the appropriate rules have been installed.
Rather than bootstrapping communication by having the switches construct a spanning tree [13],
we advocate running a link-state protocol amongst the switches. Link-state routing enables the
switches to compute paths and learn about topology changes and host location changes without
involving the controller, reducing overhead and also removing the controller from the critical path
62
of failure recovery. In addition, link-state routing scales to large networks, enables switches to
direct packets through intermediate nodes, and reacts quickly to switch failure [5]. As such,
DIFANE runs a link-state routing protocol amongst the switches, while also supporting flow rules
that allow customized forwarding of traffic between end hosts. The controller also participates in
link-state routing to reach the switches and learn of network topology changes.2
3.3
DIFANE Architecture
The DIFANE architecture consists of a controller that generates the rules and allocates them to
the authority switches, as shown in Figure 3.1. Authority switches can be a subset of existing
switches in the network (including ingress/egress switches), or dedicated switches that have larger
memory and processing capability.
Upon receiving traffic that does not match the cached rules, the ingress switch encapsulates
and redirects the packet to the appropriate authority switch based on the partition information.
The authority switch handles the packet in the data plane and sends feedback to the ingress
switch to cache the relevant rule(s) locally. Subsequent packets matching the cached rules can be
encapsulated and forwarded directly to the egress switch.
In this section, we first discuss how the controller partitions the rules and distributes the
authority and partition rules to the switches. Next, we describe how a switch directs packets
through the authority switch and caches the necessary rules, using link-state routing to compute
the path to the authority switch. Finally, we show that the data-plane functionality of DIFANE
can be easily implemented on today’s flow-based switches using wildcard rules.
3.3.1
Rule Partition and Allocation
As shown in Figure 3.2, we use the controller to pre-compute the low-level rules, generate partition
rules that describe which low-level rules are stored in which authority switches, and then distribute
the partition rules to all the switches. The partition rules are represented by coarse-grained
wildcard rules on the switches.
2 The links between the controller and switches are set with high link-weights so that traffic between switches do
not go through the controller.
63
Controller
Policies
Map
Rules
Partition
Authority rules
for Switch A
... ...
Partition
rules
Authority rules
for Switch D
Figure 3.2: Rule operations in the controller.
Precompute low-level rules:
The controller pre-computes the low-level rules based on the
high-level policies by simply substituting high-level names with network addresses. Since low-level
rules are pre-computed and installed in the TCAM of switches, we can always process packets in
the fast path. Most kinds of policies can be translated to the low-level rules in advance because
the controller knows the addresses of the hosts when the hosts first connect to the ingress switch,
and thus can substitute the high-level names with addresses. However, precomputation is not
an effective solution for policies (like traffic engineering) that depend on dynamically changing
network state.
Use partitioning to subdivide the space of all rules:
Hashing is an appealing way to
subdivide the rules and direct packets to the appropriate authority switch. While useful for flat
keys like an IP or MAC address [5, 55], hashing is not effective when the keys can have wildcards
in arbitrary bit positions. In particular, packets matching the same wildcard rule would have
different hash values, leading them to different authority switches; as a result, multiple authority
switches would need to store the same wildcard rule. Instead of relying on hashing, DIFANE
partitions the rule space, and assigns each portion of rule space to one or more authority switches.
Each authority switch stores the rules falling in its part of the partition.
64
F1
F2
R1 A
R2
R6
R4
C D
B
R5
R3
R7
(a) Low-level rules and the partition
Type
Cache
rules
Authority
rules
Priority
210
209
...
F1
00**
1110
...
F2
111*
11**
...
110
00**
001*
109
0001
0***
15
14
13
5
...
0***
0***
11**
0***
...
000*
1***
****
000*
...
Partition
rules
Action
Encap, forward to B
Drop
... ...
Encap, forward to D,
trigger ctrl. plane func.
Drop,
trigger ctrl. plane func.
Encap, redirect to B
Encap, redirect to C
Encap, redirect to D
Encap, redirect to B ′
... ...
Timeout
10 sec
10 sec
...
Note
R3
R7
...
∞
R1
∞
R2
∞
∞
∞
∞
...
Primary
Backup
...
(b) Wildcard rules in the TCAM of Switch A
Figure 3.3: Wildcard rules in DIFANE (A-D are authority switches).
Run the partitioning algorithm on the controller: Running the partitioning algorithm on
the switches themselves would introduce a large overhead, because they would need to learn the
rules from the controller, run the partitioning algorithm, and distribute the results. In contrast,
the controller is a more natural place to run the partitioning algorithm. The controller is already
responsible for translating policies into rules and can easily run the partitioning algorithm periodically, as the distribution of low-level rules changes. We expect the controller would recompute the
partition relatively infrequently, as most rule changes would not require rebalancing the division of
rule space. Section 3.4 discusses how DIFANE handles changes to rules with minimal interruption
to the data traffic.
65
Represent the partition as a small collection of partition rules: Low-level rules are defined
as actions on a flow space. The flow space usually has seven dimensions (source/destination IP
addresses, MAC addresses, ports, the protocol) or more. Figure 3.3(a) shows a two-dimensional
flow space (F1 , F2 ) and the rules on it. The bit range of each field is from 0 to 15 (i.e., F1 = F2 =
[0..15]). For example, F1 , F2 can be viewed as the source/destination fields of a packet respectively.
Rule R2 denotes that all packets which are from source 1 (F1 = 1) and forwarded to a destination
in [0..7] (F2 = [0..7]) should be dropped.
The controller partitions the flow space into M ranges, and assigns each range to an authority
switch. The resulting partition can be expressed concisely as a small number of coarse-grain
partition rules, where M is proportional to the number of authority switches rather than the
number of low-level rules. For example, in Figure 3.3(a), the flow space is partitioned into four
parts by the straight lines, which are represented by the partition rules in Figure 3.3(b). Section 3.5
discusses how the controller computes a partition of overlapping wildcard rules that reduces TCAM
usage.
Duplicate authority rules to reduce stretch and failure-recovery time: The first packet
covered by an authority rule traverses a longer path through an authority switch. To reduce the
extra distance the traffic must travel (i.e., “stretch”), the controller can assign each of the M
ranges to multiple authority switches. For example, if each range is handled by two authority
switches, the controller can generate two partition rules for each range, and assign each switch
the rule that would minimize stretch. That way, on a cache miss,3 a switch directs packets to the
closest authority switch responsible for that range of rules. The placement of multiple authority
switches is discussed in Section 3.5.
Assigning multiple authority switches to the same range can also reduce failure-recovery time.
By pushing backup partition rules to every switch, a switch can quickly fail over to the backup
authority switch when the primary one fails (see Section 3.4). This requires each switch to store
more partition rules (e.g., 2M instead of M ), in exchange for faster failure recovery. For example,
in Figure 3.3(b), switch A has a primary partition rule that directs packets to B and a backup
one that directs packets to B ′ .
3 In DIFANE, every packet matches some rule in the switch. “Cache miss” in DIFANE means a packet does not
match any cache rules, but matches a partition rule instead.
66
3.3.2
Packet Redirection and Rule Caching
The authority switch stores the authority rules. The ingress switch encapsulates the first packet
covered by an authority switch and redirects it to the authority switch.4 The authority switch
processes the packet and also caches rules in the ingress switch so that the following packets can
be processed at the ingress switch.
Packet redirection: In the ingress switch, the first packet of a wildcard flow matches a partition
rule. The partition rule indicates which authority switch maintains the authority rules that are
related to the packet. For example, in Figure 3.3 a packet with (F1 = 9, F2 = 7) hits the primary
partition rule for authority switch B and should be redirected to B. The ingress switch encapsulates the packet and forwards it to the authority switch. The authority switch decapsulates the
packet, processes it, re-encapsulates it, and forwards it to the egress switch.
Rule Caching:
To avoid redirecting all the data traffic to the authority switch, the authority
switch caches the rules in the ingress switch.5 Packets that match the cache rules are encapsulated
and forwarded directly to the egress switch (e.g., packets matching R3 in Figure 3.3(b) are encapsulated and forwarded to D). In DIFANE “miss” packets do not wait for rule caching, because
they are sent through the authority switch rather than buffered at the ingress switch. Therefore,
we can run a simple caching function in the control plane of the authority switch to generate
and install cache rules in the ingress switch. The caching function is triggered whenever a packet
matches the authority rules in the authority switch. The cache rule has an idle timeout so that it
can be removed by the switch automatically due to inactivity.
3.3.3
Implement DIFANE with Wildcard Rules
All the data plane functions required in DIFANE can be expressed with three sets of wildcard
rules of various granularity with simple actions, as shown in Figure 3.3(b).
Cache rules: The ingress switches cache rules so that most of the data traffic hits in the cache
and is processed by the ingress switch. The cache rules are installed by the authority switches in
the network.
4 With encapsulation, the authority switch knows the address of the ingress switch from the packet header and
sends the cache rules to the ingress switch.
5 Here we assume that we cache flow rules only at the ingress switch. We discuss the design choices of where to
cache flow rules in our Section 4.6.
67
Authority rules: Authority rules are only stored in authority switches. The controller installs
and updates the authority rules for all the authority switches. When a packet matches an authority
rule, it triggers a control-plane function to install rules in the ingress switch.
Partition rules:
The controller installs partition rules in each switch. The partition rules are
a set of coarse-grained rules. With these partition rules, we ensure a packet will always match at
least one rule in the switch and thus always stay in the data plane.
The three sets of rules can be easily expressed as a single list of wildcard rules with different
priorities. Priorities are naturally supported by TCAM. If a packet matches multiple rules, the
packet is processed based on the rule that has the highest priority. The cached rules have highest
priority because packets matching cache rules do not need to be directed to authority switches.
In authority switches, authority rules have higher priority than partition rules, because packets
matching authority rules should be processed based on these rules. The primary partition rules
have higher priority than backup partition rules.
Since all functionalities in DIFANE are expressed with wildcard rules, DIFANE does not require
any data-plane modifications to the switches and only needs minor software extensions in the
control plane of the authority switches.
3.4
Handling Network Dynamics
In this section, we describe how DIFANE handles dynamics in different parts of the network:
To handle rule changes at the controller, we need to update the authority rules in the authority
switches and occasionally repartition the rules. To handle topology changes at the switches, we
leverage link-state routing and focus on reducing the interruptions of authority switch failure
and recovery. To handle host mobility, we dynamically update the rules for the host, and use
redirection to handle changes in the routing rules.
3.4.1
Changes to the Rules
The rules change when administrators modify the policies, or network events (e.g., topology
changes) affect the mapping between policies and rules. The related authority rules, cache rules,
and partition rules in the switches should be modified correspondingly.
68
Authority rules are modified by the controller directly:
The controller changes the
authority rules in the related authority switches. The controller can easily identify the related
authority switches based on the partition it generates.
Cache rules expire automatically:
Cached copies of the old rules may still exist in some
ingress switches. These cache rules will expire after the timeout time. For critical changes (e.g.,
preventing DoS attacks), the authority switches can get the list of all the ingress switches from
the link-state routing and send them a message to evict the related TCAM entries.
Partition rules are recomputed occasionally:
When the rules change, the number of au-
thority rules in the authority switches may become unbalanced. If the difference in the number of
rules among the authority switches exceeds a threshold, the controller recomputes the partition of
the flow space. Once the new partition rules are generated, the controller notifies the switches of
the new partition rules, and updates the authority rules in the authority switches.
The controller cannot update all the switches at exactly the same time, so the switches may
not have a consistent view of the partition during the update, which may cause transient loops
and packet loss in the network. To avoid packet loss, the controller simply updates the switches
in a specific order. Assume the controller decides to move some authority rules from authority
switch A to B. The controller first sends the authority rules to authority switch B, before sending
the new partition rules for A and B to all the switches in the network. Meanwhile, switches can
redirect the packets to either A or B for the authority rules. Finally, the controller deletes the
authority rules in switch A. In this way, we can prevent packet loss during the change. The same
staged update mechanism also applies to the partition change among multiple authority switches.
3.4.2
Topology Dynamics
Link-state routing enables the switches to learn about topology changes and adapt routing quickly.
When authority switches fail or recover, DIFANE adapts the rules to reduce traffic interruption.
Authority switch failure:
When an authority switch fails, packets directed through it are
dropped. To minimize packet loss, we must react quickly to authority switch failures. We design
a distributed authority switch takeover mechanism. As discussed in Section 3.3.1, the controller
assigns the same group of authority rules to multiple authority switches to reduce stretch and
69
failure-recovery time. Each ingress switch has primary partition rules directing traffic to their
closest authority switch and backup partition rules with lower priority that directing traffic to
another authority switch when the primary one fails.
The link-state routing protocol propagates a message about the switch failure throughout the
network. Upon receiving this message, the switches invalidate their partition rules that direct
traffic to the failed authority switch. As a result, the backup partition rule takes effect and
automatically directs packets through the backup authority switch. For the switches that have
not yet received the failure information, the packets may get sent towards the failed authority
switch, but will finally get dropped by a switch who has updated its switch forwarding table.6
Authority switch addition/recovery:
We use the controller to handle switches joining in
the network, because it does not require fast reaction compared to authority switch failures. To
minimize the change of the partition rules and authority rules, the controller randomly picks an
authority switch, divides its flow range evenly into two parts. The controller then moves one part
of the flow range to the new switch, and installs the authority rules in the new switch. Finally the
controller updates the partition rules correspondingly in all the switches.
3.4.3
Host Mobility
In DIFANE, when a host moves, its MAC and perhaps IP address stays the same. The rules in
the controller are defined based on these identifiers, and thus do not change as hosts move. As a
result, the partition rules and the authority rules also stay the same.7 Therefore we only need to
consider the changes of cache rules.
Installing rules at the new ingress switch on demand:
When a host connects to a new
ingress switch, the switch may not have the cache rules for the packets sent by the hosts. So the
packets are redirected to the responsible authority switch. The authority switch then caches rules
at the new ingress switch.
Removing rules from old ingress switch by timeout: Today’s flow-based switches usually
have a timeout for removing the inactive rules. Since the host’s old ingress switch no longer
6 If the switch can decapsulate the packet and encapsulate it with the backup authority switch as the destination,
we can avoid such packet loss.
7 In some enterprises, a host changes its identifier when it moves. The rules also change correspondingly. We can
use the techniques in Section 3.4.1 to handle the rule changes.
70
receives packets from the moved host, the cache rules at the switch are automatically removed
once the timeout time expires.
Redirecting traffic from old ingress switch to the new one: The rules for routing packets
to the host change when the host moves. When a host connects to a new switch, the controller
gets notified through the link-state routing and constructs new routing rules that map the address
of the host to the corresponding egress switch. The new routing rules are then installed in the
authority switches.
The cached routing rules in some switches may be outdated. Suppose a host H moves from
ingress switch Sold to Snew . The controller first gets notified about the host movement. It then
installs new routing rules in the authority switch, and also installs a rule in Sold redirecting packets
to Snew . If an ingress switch A receives a packet whose destination is H, A may still send the
packet to the old egress point Sold if the cache rule has not expired. Sold then redirects packets
to Snew . After the cache rule expires in switch A, A directs the packets to the authority switch
for the correct egress point Snew and caches the new routing rule.
3.5
Handling Wildcard Rules
Most flow-management systems simply use microflow rules [13] or transform overlapping wildcard
rules into a set of non-overlapping wildcard rules. However these methods significantly increase
the number of rules in switches, as shown in our evaluation in Section 4.5. To the best of our
knowledge, there is no systematic and efficient solution for handling overlapping wildcard rules in
network-wide flow-management systems. In this section, we first propose a simple and efficient
solution for multiple authority switches to independently insert cache rules in ingress switches.
We then discuss the key ideas of partitioning overlapping wildcard rules
3.5.1
Caching Wildcard Rules
Wildcard rules complicate dynamic caching at ingress switches. In the context of access control,
for example in Figure 3.4, the packet (F1 = 7, F2 = 0) matches an “accept” rule R3 that overlaps
with “deny” rule R2 which has higher priority. Simply caching R3 is not safe. If we just cache
R3 in the ingress switch, another packet (F1 = 7, F2 = 5) could incorrectly pass the cached rule
71
Rule
R1
R2
R3
R4
F1
4
0-7
6-7
14-15
F2
0-15
5-6
0-15
0-15
Action
Accept
Drop
Accept
Accept
(a) Wildcard rules listed in the decreasing
order of priority. (R1 > R2 > R3 > R4 )
F1
F2
B1
R2
R4
R1 R3
Cut B
B2
A1
Cut A
A2
(b) Graphical view and two partition solutions.
Figure 3.4: An illustration of wildcard rules.
R3 , because the ingress switch is not aware of the rule R2 . Thus, because rules can overlap with
each other, the authority switch cannot solely cache the rule that a packet matches. This problem
exists in all the flow management systems that cache wildcard rules and therefore it is not trivial
to extend Ethane controllers [13] to support wildcards.
To address this problem, DIFANE constructs one or more new wildcard rules that cover the
largest flow range (i.e., a hypercube in a flow space) in which all packets take the same action. We
use Figure 3.4 to illustrate the solution. Although the rules overlap, which means a packet may
match multiple rules, the packet only takes the action of the rule with the highest priority. That is,
each point in the flow space has a unique action (which is denoted by the shading in each spot in
Figure 3.4(b)). As long as we cache a rule that covers packets with the same action (i.e., spots with
the same shading), we ensure that the caching preserves semantic correctness. For example, we
cannot cache rule R3 because the spots it covers have different shading. In contrast, we can safely
cache R1 because all the spots it covers has the same shading. For the packet (F1 = 7, F2 = 0), we
construct and cache a new rule: F1 = [6..7], F2 = [0..3].
The problem of constructing new wildcard rules for caching at a single switch was studied
in [57]. Our contribution lies in extending this approach to multiple authority switches, each of
72
which can independently install cache rules at ingress switches. Given such a setting, we must
prevent authority switches from installing conflicting cache rules. To guarantee this, DIFANE
ensures that the caching rules installed by different authority switches do not overlap. This is
achieved by allocating non-overlapping flow ranges to the authority switches, and only allowing
the authority switch to install caching rules in its own flow range. We later evaluate our caching
scheme in Section 4.5.
3.5.2
Partitioning Wildcard Rules
Overlapping wildcard rules also introduce challenges in partitioning. We first formulate the partition problem: The controller needs to partition rules into M parts to minimize the total number of
TCAM entries across all M authority switches with the constraint that the rules should not take
more TCAM entries than are available in the switches. There are three key ideas in the partition
algorithm:
Allocating non-overlapping flow ranges to authority switches:
As discussed in the
caching solution, we must ensure that the flow ranges of authority switches do not overlap with
each other. To achieve this goal, DIFANE first partitions the entire flow space into M flow ranges
and then stores rules in each flow range in an authority switch. For example, the “Cut A” shown
in Figure 3.4(b) partitions the flow space on field F1 into two equal flow ranges A1 and A2 . We
then assign R1 , R2 and R3 in A1 to one authority switch, and R4 to another.
DIFANE splits the rules so that each rule only belongs to one authority switch. With
the above partitioning approach, one rule may span multiple partitions. For example, “Cut B”
partitions the flow space on field F2 , which results in the rules R1 , R3 , and R4 spanning the two
flow ranges B1 and B2 . We split each rule into two independent rules by intersecting it with the
two flow ranges. For example, the two new rules generated from rule R4 are F1 = [14..15], F2 = [0..7]
→ Accept and F1 = [14..15], F2 = [8..15] → Accept. These two independent rules can then be stored
in different authority switches. Splitting rules thus avoids the overlapping of rules among authority
switches, but at the cost of increased TCAM usage.
73
To reduce TCAM usage, we prefer the cuts to align with rule boundaries. For example,
“Cut A” is better than “Cut B” because “Cut A” does not break any rules. We also observe that
cut on field F1 is better than F2 since we have more rule boundaries to choose.
Based on these observations, we design a decision-tree based partition algorithm. We first
formulate the rule partition problem as follows: Assume that there are M candidate authority
switches, each of which can store up to S TCAM entries. For a given set of N low-level rules
of K dimensions, we would like to partition the flow space into n hypercubes (n ≤ M ), because
hypercubes are easy to represent as wildcard partition rules. Each of the hypercubes is represented
by a K-tuple of ranges, [l1 ..r1 ], . . . , [lK ..rK ], and is stored in an authority switch. The optimization
objective is to minimize the total number of TCAM entries in all n authority switches. The flow
partition problem is NP-hard for K ≥ 2.8 Therefore, we instead design a heuristic algorithm for
partitioning rules.
Rule \ Field
R1
R2
R3
R4
R5
R6
R7
R8
F1
0-1
0-1
0-1
0-1
0-15
0-15
0-15
0-15
F2
14-15
14-15
8-11
8-11
0-7
14-15
14-15
0-15
F3
2
1
0-3
2
0-3
2
2
0-3
F4
0-3
2
2
3
1
1
2
0-3
F5
0
0
1
1
0
0
0
0-1
Action
accept
accept
deny
deny
accept
accept
accept
deny
(a) A group of wildcard rules
Cut on
Field 2
Root
[0,7]
R5
R8^{F2=[0,7]}
[8,11]
[12,15]
R8^{F2=[8,11]}
Cut on Field 3
[0,1]
R2
R8^{F2=[12,15]}
^{F3=[0,1]}
[2,3]
R1, R6, R7
R8^{F2=[12,15]}
^{F3=[2,3]}
(b) The decision tree for the rules
Figure 3.5: Construct decision tree for a group of rules.
8 The
proof of the NP-hardness of the partition problems is omitted due to lack of space.
74
Algorithm 1 Heuristic partition algorithm using decision tree
Initialization:
Step 1 k = 0. T0 is the tree node which represents the entire flow range.
Split the flow range:
Step 2 Incrementk. Pick up a tree node Tk to split.
Tk is a leaf node in the decision tree that contain more than S TCAM entries to represent its
hypercube Ck .
If we cannot find such a node, stop.
Step 3 Select a flow dimension i that have maximum number of unique
P components ui .
Step 4 Pick w boundaries of the unique components that minimizes ( 1≤t≤w f (Ckt ) − f (Ck ))/w.
Step 5 Put all the child node of Ti in the tree.
Step 6 Goto Step 2.
The complete algorithm is shown in Algorithm 1, which consists of two key ideas:
Use a decision tree to represent the partition: The root node of the decision tree denotes the
hypercube of the entire flow space. Similarly, each node in the decision tree denotes a hypercube
of flow range and maintains all the rules intersecting with the hypercube. We start with the root
node (Step 1). In each round of the splitting process, we pick a node in the decision tree which
has more than S authority rules, and split it into a group of child nodes, each of which a subset
flow range of its parent node (Step 2). The splitting process terminates when each leaf node has
fewer than S authority rules. In the end, the authority rules in each leaf node will be assigned to
an authority switch.
Cut based on rule boundaries:
We first choose the dimension i that has the maximum
number of unique components (i.e., non-overlapping ranges) as the dimension to split (Step 3).
This gives us a better chance to be able to split the flow range into balanced pieces. For example,
in Figure 3.5, field F2 has four unique components [0..7], [8..11], [12..13], [14..15].
The next challenge is to split the hypercube in the selected dimension. As we discussed earlier,
partitioning the flow range equally may not be the best choice. It leads to many rules that span
across multiple partitions, and hence yields more authority rules. Instead, we partition the flow
space based on the boundaries of the unique components (Step 4). Let function f (C) be the
number of required TCAM entries for hypercube C. Assume that Ck is the hypercube we want
to split in the k-th round of our algorithm. We select w boundaries of the unique components in
dimension i (b1 . . . bw ) and the resulting sub-hypercubes Ck1 . . . Ckw such that the average increase
P
of authority rules per cut is minimized: U = ( 1≤t≤w f (Ckt ) − f (Ck ))/w. We enumerate all the
boundary selections and choose the one with minimal U .
75
Figure 3.5 illustrates an example of rule partitioning. Assume that we have S = 4 in each
authority switch. Using our partition algorithm, we can construct a decision tree as shown in
Figure 3.5(b) for the rules shown in Figure 3.5(a). In the first round, we choose the dimension on
field F2 to partition the root node, because it has the maximum number of unique ranges. We
then divided the root node into three children nodes on field F2 : [0..7], [8..11], [12..15]. This yields
U = 0 because rules R3 , R4 , R8 that fall in the second child of F2 = [8..11] all take the deny actions.
In the second round, since the third child node requires 5 authority rules, we further split it into
two children nodes on field F3 .
Note that, although our partition algorithm is motivated by both HiCuts [58] and HyperCuts [59], which explored the efficient software processing of packet classification rules in one
switch with the help of a decision tree, we differ in our optimization goals. Both HiCuts and
HyperCuts sought to speed up software processing of the rules, while DIFANE aims at minimizing the TCAM usage in switches, because the partition and authority rules are all processed in
hardware. This leads to two key design differences in our algorithm: (i) We choose to cut the
selected dimension based on the rule boundaries, while HiCuts and HyperCuts cut the selected
dimension equally for c cuts. (ii) We choose the cuts so that the number of TCAM entries per
cut is minimized. In HiCuts and HyperCuts, they optimize on the number of cuts, in order to
minimize the size of the tree (and especially its depth). DIFANE allows a slightly deeper decision
tree if it reduces TCAM usage.
In summary, DIFANE partitions the entire rule space into M independent portions, and thus
each authority switch is assigned a non-overlapping portion. However, within the portion managed
by a single authority switch, DIFANE allows overlapping or nested rules. This substantially reduces
the TCAM usage of authority switches (see Section 4.5).
Duplicating authority rules to reduce stretch: We can duplicate the rules in each partition
on multiple authority switches to reduce stretch and to react quickly to authority switch failures.
Due to host mobility, we cannot pre-locate authority switches to minimize stretch. Instead, we
assume traffic that is related to one rule may come from any ingress switches and place replicated
authority switches to reduce the average stretch. One simple method is to randomly place the
replicated switches to reduce stretch. Alternatively, by leveraging an approximation algorithm for
76
the “k-median problem” [60], we can place the replicated authority switches so that they have
minimal average stretch to any pair of switches. Both schemes are evaluated in Section 4.5.
3.6
Design and Implementation
In this section, we present our design and implementation of DIFANE. First, we describe how
our prototype handles multiple sets of rules from different kinds of high-level policies for different
management functions. Second, we describe the prototype architecture, which just add a few
control-plane functions for authority switches to today’s flow-based switches.
3.6.1
Managing Multiple Sets of Rules
Different management functions such as access control, measurement and routing may have totally
different kinds of policies. To make our prototype efficient and easy to implement, we generate
different sets of rules for different policies, partition them using a single partition algorithm, and
process them sequentially in the switch.
Generate multiple sets of low-level rules:
Translating and combining different kinds of
high-level policies into one set of rules is complicated and significantly increases TCAM usage.
For example, if the policies are to monitor web traffic, and perform destination based routing,
we have to provide rules for (dst, port 80) and (dst, other ports) for each destination dst. If the
administrator changes the policy of monitoring port 21 rather than port 80, we must change the
rules for every destination. In contrast, if we have different sets of rules, we only need one routing
rule for each destination and a single measurement rule for port 80 traffic which is easy to change.
To distribute multiple sets of rules, the controller first partitions the flow space to minimize
the total TCAM usage. It then assigns all the rules (of different management modules) in one
flow range to one authority switch. We choose to use the same partition for different sets of lowlevel rules so that packets only need to be redirected to one authority switch to match all sets of
authority rules.9
9 One can also choose to provide a different partition of the flow space for different sets of low-level rules, but
packets may be redirected to multiple authority switches to match the authority rules of different management
modules.
77
TCAM in a switch
In
pkts
Access
control
rules
Routing
rules
Measurement rules
Switch
connect
rules
Out
pkts
Figure 3.6: Rules for various management modules.
Processing packets through multiple sets of rules in switches: In switches we have one set
of rules for each management module.10 We process the flow rules sequentially through the rules
for different modules as shown in Figure 3.6. We put access control rules first to block malicious
traffic. Routing rules are placed later to identify the egress switch for the packets. Finally, the
link-state routing constructs a set of switch connection rules to direct the packets to their egress
switches.
To implement sequential processing in the switch where all the rules share the same TCAM, the
controller sets a “module identifier” in the rules to indicate the module they belong to. The switch
first initializes a module identifier in the packet. It then matches the packet with the rules that
have the same module identifier. Next, the switch increments the module identifier in the packet
and matches to the next set of rules. By processing the packet several times through the memory,
the switch matches the packet to the rules for different modules sequentially. The administrator
specifies the order of the modules by giving different module identifiers for the high-level policies
in the controller.
A packet may be redirected to the authority switch when it is in the middle of the sequential
processing (e.g., while being processed in the measurement module). After redirection, the packet
will be processed through the following modules in the authority switch based the module identifier
in the packet.
3.6.2
DIFANE Switch Prototype
Figure 3.7 shows both the control and data plane of our DIFANE switch prototype.
10 To
make the rule processing simple, we duplicate the same set of partition rules in the management modules.
78
Data packets
Control msgs
Controller
Install auth.
and partition
rules
Recv cache Send cache
updates
updates
Control
Plane
Data
Plane
(Click)
In
pkts.
Link-state
Protocol
(XORP)
Cache
manager
Trigger
cache
manager
Cache
rules
Routing
updates
with other
switches
Forwarding
updates
Auth.
rules
Partition
rules
Pkt.
Encap.
Switch
connect
rules
Out
pkts.
Figure 3.7: DIFANE prototype implementation. (Cache manager and authority rules (shaded
boxes) only exist in authority switches.)
Control plane: We use XORP [61] to run the link-state routing protocol to maintain the switchlevel connectivity, and keep track of topology changes. XORP also sends updates of the switch
connection rules in the data plane.
The authority switch also runs a cache manager which installs cache rules in the ingress switch.
If a packet misses the cache, and matches the authority rule in the authority switch, the cache
manager is triggered to send a cache update to the ingress switch of the packet. The cache manager
is implemented in software in the control plane because packets are not buffered and waiting for the
cache rule in the ingress switch. The ingress switch continues to forward packets to the authority
switch if the cache rules are not installed. The cache manager sends an update for every packet
that matches the authority rule. This is because we can infer that the ingress switch does not
have any related rules cached, otherwise it would forward the packets directly rather than sending
them to the authority switch.11
11 For UDP flows, they may be a few packets sent to the authority switch. The authority switch sends one
feedback for each UDP flow, because it takes very low overhead to send a cache update message (just one UDP
79
Data plane:
We run Click-based OpenFlow switch [53] in the kernel as the data plane of DI-
FANE. Click manages the rules for different management modules and encapsulates and forwards
packets based on the switch connection rules. We implement the packet encapsulation function
to enable tunneling in the Click OpenFlow element. We also modify the Click OpenFlow element
to support the flow rule action “trigger the cache manager”. If a packet matches the authority
rules, Click generates a message to the cache manager through the kernel-level socket “netlink”.
Today’s flow-based switches already support actions of sending messages to a local controller in
order to communicate with the centralized controller [10]. We just add a new message type of
“matching authority rules”. In addition, today’s flow-based switches already have interfaces for
the centralized controller to install new rules. The cache manager then just leverages the same
interfaces to install cache rules in the ingress switches.
3.7
Evaluation
Ideally we would like to evaluate DIFANE based on policies, topology data, and user-mobility
traces from real networks. Unfortunately, most networks today are still configured with rules
that are tightly bound to their network configurations (e.g., IP address assignment, routing, and
VLANs). Therefore, we evaluated DIFANE’s approach against the topology and access-control
rules of a variety of different networks toexplore DIFANE’s benefit across various settings. We also
perform latency, throughput, and scalability micro-benchmarks of our DIFANE prototype and a
trace-driven evaluation of our partition and caching algorithms.
To verify the design decisions in Section 3.2, we evaluate two central questions in this section:
(1) How efficient and scalable is DIFANE? (2) How well do our partition and caching algorithms
work in handling large sets of wildcard rules?
3.7.1
Performance of the DIFANE Prototype
We implemented the DIFANE prototype using a kernel-level Click-based OpenFlow switch and
compared the delay and throughput of DIFANE with NOX [10], which is a centralized solution
for flow management. For a fair comparison, we first evaluated DIFANE using only one authority
packet). In addition, we do not need to store the existing cached flow rules in the authority switch or fetch them
from the ingress switch.
80
Authority Switch
Cache Manager
NOX Controller
Data Plane
Install
Rules
Packets
Switch 1
Local Controller
Install
Rules
Packets
Switch p
Local Controller
Packets
Switch p
Switch 1
... ...
Data Plane
Packets
Data Plane
Data Plane
(a) NOX
Data Plane
Packets
Packets
Packets
... ...
(b) DIFANE.
Figure 3.8: Experiment setup. (Dashed lines are control messages; straight lines are data traffic.)
switch. Then we evaluated the throughput of DIFANE with multiple authority switches. Finally
we investigated how fast DIFANE reacts to the authority switch failures.
In the experiments, each sender sends the packets to a receiver through a single ingress switch,
which is connected directly to either NOX or a DIFANE authority switch as shown in Figure 3.8.
(In this way, the network delay from the ingress switch to NOX and the DIFANE authority switch
is minimized. We evaluate the extra delay caused by redirecting through authority switches in
Section 3.7.2.) With NOX, when a packet does not match a cached rule, the packet is buffered
in the ingress switch before NOX controller installs a rule at the ingress switch. In contrast, in
DIFANE the authority switch redirects the packet to the receiver in the data plane and installs
a rule in the ingress switch at the same time. We generate flows with different port numbers,
and use a separate rule for each flow. Since the difference between NOX and DIFANE lies in the
processing of the first packet, we generate each flow as a single 64 Byte UDP packet. Based on
the measurements, we also calculate the performance difference between NOX and DIFANE for
flows of normal sizes. Switches, NOX, and traffic generators (“clients”) run on separate 3.0 GHz
64-bit Intel Xeon machines to avoid interference between them.
(1) DIFANE achieves small delay for the first packet of a flow by always keeping
packets in the fast path. In Figure 3.9, we send traffic at 100 single-packet flows/s and measure
the round-trip time (RTT) of the each packet being sent through a switch to the receiver and an
ACK packet being sent back. Although we put NOX near the switch, the packets still experience
a RTT of 10 ms on average, which is not acceptable for those networks that have tight latency
requirement such as data centers. In DIFANE, since the packets stay in the fast path (forwarded
through an authority switch), the packets only experience 0.4 ms RTT on average. Since all the
81
Cumulative fraction
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
DIFANE
NOX
0.1
1
10
100
RTT (ms)
Figure 3.9: Delay comparison of DIFANE and NOX.
Throughput (flows/sec)
No. of switches
1
2 3 4 56 810
1M
500K
200K
100K
50K
DIFANE
NOX
20K
10K
10K 20K 50K 100K200K 500K 1M
Sending rate (flows/sec)
Figure 3.10: Throughput comparison of DIFANE and NOX.
following packets take 0.3 ms RTT for both DIFANE and NOX, we can easily calculate that to
transfer a flow of a normal size 35 packets, which is based on the measurement in the paper [62]),
the average packet transfer time is 0.3 ms (=(0.3*34+0.4)/35) transferring time for DIFANE but
0.58 ms (=(0.3*34+10)/35) for NOX. Others’ tests of NOX with commercial OpenFlow switches
observed similar delay [63].
(2) DIFANE achieves significantly higher throughput than NOX. We then increase the
number of switches (p) to measure the throughput of NOX and DIFANE. In Figure 3.10, we show
the maximum throughput of flow setup for one client using one switch. In DIFANE, the switch was
able to achieve the client’s maximum flow setup rate, 75K flows/s, while the NOX architecture was
only able to achieve 20K flows/s. This is because, while all packets remain in the fast path (the
software kernel) in DIFANE, the OpenFlow switch’s local controller (implemented in user-space)
becomes a bottleneck before NOX does. Today’s commercial OpenFlow switches can only send
82
60-330 flows/s to the controller due to the limited CPU resources in the controller [64]. Section 3.8
discusses how to run DIFANE on today’s commercial switches.
As we increase the number of ingress switches—each additional data-point represents an additional switch and client as shown in the upper x-axis—we see that the NOX controller soon
becomes a bottleneck: With four switches, a single NOX controller achieves a peak throughput
of 50K single-packet flows/s. Suppose a network has 1K switches, a single NOX controller can
only support 50 new flows per second for each switch simultaneously. In comparison, the peak
throughput of DIFANE with one authority switch is 800K single-packet flows/s.
Admittedly, this large difference exists because DIFANE handles packets in the kernel while
NOX operates in user space. However, while it is possible to move NOX to the kernel, it would
not be feasible to implement the entire NOX in today’s switch hardware because the online rule
generation too complex for hardware implementation. In contract, DIFANE is meant for precisely
that — designed to install a set of rules in the data plane.12
We then evaluate the performance of the cache manager in authority switches. When there are
10 authority rules, the cache manager can handle 30K packets/s and generate one rule for each
packet. When there are 9K authority rules, the cache manager can handle 12K packets/s. The
CPU is the bottleneck of the cache manager.
(3) DIFANE scales with the number of authority switches.
Our experiments show
that DIFANE’s throughput increases linearly with the number of authority switches. With four
authority switches, the throughput of DIFANE reaches over 3M flows/s. Administrators can
determine the number of authority switches according to the size and the throughput requirements
of their networks.
(4) DIFANE recovers quickly from authority switch failure. Figure 3.11 shows the effect
of an authority switch failure. We construct a diamond topology with two authority switches,
both connecting to the ingress and the egress switches. We set the OSPF hello interval to 1 s,
and the dead interval to 3 s. After the authority switch fails, OSPF notifies the ingress switch. It
takes less than 10 ms for the ingress switch to change to another authority switch after the dead
12 Today’s TCAM with pipelined processing only takes 3–4 ns per lookup [65], which is more than three orders
of magnitude faster than in software.
83
Packet loss rate (%)
100
80
60
40
Switch
fails
20
Detect
failure
0
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
Time (sec)
Figure 3.11: Authority switch failure.
Network
Campus
VPN
IPTV
IP
# switches/routers
∼1700
∼1500
∼3000
∼2000
# Rules
30K
59K
5M
8M
Table 3.1: Network characteristics.
interval, at which time the ingress switch sets the backup partition rule as the primary one, and
thus connectivity is restored.
3.7.2
Evaluation of Partitioning and Caching
We now evaluate DIFANE’s partitioning algorithm using the topologies and access-control rules
from several sizable networks (as of Sept. 10, 2009) including a large-scale campus network [36]
and three large backbone networks that are operated by a tier-1 ISP for its enterprise VPN, IPTV,
and traditional IP services. The basic characteristics of these networks are shown in Table 3.1. In
these networks, each access control rule has six fields: ingress interface, source IP/port, destination
IP/port, and protocol. Access control rules are configured on the ingress switches/routers. It is
highly likely that different sets of rules are configured at different switches and routers, hence one
packet may be permitted in one ingress switch but denied at another. In addition, as Table 3.1
shows, there are a large number of access control rules configured in these networks. This is due
to the large number of ingress routers that need to have access control rules configured and the
potentially large number rules that need to be configured on even a single router. For example,
ISPs often configure a set of rules on each ingress switch to protect their infrastructures and
important servers from unauthorized customers. This would easily result in a large number of
84
Cumulative fraction
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
IPTV
VPN
Campus
IP
1
10
100
1K
10K
No. of non-overlapping / No. of overlapping rules
No. of auth. switches
Figure 3.12: Comparison of overlapping and non-overlapping rules.
1000
IP
IPTV
VPN
Campus
100
10
1
1K
10K
100K
1000K 5000K
No. of TCAM entries per auth. switch
Figure 3.13: Evaluation on number of authority switches.
rules on an ingress switch if there are a large number of customers connected to the switch and/or
these customers make use of a large amount of non-aggregatable address space.
In the rest of this section, we evaluate the effect of overlapping rules, the number of authority
switches needed for different networks, the number of extra rules needed after the partitioning,
the miss rate of caching wildcard rules, and the stretch experienced by packets that travel through
an authority switch.
(1) Installing overlapping rules in an authority switch significantly reduces the memory requirement of switches:
In our set of access control rules, the use of wildcard rules
can result in overlapping rules. One straight forward way to handle these overlapping rules is to
translate them into non-overlapping rules which represent the same semantics. However, this is
not a good solution because Figure 3.12 shows that the resulting non-overlapping rules require one
or two orders of magnitude more TCAM space than the original overlapping rules. This suggests
that the use of overlapping wildcard rules can significantly reduce the number of TCAM entries.
85
% of extra TCAM entries
12
10
8
6
4
2
0
0
2
4
6
8
10
No. of splits
Figure 3.14: The overhead of rule partition.
(2) A small number of authority switches are needed for the large networks we evaluated.
Figure 3.13 shows the number of authority switches needed under varying TCAM
capacities. The number of authority switches needed decreases almost linearly with the increase
of the switch memory. For networks with relatively few rules, such as the campus and VPN
networks, we would require 5–6 authority switches with 10K TCAM in each (assuming we need
16B to store the six fields and action for a TCAM entry, we need about 160KB of TCAM in
each authority switch). To handle networks with many rules, such as the IP and IPTV networks,
we would need approximately 100 authority switches with 100K TCAM entries (1.6MB TCAM)
each.13 The number of the authority switches is still relatively small compared to the network size
(2K - 3K switches).
(3) Our partition algorithm is efficient in reducing the TCAM usage in switches. As
shown in Figure 3.4, depending on the rules, partitioning wildcard rules can increase the total
number of rules and the TCAM usage for representing the rules. With the 6-tuple access-control
rules in the IP network, the total number of TCAM entries increases only by 0.01% if we distribute
the rules over 100 authority switches. This is because most of the cuts are on the ingress dimension
and, in the data set, most rules differ between ingresses. To evaluate how the partition algorithm
handles highly overlapping rules, we use our algorithm to partition the 1.6K rules in one ingress
router in the IP network. Figure 3.14 shows that we only increase the number of TCAM entries
by 10% with 10 splits (100–200 TCAM entries per split).
13 Today’s
commercial switches are commonly equipped with 2 MB TCAM.
86
Cache miss rate (%)
100
10
1
microflow
wildcard
0.1
0.01
0.001
0.0001
10
100
1K
Cache size per switch (TCAM entries)
Cumulative fraction
Figure 3.15: Cache miss rate.
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
k-med,10
k-med,3
k-med,1
rand,10
rand,3
rand,1
1
1.5
2
Stretch
3
4
5
Figure 3.16: The stretch of campus network. (We place 1,3,10 authority switches for each set of
the authority rules using k-median and random algorithms respectively.)
(4) Our wildcard caching solution is efficient in reducing cache misses and cache
memory size. We evaluate our cache algorithm with packet-level traces of 10M packets collected
in December 2008 and the corresponding access-control lists (9K rules) in a router in the IP
network. Figure 3.15 shows that if we only cache micro-flow rules, the miss rate is 10% with 1K
cache entries. In contrast, with wildcard rule caching in DIFANE, the cache miss rate is only
0.1% with 100 cache entries: 99.9% of packets are forwarded directly to the destination, while
only 0.1% of the packets take a slightly longer path through an authority switch. Those ingress
switches which are not authority switches only need to have 1K TCAM entries for cache rules
(Figure 3.15) and 10 - 1000 TCAM entries for partition rules (Figure 3.13).
(5) The stretch caused by packet redirection is small.
We evaluated the stretch of two
authority switch placement schemes (random and k-median) discussed in Section 3.5. Figure 3.16
shows the distribution of stretch (delay normalized by that of the shortest path) among all sourcedestination pairs in the campus network. With only one authority switch for each set of authority
87
rules, the average stretch is twice the delay of the shortest path length in the random scheme.
Though some packets experience 10 times the delay of the shortest path, this usually happens
to those pairs of nodes that are one or two hops away from each other; so the absolute delay of
these paths is not large. If we store one set of rules at three random places, we can reduce stretch
(the stretch is 1.8 on average). With 10 copies of rules, the stretch is reduced to 1.5. By placing
the authority switches with the k-median scheme, we can further reduce the stretch (e.g., with 10
copies of rules, the stretch is reduced to 1.07).
3.8
DIFANE Deployment Scenarios
DIFANE proposes to use authority switches to always keep packets in the data plane. However,
today’s commercial OpenFlow switches have resource constraints in the control plane. In this
section, we describe how DIFANE can be deployed in today’s switches with resource constraints and
in future switches as a clean-slate solution. We provide three types of design choices: implementing
tunneling with packet encapsulation or VLAN tags; performing rule caching in the authority
switches or in the controller; choosing normal switches or dedicated switches as authority switches.
Deployment with today’s switches:
Today’s commercial OpenFlow switches have resource
constraints in the control plane. For example, they do not have enough CPU resources to generate
caching rules or have hardware to encapsulate packets quickly. Therefore we use VLAN tags to
implement tunneling and move the wildcard rule caching to the DIFANE controller. The ingress
switch tags the “miss” packet and sends it to the authority switch. The authority switch tags the
packet with a different VLAN tag and sends the packet to the corresponding egress switch. The
ingress switch also sends the packet header to the controller, and the controller installs the cache
rules in the ingress switch.
Performing rule caching in the controller resolves the limitations of today’s commercial OpenFlow switches for two reasons. (i) Authority switches do not need to run caching functions. (ii)
The authority switches do not need to know the addresses of the ingress switch. We can use
VLAN tagging instead of packet encapsulation, which can be implemented in hardware in today’s
switches.
88
This deployment scenario is similar to Ethane [13] in that it also has the overhead of the ingress
switch sending packets to the controller and the controller installing caching rules. However, the
difference is that DIFANE always keeps the packet in the fast path. Since we need one VLAN
tag for each authority switch (10 - 100 authority switches) and each egress switch (at most a
few thousand switches), we have enough VLAN tags to support tunneling in DIFANE in today’s
networks.
Clean slate deployment with future switches: Future switches can have more CPU resources
and hardware-based packet encapsulation techniques. In this case, we can have a clean slate design.
The ingress switch encapsulates the “miss” packet with its address as the source address. The
authority switch decapsulates the packet, gets the address of the ingress switch and re-encapsulates
the packet with the egress switch address as the packet’s destination address. The authority switch
also installs cache rules to the ingress switch based on the address it gets from the packet header.
In this scenario, we can avoid the overhead and single point of failure of the controller. Future
switches should also have high bandwidth channel between the data plane and the control plane
to improve the caching performance.
Deployment of authority switches:
There are two deployment scenarios for authority
switches: (i) The authority switches are just normal switches in the network that can be taken
over by other switches when they fail; (ii) The authority switches are dedicated switches that have
larger TCAM to store more authority rules and serve essentially as a distributed data plane of the
centralized controller. All the other switches just need a small TCAM to store a few partition rules
and the cache rules. In the second scenario, even when DIFANE has only one authority switch
that serves as the data plane of the controller, DIFANE and Ethane [13] are still fundamentally
different in that DIFANE pre-installs authority rules in TCAM and thus always keeps the packet
in the fast path.
3.9
Flexible Management Support
Recently proposed flow-based management solutions [13, 49, 50, 51, 52] can easily run on top
of DIFANE, by defining their own policies and translating them into rules, while capitalizing on
our support for distributed rule processing for better scalability and performance. In addition,
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DIFANE is also flexible to support some other proposed techniques and management functions for
managing how rules are handled.
Support scalable routing with packet redirection: SEATTLE [5] performs packet redirection based on the hash of a packet’s destination MAC address, and reactively caching information
about the host’s current location. SEATTLE can be easily implemented within our architecture
even when the flow-based switches do not support hashing. In particular, the DIFANE controller
could generate routing rules that map a destination MAC address to the switch where the host
is located. The partitioning algorithm could divide the space of rules by cutting along the destination address dimension to generate partition rules, with wildcards in some bit positions of the
destination address, and with wildcards in all other header fields. When an ingress switch does not
have a cached rule that matches an incoming packet, the partition rule directs the packet through
the appropriate authority switch. This triggers the authority switch to install the rules for the
destination address at the ingress switch.
Similarly, DIFANE could support ViAggre [56] by creating partition rules based on the destination IP address space (rather than MAC addresses), so ingress switches forward packets to
authority switches with more-specific forwarding-table entries.
Handle measurement rules in both authority and ingress switches. In DIFANE packets
may be processed in the ingress switch or in the authority switch. If we have a measurement rule
that accumulates the statistics of a flow, we need to install it in both the ingress and the authority
switch. The controller installs these measurement flow rules in the authority switches, which then
installs the rules in the ingress switches. A packet matches one of the cached rule is counted at
the ingress switch. Otherwise, it is redirected to an authority switch and counted there.
The controller can use either pull or push method to collect flow information from the authority
switches and ingress switches. The cache rules in the ingress switch may be swapped out if the
cache rule is not used for the timeout time or there is not enough memory. In this case, the ingress
switch notifies the controller and sends the data of the cache rule to the controller, which is already
supported by flow-based switches today.
Most network management functions can be achieved by caching rules only at the
ingress switch.
We choose to cache rules only at the ingress switch for lower overhead. One
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alternative is to cache rules at every switch on the path a packet transfers. The authority switch
would have to determine all the switches on the packet’s path and install the rule in them.
In fact, caching rules only at the ingress can meet most of the requirements of management
modules. For example, access control rules are checked at the ingress switch to block the malicious
traffic before they enter the network. Measurement rules are usually applied at the ingress switch
to count the number of packets or the amount of traffic. Routing rules are used at the ingress switch
to select the egress point for the packets. Packets are then encapsulated and forwarded directly to
the egress switch without matching routing rules at other switches. Customized routing can also
be supported by tagging the packets and selecting pre-computed paths at the ingress switch.
3.10
Summary
We design and implement DIFANE, a distributed flow management architecture that distributes
rules to authority switches and handles all data traffic in the fast path. DIFANE can handle
wildcard rules efficiently and react quickly to network dynamics such as policy changes, topology
changes and host mobility. DIFANE can be easily implemented with today’s flow-based switches.
Our evaluation of the DIFANE prototype, various networks, and large sets of wildcard rules shows
that DIFANE is scalable with networks with a large number of hosts, flows and rules.
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Chapter 4
SNAP: Scaling Performance
Diagnosis on Hosts
This chapter focuses on scaling the management task of performance diagnosis. Network performance problems are notoriously tricky to diagnose, and this is magnified when applications are
often split into multiple tiers of application components spread across thousands of servers in a
data center. Problems often arise in the communication between the tiers, where either the application or the network (or both!) could be to blame. In this chapter, we present SNAP, a scalable
network-application profiler on hosts.
SNAP guides developers in identifying and fixing performance problems. SNAP passively collects TCP statistics and socket-call logs with low computation and storage overhead, and correlates
across shared resources (e.g., host, link, switch) and connections to pinpoint the location of the
problem (e.g., send buffer mismanagement, TCP/application conflicts, application-generated microbursts, or network congestion). Our one-week deployment of SNAP in a production data center
(with over 8,000 servers and over 700 application components) has already helped developers uncover 15 major performance problems in application software, the network stack on the server,
and the underlying network.
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4.1
Introduction
Modern data-center applications, running over networks with unusually high bandwidth and low
latency, should have great communication performance. Yet, these applications often experience low throughput and high delay between the front-end user-facing servers and the back-end
servers that perform database, storage, and indexing operations. Troubleshooting network performance problems is hard. Existing solutions—like detailed application-level logs or fine-grain
packet monitoring—are too expensive to run continuously, and still offer too little insight into
where performance problems lie. Instead, we argue that data centers should perform continuous,
lightweight profiling of the end-host network stack, coupled with algorithms for classifying and
correlating performance problems.
4.1.1
Troubleshooting Network Performance
The nature of the data-center environment makes detecting and locating performance problems
particularly challenging. Applications typically consist of tens to hundreds of application components, arranged in multiple tiers of front-ends and back-ends, and spread across hundreds to tens
of thousands of servers. Application developers are continually updating their code to add features
or fix bugs, so application components evolve independently and are updated while the application
remains in operation. Human factors also enter into play: most developers do not have a deep
understanding of how their design decisions interact with TCP or the network. There is a constant
influx of new developers for whom the intricacies of Nagle’s algorithm, delayed acknowledgments,
and silly window syndrome remains a mystery.1
As a result, new network performance problems happen all the time. Compared to equipment
failures that are relatively easy to detect, performance problems are tricky because they happen
sporadically and many different components could be responsible. The developers sometimes
blame “the network” for problems they cannot diagnose; in turn, the network operators blame the
developers if the network shows no signs of equipment failures or persistent congestion. Often,
they are both right, and the network stack or some subtle interaction between components is
actually responsible [66, 67]. For example, an application sending small messages can trigger
1 Some applications use UDP, and re-implement reliability, error detection, and flow control; however, these
mechanisms can also introduce performance problems.
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Nagle’s algorithm in the TCP stack, causing transmission delays leading to terrible application
throughput.
In the production data center we study, the process of actually detecting and locating even a
single network performance problem typically requires tens to hundreds of hours of the developers’
time. They collect detailed application logs (too heavy-weight to run continuously), deploy dedicated packet sniffers (too expensive to run ubiquitously), or sample the data (too coarse-grained
to catch performance problems). They then pore over these logs and traces using a combination
of manual inspection and custom-crafted analysis tools to attempt to track down the issue. Often
the investigation fails or runs out of time, and some performance problems persist for months
before they are finally caught and corrected.
4.1.2
Lightweight, Continuous Profiling
In this chapter, we argue that the data centers should continuously profile network performance,
and analyze the data in real time to help pinpoint the source of the problems. Given the complexity
of data-center applications, we cannot hope to fully automate the detection, diagnosis, and repair
of network performance problems. Instead, our goal is dramatically reducing the demand for
developer time by automatically identifying performance problems and narrowing them down to
specific times and places (e.g., send buffer, delayed ACK, or network congestion). Any viable
solution must be
• Lightweight: Running everywhere, all the time, requires a solution that is very lightweight
(in terms of CPU, storage, and network overhead), so as not to degrade application performance.
• Generic: Given the constantly changing nature of the applications, our solution must detect
problems without depending on detailed knowledge of the application or its log formats.
• Precise: To provide meaningful insights, the solution must pinpoint the component causing
network performance problems, and tease apart interactions between the application and
the network.
Finally, the system should help two very different kinds of users: (i) a developer who needs to
detect, diagnose, and fix performance problems in his particular application and (ii) a data-center
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operator who needs to understand performance problems with the underlying platform so that
he can tune the network stack, change server placement, or upgrade network equipment. In this
paper, we present SNAP (Scalable Network-Application Profiler), a tool that enables application
developers and data-center operators to detect and diagnose these performance problems. SNAP
represents an “existence proof” that a tool meeting our three requirements can be built, deployed
in a production data center, and provide valuable information to both kinds of users.
SNAP capitalizes on the unique properties of modern data centers:
• SNAP has full knowledge of the network topology, the network-stack configuration, and
the mapping of applications to servers. This allows SNAP to use correlation to identify
applications with frequent problems, as well as congested resources (e.g., hosts or links) that
affect multiple applications.
• SNAP can instrument the network stack to observe the evolution of TCP connections directly, rather than trying to infer TCP behavior from packet traces. In addition, SNAP can
collect finer-grain information, compared to conventional SNMP statistics, without resorting
to packet monitoring.
In addition, once the developers fix a problem (or the operator tunes the underlying platform),
we can verify that the change truly did improve network performance.
4.1.3
SNAP Research Contributions
SNAP passively collects TCP statistics and socket-level logs in real time, classifies and correlates
the data to pinpoint performance problems. The profiler quickly identifies the right location (end
host, link, or switch), the right layer (application, network stack, or network), at the right time.
Our major contributions of the chapter are:
Efficient, systematic profiling of network-application interactions: SNAP provides a simple, efficient way to detect performance problems through real-time analysis of passively-collected
measurements of the network stack. We provide a systematic way to identify the component (e.g.,
sender application, send buffer, network, or receiver) responsible for the performance problem.
SNAP also correlates across connections that belong to the same application, or share underlying
resources, to provide more insight into the sources of problems.
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Topology and
Mapping between
connections and apps
At each host for every connnection
Socket logs
TCP stats
TCP performance
classifier
Cross-Connection
Correlation
Offending app,
host, link, or switch
Figure 4.1: SNAP socket-level monitoring and analysis
Performance characterization of a production data center:
We deployed SNAP in a
data center with over 8,000 servers, and over 700 application components (including map-reduce,
storage, database, and search services). We characterize the sources of performance problems,
which helps data-center operators improve the underlying platform and better tune the network.
Case studies of performance bugs detected by SNAP: SNAP pinpointed 15 significant and
unexpected problems in application software, the network stack, and the interaction between the
two. SNAP saved the developers significant effort in locating and fixing these problems, leading
to large performance improvements.
Section 4.2 presents the design and development of SNAP. Section 4.3 describes our data-center
environment and how SNAP was deployed. Section 4.4 validates SNAP against both labeled data
(i.e., known performance problems) and detailed packet traces. Then, we present an evaluation of our one-week deployment of SNAP from the viewpoint of both the data-center operator
(Section 4.5) and the application developer (Section 4.6). Section 4.7 shows how to reduce the
overhead of SNAP through dynamic tuning of the polling rate. Section 4.8 discusses related work
and Section 4.9 concludes the section.
4.2
Design of the SNAP Profiler
In this section, we describe how SNAP pinpoints performance problems. Figure 4.1 shows the main
components of our system. First, we collect TCP-connection statistics, augmented by socket-level
logs of application read and write operations, in real time with low overhead. Second, we run a
96
TCP classifier that identifies and categorizes periods of bad performance for each socket, and logs
the diagnosis and a time sequence of the collected data. Finally, based on the logs, we have a
centralized correlator that correlates across connections that share a common resource or belong
to the same application to pinpoint the performance problems.
4.2.1
Socket-Level Monitoring of TCP
Data centers host a wide variety of applications that may use different communication methods
and design patterns, so our techniques must be quite general in order to work across the space.
The following three goals guided the design of our system, and led us away from using the SNMP
statistics, packet traces, or application logs.
(i) Fine-grained profiling:
The data should be fine-grained enough to indicate performance
problems for individual applications on a small timescale (e.g, tens of milliseconds or seconds).
Switches typically only capture link loads at a one-minute timescale, which is far too coarse-grained
to detect many performance problems. For example, the TCP incast problem [67], caused by micro
bursts of traffic at the timescale of tens of milliseconds, is not even visible in SNMP data.
(ii) Low overhead: Data centers can be huge, with hundreds of thousands of hosts and tens of
thousands sockets on each host. Yet, the data collection must not degrade application performance.
Packet traces are too expensive to capture in real time, to process at line speed, or to store on
disk. In addition, capturing packet traces on high-speed links (e.g., 1-10 Gbps in data centers)
often leads to measurement errors including drops, additions, and resequencing of packets [68].
Thus it is impossible to capture packet trace everywhere, all the time to catch new performance
problems.
(iii) Generic across applications:
Individual applications often generate detailed logs, but
these logs differ from one application to another. Instead, we focus on measurements that do not
require application support so our tool can work across a variety of applications.
Through our work on SNAP, we found that the following two kinds of per-socket information
can be collected cheaply enough to be used in analysis of large-scale data center applications, while
still providing enough insight to diagnose where the performance problem lie (whether they are
from the application software, from network issues, or from the interaction between the two).
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Statistic
CurAppWQueue
MaxAppWQueue
#FastRetrans
#Timeout
#SampleRTT
#SumRTT
RwinLimitTime
CwinLimitTime
SentBytes
Cwin
Rwin
Definition
# of bytes in the send buffer
Max # of bytes in send buffer
over the entire socket lifetime
Total # of fast retransmissions
Total # of timeouts
Total # of RTT samples
Sum of RTTs that TCP samples
Cumulated time an application
is receiver window limited
Cumulated time an application
is congestion window limited
Cumulated # of bytes the socket
has sent over the entire lifetime
Current congestion window
Announced receiver window
Table 4.1: Key TCP-level statistics for each socket [1]
Locations
Sender app
Send buffer
Network
Receiver
Problems
Sender app limited
Send buffer limited
Fast retransmission
Timeout
App/Net
App
App and Net
Net
Net
Delayed ACK
App and Net
Receiver window limited
App and Net
Detection method
Not any other problems
CurAppWQueue ≈ MaxAppWQueue
diff(#FastRetrans) > 0
diff(#Timeout) > 0)
diff(SumRTT) > diff(SampleRTT)
* MaxQueuingDelay
diff(#RwinLimitTime) > 0
Table 4.2: Classes of network performance for a socket
TCP-level statistics:
RFC 4898 [1] defines a mechanism for exposing the internal counters
and variables of a TCP state-machine that is implemented in both Linux [69] and Windows [70].
We select and collect the statistics shown in Table 4.1 based on our diagnosis experience2 , which
together expose the data-transfer performance of a socket. There are two types of statistics:
(1) instantaneous snapshots (e.g., Cwin) that show the current value of a variable in the TCP
stack; and (2) cumulative counters (e.g., #FastRetrans) that count the number of events (e.g., the
number of fast retransmissions) that happened over the lifetime of the socket. #SampleRTT and
SumRTT are the cumulative values of the number of packets TCP sampled and the sum of the
RTTs for these sampled packets. To calculate the retransmission timeout (RTO), TCP randomly
2 There are a few other variables in the TCP stack such as the time TCP spends in SlowStart stage, which are
also useful but we did not mention for simplicity.
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samples one packet in each congestion window, and measures the time from the transmission of a
packet to the time TCP receives the ACK for the packet as the RTT for this packet.
These statistics are updated by the TCP stack as individual packets are sent and received,
making it too expensive to log every change of these values. Instead, we periodically poll these
statistics.
For the cumulative counters, we calculate the difference between two polls (e.g.,
diff(#FastRetrans)). For snapshot values, we sample with a Poisson interval. According to the
PASTA property (Poisson Arrivals See Time Averages), the samples are a representative view of
the state of the system.
Socket-call logs:
Event-tracing systems in Windows [71] and Linux [72] record the time and
number of bytes (ReadBytes and WriteBytes) whenever the socket makes a read/write call. Socketcall logs show the applications’ data-transfer behavior, such as how many connections they initiated, how long they maintain each connection, and how much data they read/write (as opposed to
the data that TCP actually transfers, i.e., SentBytes). These logs supplement the TCP statistics
with application behavior to help developers diagnose problems. The socket-level logs are collected
in an event-driven fashion, providing fine-grained information with low overhead. In comparison,
the TCP statistics introduce a trade-off between accuracy and the polling overhead. For example,
if SNAP polls TCP statistics once per second, a short burst of packet losses is hard to distinguish
from a modest loss rate throughout the interval.
In summary, SNAP collects two types of data in the following formats: (i) timestamp, 4-tuples
(source and destination address/port), ReadBytes, and WriteBytes; and (ii) timestamp, 4-tuples,
TCP-level logs (Table 4.1). SNAP uses TCP-level logs to classify the performance problems and
pinpoint the location of the problem, and then provides both the relevant TCP-level and socketlevel logs for the affected connections for that period of time. Developers can use these logs to
quickly find the root cause of performance problems.
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4.2.2
Classifying Single-Socket Performance
Although it is difficult to determine the root cause of performance problems, we can pinpoint the
component that is limiting performance. We classify performance problems in terms of the stages
of data delivery, as summarized in the two columns of Table 4.23 :
1. Application generates the data: The sender application may not generate the data fast
enough, either by design or because of bottlenecks elsewhere (e.g., CPU, memory, or disk). For
example, the sender may write a small amount of data, triggering Nagle’s algorithm [73] which
combines small writes together into larger packets for better network utilization, at the expense
of delay.
2. Data are copied from the application buffer to the send buffer: Even when the
network is not congested, a small send buffer can limit throughput by stalling application writes.
The send buffer must keep data until acknowledgments arrive from the receiver, limiting the buffer
space available for writing new data.
3. TCP sends the data to the network: A congested network may drop packets, leading
to lower throughput or higher delay. The sender can detect packet loss by receiving three duplicate
ACKs, leading to a fast retransmission. When packet losses do not trigger a triple duplicate ACK,
the sender must wait for a retransmission timeout (RTO) to detect loss and retransmit the data.
4.
Receiver receives the data and sends an acknowledgment: The receiver may
not read data, or acknowledge their arrival, quickly enough. The receiver window can limit the
throughput if the receiver is not reading the data quickly enough (e.g., caused by a CPU starvation), allowing data to fill the receive buffer. A receiver delays sending acknowledgments in the
hope of piggybacking the ACK on data in the reverse direction. The receiver acknowledges every
other packet and waits up to 200 ms before sending an ACK.
The TCP statistics provide direct visibility into certain performance problems like packet
loss and receiver-window limits, where cumulative counts (e.g., #Timeout, #FastRetrans, and
RwinLimitTime) indicate whether the problem occurred at any time during the polling interval.
Detecting other problems relies on an instantaneous snapshot, such as comparing the current
backlog of the send buffer (CurAppWQueue) to its maximum size (MaxAppWQueue); polling with
3 The table only summarizes major performance problems and can be extended to cover other problems such as
out-of-order packets.
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a Poisson distribution allows SNAP to accurately estimate the fraction of time a connection is
send-buffer limited. Pinpointing other latency problems requires some notion of expected delays.
For example, the RTT should not be larger than the propagation delay plus the maximum queuing
delay (MaxQueuingDelay) (whose value is measured in advance by operators), unless a problem
like delayed ACK occurs. SNAP incorporates knowledge of the network configuration to identify
these parameters.
SNAP detects send-buffer, network, and receiver problems using the rules listed in the last
column of Table 4.2, where multiple problems may take place for the same socket during the same
time interval. If any of these problems are detected, SNAP logs the diagnosis and all the variables
in Table 4.1—as well as WriteBytes from the socket-call data—to provide the developers with
detailed information to track down the problem. In the absence of any of the previous problems,
we classify the connection as sender-application limited during the time interval, and log only
the socket-call data to track application behavior. Being sender-application limited should be the
most common scenario for a connection.
4.2.3
Correlation Across TCP Connections
Although SNAP can detect performance problems on individual connections in isolation, combining information across multiple connections helps pinpoint the location of the problem. As such,
a central controller analyzes the results of the TCP performance classifier, as shown earlier in
Figure 4.1. The central controller can associate each connection with a particular application and
with shared resources like a host, links, and switches.
Pinpointing resource constraints (by correlating connections that share a host, link, or
switch): Topology and routing data allow SNAP to identify which connections share resources
such as a host, link, top-of-rack switch, or aggregator switch. SNAP checks if a performance
problem (as identified by the algorithm in Table 4.2) occurs on many connections traversing the
same resource at the same time. For example, packet losses (i.e., diff(#FastRetrans) > 0 or
diff(#Timeout) > 0) on multiple connections traversing the same link would indicate a congested
link. This would detect congestion occurring on a much smaller timescale than SNMP could
measure. As another example, send-buffer problems for many connections on the same host could
101
indicate that the machine has insufficient memory or a low default configuration of the send-buffer
size.
Pinpoint application problem (by correlating across connections in the same application):
SNAP also receives a mapping of each socket (as identified by the four-tuple) to an
application. SNAP checks if a performance problem occurs on many connections from the same
application, across different machines and different times. If so, the application software may
not interact well with the underlying TCP layer. With SNAP, we have found several application
programs that have severe performance problems and are currently working with developers to
address them, as discussed in Section 4.6.
The two kinds of correlation analysis are similar, except for (i) sets of connections to compare
S (i.e., connections sharing a resource vs. belonging to the same service) and (ii) the timescale
for the comparison — correlation interval T (i.e., transient resource constraining events taking a
few minutes or hours vs. permanent service code problems that lasts for days).
We use a simple linear correlation heuristic that works well in our setting Given a set of
connections S and a correlation interval T , the SNAP correlation algorithm outputs whether
these connections have correlated performance problems, and provides a time sequence of SNAP
logs for operators and developers to diagnose.
−−−−−→
We construct a performance vector PT (c, t) = (timek (p1 , c), ..., timek (p5 , c))k=1..⌈T /t⌉ , where t
is an aggregation time interval in T and timek (pi )(i = 1..5) denotes the total time that connection
c is having problem pi during time period [(k − 1)t, kt].4 We pick c1 and c2 in S, calculate the
Pearson correlation coefficient, and check if the average across all pairs of connections (Average
Correlation Coefficient ACC) is larger than a threshold α:
ACC =
avg
−−−−−→ −−−−−→
(cor(PT (c1 , t), PT (c2 , t)) > α,
c1 ,c2 ∈S,c1 6=c2
where
P
(xi − x̄)(yi − ȳ)
−
→
→
−
.
cor( x , y ) = pPi
2
2
i (xi − x̄) (yi − ȳ)
4 p (i = 1..5) are the problems of send buffer limited, fast retransmission, timeout, delayed ACK and receiver
i
window limited respectively. We do not include sender application limited because its time could be determined
given the times of the first five problems.
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Characteristic
#Hosts
#Applications
Operating systems
Default send buffer
Maximum segment size (MSS)
Minimum retrans. timeout
Delayed ACK timeout
Nagle’s algorithm
Slow start restart
Receiver window autotuning
Value
8K
700
Win 2003,2008R2
8 KB
1460 Bytes
300 ms
200 ms
mostly off
off
off
Table 4.3: Characteristics in the production data center.
If the correlation coefficient is high, SNAP reports that the connections in S have a common
problem.
To extend this correlation for different classes of problems (e.g., one connection’s
delayed ACK problem triggers the sender application limited problem on another connection), we
can extend our solution to use other inference techniques [74, 75] or principal component analysis
(PCA) [76].
In practice, we must choose t carefully. With a large value of t, SNAP only compares the
coarse-grained performance between connections; for example, if t = T , we only check if two
connections have the same performance problem with the same percentage of time. With a small
t, SNAP can detect fine-grained performance problems (e.g., two connections experiencing packet
loss at almost the same time), but are susceptible to clock differences of the two machines and any
differences in the polling rates for the two connections. The aggregation interval t should be large
enough to mask the differences between the clocks and cannot be smaller than the least common
multiple of the polling intervals of the connections.
4.3
Production Data Center Deployment
We deployed SNAP in a production data center. This section describes the characteristics of the
data center and the configuration of SNAP, to set the stage for the following sections.
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4.3.1
Data Center Environment
The data center consists of 8K hosts and runs 700 application components, with the configuration
summarized in Table 4.3. The hosts run either Windows Server 2008 R2 or Windows Server 2003.
The default send buffer size is 8K, and the maximum segment size is 1460 Bytes. The minimum
retransmission timeout for packet loss is set to 300 ms, and the delayed-acknowledgment timeout
is 200 ms. These values in Windows OS are configured for Internet traffic with long RTT.
While the OS enables Nagle’s algorithm (which combines small writes into larger packets) by
default, most delay-sensitive applications disable Nagle’s algorithm using the NO DELAY socket
option.
Most applications in the data center use persistent connections to avoid establishing new TCP
connections whenever they have data to transmit. Slow-start restart is disabled to reduce the delay
arising when applications transfer a large amount of data after an idle period over a persistent
connection.
Receiver-window autotuning—a feature in Windows Server 2008 that allows TCP to dynamically tune the receiver window size to maximize throughput—is disabled to avoid bugs in the TCP
stack (e.g., [77]). Windows Server 2003 does not support this feature.
4.3.2
SNAP Configuration
We ran SNAP continuously for a week in August 2010. The polling interval for TCP statistics
follows the Poisson distribution with an average inter-arrival time of 500 ms. We collected the
socket-call logs for all the connections from and to the servers running SNAP. Over the week, we
collected less than 1 GB on each host per day and the total is just terabytes of logs for the week.
This is a very small amount of data compared to packet traces which take more than 180 GB per
host per day at a 1 Gbps link, even if we just keep packet header information.
To identify the connections sharing the same switch, link, and application, we collect the
information about the topology, routing, and the mapping between sockets and applications in the
data center. We collect topology and routing information from the data center configuration files.
To identify the mapping between the sockets and applications, we first run a script at each machine
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to identify the process that created each socket. We then map the processes to the application
based on the configuration file for the application deployment.
To correlate performance problems across connections using the correlation algorithm we proposed in Section 4.2.3, we chose two seconds as the aggregation interval t to summarize the time
on each performance problems to mask time difference between machines. To pinpoint transient
resource constraints which usually last for minutes or hours, we chose one hour as the correlation
interval T . To pinpoint problems from application code which usually last for days, we chose 24
hours as the correlation interval T . We chose the correlation threshold α = 0.4.5
4.4
SNAP Validation
To validate the design of SNAP in Section 4.2 and evaluate whether SNAP can pinpoint the
performance problems at the right place and time, we take two approaches: First, we inject a few
known problems in our production data center and check if SNAP correctly catches these problems;
Second, to validate the decision methods that use inference to determine the performance class in
Table 4.2 rather than observing from TCP statistics directly, we compare SNAP results against
packet traces.
4.4.1
Validation by Injecting Known Bugs
To validate SNAP, we injected a few known data-center networking problems and verified if SNAP
correctly classifies those problems for each connection. Next, running our correlation algorithm on
the SNAP logs of these labeled problems together with the other logs from the data center, SNAP
correctly pinpointed all the labeled problems. For brevity, we first discuss two representative
problems in detail and then show how SNAP pinpoints problematic host for each of them.
Problems in receive-window autotuning:
We first injected a receiver-window autotuning
problem: This problem happens when a Windows Server 2008 R2 machine initiates a TCP connection to a Windows Server 2003 machine with a SYN packet that requests the receiver window
autotuning feature. But due to a bug in the TCP stack of the Windows Server 20036, the 2003
5 It is hard to determine the threshold α in practice. Operators can choose the top n shared resources/application
code to investigate their performance problems.
6 This bug is later fixed with a patch, but some machines do not have the latest patch.
105
server does not parse the request for the receiver window autotuning feature correctly, and returns
the SYN ACK packet with a wrong format. As a result, the 2008 server tuned its receiver window
to four Bytes, leading to low throughput and long delay.
To inject this problem, we picked ten hosts running Windows 2008 in the data center and turn
on their receiver window autotuning feature. Each of the ten hosts initiated TCP connections to
a HTTP server running Windows 2003 to fetch 20 files of 5KB each from a host running Windows
2003.7 It took the Windows 2003 server more than 5 seconds to transfer each 5KB file. SNAP
correctly reported that all these connections are receiver window limited all the time, and SNAP
logs showed that the announced receiver window size (RWin) is 4 Byte.
TCP incast:
TCP incast [67] is a common performance problem in data centers. It happens
when an aggregator distributes a request to a group of workers, and after processing the requests,
these workers send the responses back at almost the same time. These responses together overflow
the switch on the path and experience significant packet losses.
We wrote an application that generates a TCP incast traffic pattern. To limit the effect of our
experiment to the other applications in the production data center, we picked 36 hosts under the
same top-of-rack switch (TOR), used one host as the aggregator to send requests to the remaining
35 hosts which serve as workers. These workers respond with 100KB data immediately after they
receive the requests. After receiving all the responses, the aggregator sends another request to the
workers. The aggregator sends 20 requests in total.
SNAP correctly identified that seven of the 35 connections have experienced a significant
amount of packet loss causing retransmission timeouts. This is verified from our application logs
which show that it takes much longer time to get the response through the seven connections than
the rest of the connections.8
Correlation to pinpoint resource constraints for the two problems: We mixed the SNAP
logs of the receiver window autotuning problem and TCP incast with the logs of an hour period
7 We ran ten hosts to the same 2003 server to validate if the SNAP can correlate these connections and pinpoint
the server.
8 In this experiment, SNAP can only tell that the connections have correlated timeouts. If the same problem
happens for different aggregators running the same application code, we can tell that the application code causes
the timeouts. If SNAP reports all the connections have simultaneous small writes (identified from socket call logs)
and correlated timeouts, we can infer that the application code has incast problems.
106
Fraction of Machines
0.1
0.08
0.06
0.04
0.02
0
0
0.2
0.4
0.6
0.8
1
Average correlation coefficient (ACC)
Figure 4.2: PDF of #Machines with different average correlation coefficient.
collected at all other machines in the data center. Then we ran SNAP correlation algorithm across
the connections sharing the same machine.
SNAP correctly identified the Windows Server 2003 servers that have receiver-window limited
problems across 5-10 connections with an average correlation coefficient (ACC) of 0.8. SNAP
also correctly identified the aggregator machine because the ACC across all the connections that
traverse the TOR is 0.45. Both are above the threshold α = 0.4, which is chosen based on the
discussion in Section 4.3.
Our correlation algorithm clearly distinguished the two injected problems with the performance
of connections on the other machines in the data center. Figure 4.2 presents the probability density
function (PDF) of the number of machines with different values of ACC. Only 2.7% of the machines
have an ACC larger than 0.4. In addition to the two injected problems, the other machines with
ACC > 0.4 may also indicate some problems that happen during our experiment, but we have not
verified these problems yet.
4.4.2
Validation Against Packet Traces
We also need to validate the performance-classification algorithm defined in Table 4.2. The detection methods for the performance class of fast retransmissions, timeouts, receiver window limited
is always accurate because these statistics are directly observed phenomena (e.g., #Timeouts)
from the TCP stack. The accuracy of identifying send buffer problems is closely related to the
107
probability of detecting the moments when the send buffer is full in the Poisson sampling, which
is well studied in [78].
There is a tradeoff between the overhead and accuracy of identifying delayed ACK. The accuracy of identifying the delayed ACK and small writes classes is closely related to the estimation of
the RTT. However, we cannot get per-packet RTT from the TCP stack because it is a significant
overhead to log data for each packet. Instead, we get the sum of estimated RTTs (SumRTT) and
the number of sampled packets (SampleRTT) from the TCP stack.
We evaluate the accuracy of identifying delayed ACK in SNAP by comparing SNAP’s results
with the packet trace. We picked two real-world applications from the production data center for
which SNAP detects delayed ACK problems: One connection serves as an aggregator distributing
requests for a Web application that has the delayed ACK problems for 100% of the packets9 .
Another belongs to a configuration-file distribution service for various jobs running in the data
center, which has 75% of the packets on average experiencing delayed ACK. While running SNAP
with various polling rates, we captured packet traces simultaneously. We then compared the results
of SNAP with the number of delayed-ACK incidents we identify from packet traces.
To estimate the number of packets that experience delayed ACK, SNAP should find a distribution of RTTs for the sampled packets that sum up to SumRTT. Those packets that experience
delayed ACK have a RTT around DelayedACKTimeout. The rest of the packets all experience the
maximum queuing delay. Therefore, we use the equation: (diff(#SumRTT) − diff(#SampleRTT)
* MaxQueuingDelay)/DelayedACKTimeout to count the number of packets experiencing delayed
ACK. We use MaxQueuingDelay = 10 ms and DelayedACKTimeout = 180 ms. The delayed timeout is set as 200 ms in TCP stack, but TCP timer is only accurate at 10 ms level and thus the real
DelayedACKTimeout varies around 200 ms. So we use 180 ms to be conservative on the delayed
ACK estimation.
Figure 4.3 shows the estimation error of SNAP’s results which is defined by (dt − ds )/dt , where
ds is the percentage of packets that experience delayed ACK reported by SNAP and dt is the
actual percentage of delayed ACK we get from the packet trace. For the application that always
has delayed ACK, SNAP’s estimation error is 0.006 on average. For the application that has 75%
9 This application distributes requests whose size is smaller than MSS (i.e., one packet), and waits more than
the delayed ACK timeout 200 ms before sending out another request. So the receiver has to keep each packet for
200 ms before sending the ACK to the sender.
108
SNAP Estimation Error
0.2
0.15
0.1
0.05
0
-0.05
-0.1
-0.15
-0.2
100%
75%
50 100 200 500m 1s
2s
5s 10s
Polling interval
Figure 4.3: SNAP estimation error of identifying delayed ACK problems.
of packets experiencing delayed ACK, the estimation error is within 0.2 for the polling intervals
that range from 500 ms to 10 sec.
Figure 4.3 shows that the estimation error drops from positive (underestimation) to negative
(overestimation) with the increase of the polling interval. When the polling interval is smaller than
200 ms, there is at most one packet experiencing delayed ACK in one polling interval. If a few
packets take less than MaxQueuingDelay to transfer, we would overestimate the part of SumRTT
that is contributed by these packets, and thus the rest of RTT is less than DelayedACKTimeout.
When the polling interval is large, there are more packets experiencing delayed ACK in the same
time interval. Since we have use 180 ms instead of 200 ms to detect delayed ACK, we would
underestimate those packets that take longer than 180 ms delayed ACK. Nine such packets would
contribute enough RTT for SNAP to assume one more delayed ACK.
4.5
Profiling Data Center Performance
We deployed SNAP in the production data center to characterize different classes of performance
problems, and provided information to the data-center operators about problems with the network
stack, network congestion or the interference between services. We first characterize the frequency
of each performance problem in the data center, and then discuss the key performance problems
in our data center—packet loss and the TCP send buffer.
109
Performance limitation
Sender app limited
Send buffer limited
Congestion
Receiver window limited
Delayed ACK
(belong to delay sensitive apps)
>0
97.91%
0.45%
1.90%
0.82%
65.71%
63.52%
% of conn. with prob.
for >X% of time
>25%
>50%
>75%
96.62%
89.61%
59.21%
0.06%
0.02%
0.01%
0.46%
0.22%
0.17%
0.36%
0.21%
0.15%
33.20%
10.10%
3.21%
32.82%
9.71%
3.01%
>99.9%
32.61%
0.01%
0.15%
0.11%
1.82%
1.61%
#Apps with prob.
for >X% of time
> 5%
> 50%
561
557
1
1
30
6
22
8
154
144
136
129
Table 4.4: Percentage of connections and number of applications that have different TCP performance limitations.
4.5.1
Frequency of Performance Problems
Table 4.4 characterizes the frequency of the network performance problems (defined in Table 4.2) in
our data center. Not surprisingly, the overall network performance of the data center is good. For
example, only 0.82% of all the connections were receiver limited during their lifetimes. However,
there are two key problems that the operators should address:
Operators should focus on the small fraction of applications suffering from significant
performance problems.
Several connections/applications have severe performance problems.
For example, about 0.11% of the connections are receiver-window limited essentially all the time.
Even though 0.11% sounds like a small number, when 8K machines are each running many connections, there is almost always some connection or application experiencing bad performance. These
performance problems at the “tail” of the distribution also constrain the total load operators are
willing to put in the data center. Operators should look at the SNAP logs of these connections
and work with the developers to improve the performance of these connections so that they can
safely “ramp up” the utilization of the data center.
Operators should disable delayed ACK, or significantly reduce Delayed ACK timeout:
About two-thirds of the connections experienced delayed ACK problems. Nearly 2% of
the connections suffer from delayed-ACKs for more than 99.9% of the time. We manually explore
the delay-sensitive services, and count the percentage of connections that have delayed ACK. Unfortunately, about 136 delay-sensitive applications have experienced delayed ACKs. Packets that
have delayed ACK would experience an unnecessary increase of latency by 200 ms, which is three
orders of magnitude larger than the propagation delay in the data center and well exceeds the
latency bounds for these applications. Since delayed ACK causes many problems for data-center
applications, the operators are considering disabling delayed ACK or significantly reducing the de-
110
# per second
1600
1400
1200
1000
800
600
400
200
0
fastretrans
timeout
0 2 4 6 8 10 12 14 16 18 20 22 24
Time (hour)
(#FastRetrans+1)/(\#Timeout+1)
Figure 4.4: # of fast retransmissions and timeouts over time.
100
10
1
0.1
1K
10K
100K
1M
Bytes per second
10M
Figure 4.5: Comparing #FastRetrans and #Timeouts of flows with different throughput.
layed ACK timeout. The problems of delayed ACK for data center applications are also observed
in [79].
4.5.2
Packet Loss
Operators should schedule backup jobs more carefully to avoid triggering network
congestion: Figure 4.4 shows the number of fast retransmissions and timeouts per second over
time. The percentage of retransmitted bytes increases between 2 am and 4 am. This is because
most backup applications with large bulk transfers are initiated in this time period.
Operators should reduce the number and effect of packet loss (especially timeouts)
for low-rate flows: SNAP data shows that about 99.8% of the connections have low throughput
(< 1 MB/sec). Although these low-rate flows do not consume much bandwidth and are usually not
111
the cause of network congestion, they are significantly affected by network congestion. Figure 4.5
is a scatter plot that shows the ratio of of fast retransmissions to timeouts vs. the connection
sending rate. Each point in the graph represents one polling interval of one connection. Low-rate
flows usually experience more timeouts than fast retransmission because they do not have multiple
packets in flight to trigger triple duplicate ACKs. Timeouts, in turn, limit the throughput of these
flows. In contrast, high-rate flows experience more fast retransmission than timeouts and can
quickly recover from packet losses achieving higher throughput (> 1 MB/sec).
4.5.3
Send Buffer and Receiver Window
Operators should allow the TCP stack to automatically tune the send buffer and receiver window
sizes, and consider the following two factors:
More send buffer problems on machines with more connections: SNAP reports correlated send buffer problems on hosts with more than 200 connections. This is because the larger
the send buffer for each connection, the more memory is required for the machine. As a result,
the developers of different applications on the same machine are cautious it setting the size of the
send buffer; most use the default size of 8K, which is far less than the delay-bandwidth product
in the data center and thus is more likely to become the performance bottleneck.
Mismatch between send buffer and receiver window size:
SNAP logs the announced
receiver window size when the connection is receiver limited. From the log we see that 0.1% of
the total time when the senders indicate that their connections are bottlenecked by the receiver
window, the receiver actually announced a 64 KB window. This is because the send buffer is larger
than the announced receiver size, so the sender is still bottlenecked by the receiver window.
To fix the send-buffer problems in the short term, SNAP could help developers to decide
what send buffer size they should set in an online fashion. SNAP logs the congestion window size (CWin), the amount of data the application expect to send (WriteBytes), and the
announced receiver window size (RWin) for all the connections. Developers can use this information to size the send buffer based on the total resources (e.g., set the send buffer size to
P
Cwinthisconn ∗ T otalSendBuf f erM emory/ CW in). They can also evaluate the effect of their
112
change using SNAP. In the long term, operators should have the TCP stack automatically tune
both the send-buffer and receiver-window sizes for all the connections (e.g., [69]).
4.6
Performance Problems Caught by SNAP
In this section, we show a few examples of performance problems caught by SNAP. In each example,
we first show how the performance problem is exposed by SNAP’s analysis of socket and TCP logs
into performance classifications and then correlation across connections. Next, we explain how
SNAP’s reports help guide developers to identify quickly the root causes. Finally, while outside of
SNAP’s scope, for interest value we discuss the developer’s fix or proposed fix to these problems.
For most examples, we spent a few hours or days discuss with developers to understand how their
programs work and to discover how their programs cause the problems SNAP detects. It then took
several days or weeks to iterate with developers and operators to find out the possible alternative
ways to achieve their programing goals.
4.6.1
Sending Pattern/Packet Loss Issues
Spreading application writes over multiple connections lowers throughput:
When
correlating performance problems across connections from the same application, SNAP found one
application whose connections always experienced more timeouts (diff(#Timeout)) than fast retransmission (diff(#FastRetrans)) especially when the WriteBytes is small. For example, SNAP
reported repeated periods where one connection transferred an average of five requests per second with a size of 2 KB - 20 KB, while experiencing approximately ten timeouts but no fast
retransmissions.
The developers were expecting to obtain far more than five requests per second from their
system, and when this report showing small writes and timeouts was shown to them the cause
became clear. The application sends requests to a server and waits for responses. Since some
requests take longer to process than others and developers wanted to avoid having to implement
request IDs while still avoiding head-of-line blocking, they open two connections to the server and
place new requests on whichever connection is unused.
113
However, spreading the application writes over two connections meant that often there were
not enough outstanding data on a connection to cause three duplicate ACKs and trigger fast
retransmission when a packet was lost. Instead, TCP fell back to its slower timeout mechanism.
To fix the problem, the application could send all requests over a single connection, give requests
a unique ID, and use pools of worker threads at each end.10 This would improve the chances there
is enough data in flight to trigger fast retransmission when packet loss occurs.
Congestion window failing to prevent sudden bursts: SNAP discovered that some connections belonging to an application frequently experience packet loss (#FastRetrans and #Timeout
are both high, and correlate strongly to the application and across time). SNAP’s logs expose
a time sequence of socket write logs (WriteBytes) and TCP statistics (Cwin) showing that before/during the intervals where packet loss occurs, there is a single large socket write call after
an idle period. TCP immediately sends out the data in one large chunk of packets because the
congestion window is large, but it experiences packet losses. For example, one application makes
a socket call with WriteBytes > 100 MB after an idle period of 3 seconds, the Cwin is 64 KB, and
the traffic burst leads to a bunch of packet losses.
The developers told us they use a persistent connection to avoid three-way handshake for each
data transfer. Since “slow start restart” is disabled, the congestion window size does not age out
and remains constant until there is a packet loss. As a result, the congestion window no longer
indicates the carrying capacity of the network, and losses are likely when the application suddenly
sends a congestion window worth of data.
Interestingly, the developers are opposed to enabling slow start restart, and they intentionally
manipulate the congestion window in an attempt to reduce latency. For example, if they send
64 KB data, and the congestion window is small (e.g., 1 MSS), they need at multiple round-trip
times to finish the data transfer. But if they keep the congestion window large, they can transfer
the data with one RTT. In order to have a large congestion window, they first make a few small
writes when they set up the persistent connection.
To reduce both the network congestion and delay, we need better scheduling of traffic across
applications, allowing delay-sensitive applications to send traffic bursts when there is no network
10 Note that the application should use a single connection because its requests are relatively small. For those
applications that have a large amount of data to transfer for each request, they still have to use two connections to
avoid head of line blocking during the network transfer.
114
Sender
1 2 3 4
Retransmission
timeout (300 ms)
5 6
4
Receiver
Delayed ACK
(200 ms)
Figure 4.6: Delayed ACK after a retransmission timeout.
congestion, but pacing the traffic if the network is highly used. The feedback mechanism proposed
in DCTCP [80] could be applied here.
Delayed ACK slows recovery after a retransmission timeout:
SNAP found that one
application frequently had two problems (timeout and delayed ACK) at almost the same time.
As shown in Figure 4.6, when the fourth packet of the transferred data is lost, the TCP sender
waits for a retransmission timeout (because there are not enough following packets to trigger
triple-duplicate ACKs). However, the congestion window drops to one after the retransmission.
As a result, TCP can only send a single packet, and the receiver waits for a delayed ACK timeout
before acknowledging the packet. Meanwhile, the sender cannot increase its sending window until
it receives the ACK from the receiver. To avoid this, developers are discussing the possibility
of dropping the congestion window down to two packets when a retransmission timeout occurs.
Disabling delayed ACK is another option.
4.6.2
Buffer Management and Delayed ACK
Some developers do not manage the application buffer and the socket send buffer appropriately,
leading to bad interactions between buffer management and delayed ACK.
Delayed ACK caused by setting send buffer to zero:
SNAP reports show that some
applications have delayed ACK problems most of the time and these applications had set their
send socket buffer length to 0.
Investigation found that these applications set the size of the
socket send buffer to zero in the expectation that it will decrease latency because data is not
copied to a kernel socket buffer, but sent directly from the user space buffer. However, when send
buffer is zero, the socket layer locks the application buffer until the data is ACK’d by the receiver
115
so that the socket can retransmit the data in case a packet is lost. As a result, additional socket
writes are blocked until the previous one has finished.
Whenever an application writes data that results in an odd number of packets being sent, the
last packet is not ACK’d until the delayed ACK timer expires. This effectively blocks the sending
application for 200 ms and can reduce application throughput to 5 writes per second. One team
attempted to improve application performance by shrinking the size of their messages, but ended
up creating an odd number of packets and triggering this issue — destroying the application’s
performance instead of helping it. After the developers increased the send buffer size, throughput
returned to normal.
Delayed ACK affecting throughput: SNAP reports showed that an application was writing
small amounts of data to the socket (WriteBytes) and its connections experienced both delayed
ACK and sender application limited issues. For example, during 30 minutes, the application wrote
10K records at only five records per second and with a the record size of 20–100 Bytes.
The developers explained theirs is a logging application where the client uploads records to a
server, and should be able generate far more than five records per second. Looking into the code
with the developers, we found three key problems in the design: (i) Blocking write: to simplify the
programming, the client does blocking writes and the server does blocking reads. (ii) Small receive
buffer: The server calls recv() in a loop with a 200 bytes buffer in hopes that exactly one record
is read in each receive call. (iii) Send buffer is set to zero: Since the application is delay-sensitive,
the developer set send buffer size to zero. The application records are 20–100 Bytes — much
less than the MSS of 1460 Bytes. Additionally, Nagle’s algorithm forces the socket to wait for an
ACK before it can send another packet (record).11 As a result, the single packet containing each
record always experience delayed ACK, leading to a throughput of only five records per second.
To address this problem while still avoiding the buffer copying in memory, developers changed the
sender code to write a group of requests each time. Throughput improved to 10K requests/sec
after the change—a factor of 5000 improvement.
Delayed ACK affecting performance for pipelined applications: By correlating connections to the same machine, SNAP found two connections with performance problems that co-occur
11 A
similar performance problem caused by interactions between delayed ACK and Nagle is discussed in [73].
116
Request
Client
Response
Request
Proxy
Server
Response
Req pkt
Req pkt
Ack
Ack
Response pkt
Response pkt
Delayed
Ack
(200ms)
Http.sys waits for
ACK before
fetching the next
response data
Figure 4.7: Performance problem in pipeline communication.
repeatedly: SNAP classified one connection as having a significant delayed ACK problem and the
other as having sender application problems.
Developers told us that these two connections belong to the same application and form a
pipeline pattern (Figure 4.7). There is a proxy that sits between the clients and servers and serves
as a load balancer. The proxy passes requests from the client to the server, fetches a sequence of
responses from the server, and passes them to the client. SNAP finds such a strong correlation
between the delayed ACK problem and the receiver limited problem because both stem from the
passing of the messages through the proxy.
After looking at the code, developers figured out that the proxy uses a single thread and a
single buffer for both the client and the server. The proxy waits for the ACK of every transfer (one
packet in each transfer most of the time) before fetching a new response data from the server.12
When the developers changed the proxy to use two different threads with one fetching responses
from the server and another sending responses to the client and a response queue between the two
threads, the 99% tail of the request processing time drops from 200 ms to 10 ms.
12 The proxy is using the HTTP.sys library without setting the HTTP SEND RESPONSE FLAG BUFFER DATA
flag [81], which waits for the ACK from the client before sending a “send complete” signal to the application. By
waiting for the ACK, HTTP.sys can make sure the application send buffer is not overwritten until the data is
successfully transferred.
117
CPU Overhead (%)
40
35
30
25
20
15
10
5
0
poll 5K
rt 5K
poll 1K
rt 1K
poll 100
rt 100
50 100 200
500m 1s
Interval
2s
5s
10s
Figure 4.8: The CPU overhead of polling TCP statistics (poll) and reading TCP table (rt) with
different number of connections (10, 100, 1K, 5K) and different intervals (from 50 ms to 10 sec).
4.6.3
Other Problems
SNAP has also detected other problems such as switch port failure (significant correlated packet
losses across multiple connections sharing the same switch port), receiver window negotiation
problems as reported in [77] (connections are always receiver window limited while receiver window
size stays small), receiver not reading the data fast enough (receiver window limited), and poor
latency caused by Nagle algorithm (sender application limited with small WriteBytes
4.7
Reducing SNAP CPU Overhead
To run in real time on all the hosts in the data center, SNAP must keep the CPU overhead
and data volume low. The volume of data is small because (i) SNAP logs socket calls and TCP
statistics instead of other high-overhead data such as packet traces and (ii) SNAP only logs the
TCP statistics when there is a performance problem. To reduce CPU overhead, SNAP allows the
operators to set the target percentage of CPU usage on each host. SNAP stays within a given
CPU budget by dynamically tuning the polling rate for different connections.
CPU Overhead of Profiling Since SNAP collects logs for all the connections at the host, the
overhead of SNAP consists of three parts: logging socket calls, reading the TCP table, and polling
TCP statistics.
Logging socket calls: In our data center, the cost of turning on the event tracing for socket logging
is a median of 1.6% of CPU capacity [82].
118
Cumulated fraction
1
0.8
0.6
0.4
0.2
established
0
10
100
1000
Number of connections
10000
Figure 4.9: Number of connections per machine.
Polling CPU statistics and reading TCP table: The CPU overhead of polling TCP statistics and
reading the TCP table depends on the polling frequency and the number of connections on the
machine. Figure 4.8 plots the CPU overhead on a 2.5 GHz Intel Xeon machine. If we poll TCP
statistics for 1K connections at 500 millisecond interval, the CPU overhead is less than 5%. The
CPU overhead of reading the TCP table is similar.
The CPU overhead is closely related to the number of connections on each machine. Figure 4.9
takes a snapshot of the distribution of the number of established connections per machine. There
are at most 10K established sockets and a median of 150. This means operators can configure the
interval of reading TCP table in most machines to be 500 millisecond or one second to keep the
CPU overhead lower than 5%.13 Since most of the connections in our data center are long-lived
connections (e.g., persistent HTTP connections), we can read the TCP table at a lower frequency
compared to TCP statistics polling. For the machines with many connections, we need to carefully
adjust the polling rate of TCP statistics for each connection to achieve a tradeoff between diagnosis
accuracy and the CPU overhead.
Dynamic Polling Rate Tuning To achieve the best tradeoff between CPU overhead and
accuracy, operators can first configure lCP U (uCP U ) to be the lower (upper) bound of the CPU
percentage used by SNAP. We then propose an algorithm to dynamically tune the polling rate
for different connections to keep CPU overhead between the two bounds. The basic idea of the
algorithm is to have high polling rate for those connections that are having performance issues
and have low polling rate for the others.
13 We
read TCP tables at 500 millisecond interval in our data collection.
119
CPU overhead (%)
12
CPU Usage
Target Ucpu
10
8
6
4
2
0
0
5
10
15
Time (sec)
20
25
Figure 4.10: Adjust CPU overhead by dynamically tuning TCP polling rate on a machine with
500 connections (ǫ = 1, r = 2).
We start polling all the connections on one host with the same rate (Step 1). Depending on the
number of connections on the host, we set the polling rate pr0 such that F (pr0 , #Connections) <
lCP U , where F (pr, #Connections) is a function to model the polling overhead based on the measurements in Figure 4.8. For example, based on Figure 4.8, if a machine has 1K connections, we
sample at 10 sec interval to keep the CPU overhead within 5%.
In Step 2, if the current CPU overhead is below lCP U , we pick a connection that has the most
performance problems in the past Thistory time, and increase its polling rate for more detailed
data. we use time[tnow −Thistory ,tnow ] (p, c) to record the time that connection c has problem p
over the sliding time window of size Thistory . Then we summarize all the time(p, c) over all the
performance classes p except sender application limited class that exist in the past Thistory . Note
that we also count the connections that closed in the past sliding window, to ensure we do not
inadvertently “undercount” problems affecting short-lived flows. We pick the connection c with
P
the largest p (time[tnow −Thistory ,tnow ] (p, c)) to increase its polling frequency by r.
Similarly in Step 3, we dynamically increase the polling rate by timing it with a constant
factor r for those connections that do not have many problems. Figure 4.10 shows how fast the
algorithm tunes the polling rate to keep the CPU overhead within the specified range of CPU
overhead range. We pick a machine with 500 connections, let lCP U = 9% and uCP U = 12% at
the beginning, and after 10 seconds switch the threshold to lCP U = 5% and uCP U = 8%. It takes
about 2.5 seconds for our algorithm to select the connections, increase the polling interval, and
reduce the CPU overhead down to 8%.
120
4.8
Related Work
Previous work in diagnosing performance problems focuses on either the application layer or the
network layer. SNAP addresses the interactions between them that cause particularly insidious
performance issues.
In the application layer, prior work has taken several approaches: instrumenting application
code [83, 84, 85] to find the causal path of problems, inferring the abnormal behaviors from
history logs [74, 75], or identifying fingerprints of performance problems [86]. In contrast, SNAP
focuses on profiling the interactions between applications and the network and diagnosing network
performance problems, especially ones that arise from those interactions.
In the network layer, operators use network monitoring tools (e.g., switch counters) and active
probing tools (ping, traceroute) to pinpoint network problems such as switch failures or congestion.
To diagnose network performance problems, capture and analysis of packet traces remains the goldstandard. T-RAT [87] uses packet traces to diagnosis throughput bottlenecks in Internet traffic.
Tcpanaly [68] uses packet traces to diagnose TCP stack problems. Others [88, 89] also infer the
TCP performance and its problems from packet traces. In contrast, SNAP focuses on the multitier applications in data centers where it has access to the network stack, enabling us to create
simple algorithms based on counters far cheaper to collect than packet traces to expose the network
performance problems of the applications.
4.9
Summary
SNAP combines socket-call logs of the application’s desired data-transfer behaviors with TCP
statistics from the network stack that highlight the delivery of data. SNAP leverages the knowledge of topology, routing, and application deployment in the data center to correlate performance
problems among connections, to pinpoint the congested resource or problematic software component.
Our experiences in the design, development, and deployment of SNAP demonstrate that it is
practical to build a lightweight, generic profiling tool that runs continuously in the entire data
center. Such a profiling tool can help both operators and developers in diagnosing network performance problems.
121
With applications in data centers getting more complex and more distributed, the challenges
of diagnosing the performance problems between the applications and the network will only grow
in importance in the years ahead. For future work, we hope to further automate the diagnosis
process to save developers’ efforts by exploring the appropriate variables to monitor in the stack,
studying the dependencies between the variables SNAP collects, and combining SNAP reports
with automatic analysis of application software.
122
Chapter 5
Conclusion
In conclusion, we propose a new management system that scales to many hosts, switches, and
policies, which consists of three components: BUFFALO, DIFANE, and SNAP. In this chapter, we
first discuss how these three components work together. Next, we summarize the key contributions
of the thesis. The thesis ends with a discussion of open issues and future work.
5.1
The Overall Picture of the New Management Systems
In this section, we discuss combining BUFFALO, DIFANE, and SNAP into a single management
system. As shown earlier in Figure 1.3 in Chapter 1, we have a centralized controller that configures the link weights for shortest path routing (BUFFALO), policies (DIFANE), and diagnoses
performance problems (SNAP). BUFFALO and DIFANE are located at switches — with BUFFALO providing a scalable forwarding layer and DIFANE providing a way to scalably support
policies. SNAP is located at each of the hosts collecting performance information for diagnosis.
Now we will discuss in more details how the three key components work together.
The data plane behavior of BUFFALO and DIFANE are complementary: Our BUFFALO design provides a compact way to store the forwarding table (that maps the destination
MAC addresses to the next hop) in the SRAM which performs exact match. In DIFANE, we
store low-level rules for customized routing, access control, and measurement in the TCAM which
performs wildcard matching.
123
Figure 5.1: Combining BUFFALO and DIFANE functions in the same data plane.
When BUFFALO and DIFANE work together, we use DIFANE to handle customized forwarding rules that match the destination host address to the egress switch, and use BUFFALO
to maintain the forwarding table that provides switch-to-switch reachability (Figure 5.1). We
first match the packets based on the rules in TCAM, which defines whether the packets are to
be dropped/forwarded and/or increments the counters. The routing rules in the TCAM of the
ingress switch or the authority switch only decide the egress switch that a flow of packets should
be forwarded. All the switches on the path match the packets based on the forwarding rules in
SRAM to forward the packets towards the correct egress switch.
Redirection in DIFANE and BUFFALO do not affect the performance:
Both BUF-
FALO and DIFANE leverage traffic redirection to overcome the limited memory at switches. With
BUFFALO and DIFANE working together, a packet may be first redirected to an authority switch
to hit the authority rules, and then redirected again at another switch in the path if it experiences
a false positive in the compact forwarding table.
Such redirections would not be a problem because most enterprise and data center networks
have a short end-to-end delay. Moreover, the chance of redirection is low because it only happens
when a packet experiences false positives in the bloom filters in BUFFALO or it experiences a
cache miss at the ingress switch in DIFANE. In general, it is a good tradeoff to save memory space
at switches at the expense of slightly longer latency for enterprise and data center networks.
124
The centralized controller combines DIFANE and SNAP functions:
In the new man-
agement system, the centralized controller is responsible for the interactions with operators. The
controller performs two major tasks: In DIFANE, the controller will translate the high-level policies to low-level rules, partition the rules, and then enforce them in the TCAM of the switches;
in SNAP, the controller collects the transport-layer statistics, socket-level logs, and the online
diagnosis results from all the hosts, correlates the performance problems across connections with
the knowledge of network topology, routing, and application deployment, and finally reports the
potential problems to the operators and application developers.
5.2
Deployments in Enterprises and Data Centers Differ
Although the proposed management system works for both enterprise and data center networks,
these two types of networks are different in topology, traffic pattern, and levels of control. As
a result, we find that BUFFALO and DIFANE fit enterprise networks better and SNAP works
better for data center networks. Here we discuss the differences between these two environments.
We also discuss how to make BUFFALO and DIFANE work better for data centers and how to
deploy SNAP in enterprises.
5.2.1
Differences Between Enterprise and Data Center Networks
There are three key differences between enterprise and data center networks:
Topology and traffic:
Data centers usually have specific topologies such as a fat tree, torus,
and clos, but enterprises can have any kind of topology. Therefore, for data centers much can
be gained from leveraging the specific topology in the design of the network architecture, but for
enterprises the design should work for any topology. Data centers can have a variety of traffic
patterns depending on the applications. In contrast, enterprise networks are more overprovisioned
than data centers. Therefore, it is fine to send traffic through longer paths but in data centers it is
important to reduce the bandwidth overhead of traffic redirection. Enterprise traffic is also more
sparse in traffic distribution, leading to more efficient caching of routing and access control rules.
Levels of control:
In enterprises, hosts are heterogeneous and come and go frequently, so
operators usually have little control over hosts. For example, in campuses and small companies,
125
people can bring in different laptops and mobile devices every day, and it is hard to force the
hosts to install any software or configuration.1 However, hosts in data centers have similar types
of hardware and are usually managed by a centralized controller. Therefore, enterprise networks
sometimes cannot take advantage of end-host capabilities while data center networks can.
5.2.2
Customizing the Management System for Enterprises and for Data
Centers
Now let us review the three components in our proposed management system and see how they
fit in enterprises and data centers.
BUFFALO and DIFANE naturally fit enterprise networks because they do not assume specific
topologies. Since the network is lightly loaded in enterprises, traffic indirection would not cause too
much congestion in the network. Data centers have more severe scalability problems and require
more scalable forwarding plane and policy enforcement schemes. In BUFFALO, we have shown
that the bound of extra delay is much smaller in a tree topology, but we still need to prove a better
bound for multi-rooted trees, which are common in data center. It is an interesting problem to
see how we can redesign DIFANE to leverage the specific topologies in data centers.
SNAP was designed for data center applications so it can leverage the topology, routing, and
the application deployment information to pinpoint the performance problems. We chose to deploy
SNAP at hosts to make the monitoring system more scalable and to directly tell the interactions
between applications and the network. In the enterprise environment, it is hard to deploy SNAP
directly because operators may not have control on hosts to install SNAP, or may not trust the
measurement results from the hosts. It would be interesting to find out ways to deploy SNAP at
only the server end in enterprises, or just on proxies that understand TCP. It is also interesting
to develop a secure way to run monitoring code at hosts so that hosts can trust the code and the
operators can trust the measurement results.
1 Large corporations have relatively more control on hosts because they can dictate what kinds of computers
users use and what software they can run [28].
126
5.3
Summary of Contributions
In this section, we revisit the principles we introduced in Chapter 1, and summarize the major
contributions we have in this thesis.
Placing the right functions at the right place: We revisit the placement of different network
functions to achieve better scalability and flexibility. In DIFANE, we use the centralized controller
to manage policies, but pull the function of rule processing back to the network, and distribute the
rules among authority switches to achieve better performance and scalability. In SNAP, we collect
diagnosis information and perform simple analysis at the hosts so that SNAP is more scalable than
in-network measurements. We then use the centralized controller to perform correlation across
the results from different hosts.
New algorithms and systems design: We propose new algorithms and data structures that
fit in today’s commodity switches and build new systems for enterprise and data center networks.
In BUFFALO, we propose a Bloom filter based forwarding architecture that leverages the flat
addresses and shortest path routing in edge networks. In DIFANE, we build a distributed directory
service of rules to quickly match packets to rules without the involvement of the controller. We
also design the wildcard rule partitioning algorithm which can efficiently handle a large number
of rules. Finally, in SNAP, we build a simple diagnosis system at the hosts leveraging TCP-level
statistics, and develop algorithms that correlate performance problems across connections sharing
the same resources or code.
Prototypes and deployment: To validate our algorithms and systems design, we built prototypes of BUFFALO with the Click-based modular router, DIFANE with the Click implementation
of OpenFlow, and SNAP with the Windows operating systems. SNAP has been deployed in a
production data center and identified real performance problems there.
5.4
Concluding Remarks
It is an exciting time to study the design and management of edge networks. These networks are
becoming more and more important to both people’s lives and the daily operations of corporations.
In addition, the edge networks are of high research interest because they are significantly different
127
from the backbone networks. For example, these edge networks have different types of topology,
different levels of control, and different types of traffic, which require us to rethink the design of
networks from scratch in these new settings. Unlike the Internet, most of enterprise and datacenter
networks are owned by a single entity and therefore are great opportunities for deploying these
clean slate designs in practice.
For future work, we hope to further identify the operators’ desires in edge networks and build
better architectures to support them. We also hope to customize our proposed management system
for enterprise and data center networks separately.
128
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