SplitStream: High-Bandwidth Multicast in Cooperative Environments Miguel Castro Peter Druschel

SplitStream: High-Bandwidth Multicast in Cooperative Environments Miguel Castro Peter Druschel
SplitStream: High-Bandwidth Multicast in Cooperative
Environments
Miguel Castro1
1
Peter Druschel2
Antony Rowstron1
Anne-Marie Kermarrec1
Atul Singh2
Animesh Nandi2
Microsoft Research, 7 J J Thomson Avenue, Cambridge, CB3 0FB, UK.
Rice University, 6100 Main Street, MS-132, Houston, TX 77005, USA∗.
2
ABSTRACT
Keywords
In tree-based multicast systems, a relatively small number of
interior nodes carry the load of forwarding multicast messages. This works well when the interior nodes are highlyavailable, dedicated infrastructure routers but it poses a problem for application-level multicast in peer-to-peer systems.
SplitStream addresses this problem by striping the content
across a forest of interior-node-disjoint multicast trees that
distributes the forwarding load among all participating peers.
For example, it is possible to construct efficient SplitStream
forests in which each peer contributes only as much forwarding bandwidth as it receives. Furthermore, with appropriate content encodings, SplitStream is highly robust to failures because a node failure causes the loss of a single stripe
on average. We present the design and implementation of
SplitStream and show experimental results obtained on an
Internet testbed and via large-scale network simulation. The
results show that SplitStream distributes the forwarding load
among all peers and can accommodate peers with different
bandwidth capacities while imposing low overhead for forest
construction and maintenance.
Peer-to-peer, application-level multicast, end-system multicast, content distribution, video streaming
Categories and Subject Descriptors
C.2.4 [Computer-Communications networks]: Distributed
Systems—Distributed applications; C.2.2 [Computer-Communications networks]: Network Protocols—Applications, Routing protocols; D.4.5 [Operating Systems]: Reliability—Faulttolerance; D.4.8 [Operating Systems]: Performance
General Terms
Algorithms, Measurement, Performance, Reliability, Experimentation
∗
Supported in part by NSF (ANI-0225660) and by a Texas
ATP (003604-0079-2001) grant.
Permission to make digital or hard copies of all or part of this work for
personal or classroom use is granted without fee provided that copies are
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permission and/or a fee.
SOSP’03, October 19–22, 2003, Bolton Landing, New York, USA.
Copyright 2003 ACM 1-58113-757-5/03/0010 ...$5.00.
1. INTRODUCTION
End-system or application-level multicast [8, 16, 22, 19,
40, 32, 13, 6, 23] has become an attractive alternative to IP
multicast. Instead of relying on a multicast infrastructure in
the network (which is not widely available), the participating hosts route and distribute multicast messages using only
unicast network services. In this paper, we are particularly
concerned with application-level multicast in peer-to-peer
(p2p) or cooperative environments where peers contribute
resources in exchange for using the service.
Unfortunately, conventional tree-based multicast is inherently not well matched to a cooperative environment. The
reason is that in any multicast tree, the burden of duplicating and forwarding multicast traffic is carried by the small
subset of the peers that are interior nodes in the tree. The
majority of peers are leaf nodes and contribute no resources.
This conflicts with the expectation that all peers should
share the forwarding load. The problem is further aggravated in high-bandwidth applications, like video or bulk file
distribution, where many peers may not have the capacity
and availability required of an interior node in a conventional
multicast tree. SplitStream addresses these problems by enabling efficient cooperative distribution of high-bandwidth
content in a peer-to-peer system.
The key idea in SplitStream is to split the content into k
stripes and to multicast each stripe using a separate tree.
Peers join as many trees as there are stripes they wish to
receive and they specify an upper bound on the number of
stripes that they are willing to forward. The challenge is to
construct this forest of multicast trees such that an interior
node in one tree is a leaf node in all the remaining trees and
the bandwidth constraints specified by the nodes are satisfied. This ensures that the forwarding load can be spread
across all participating peers. For example, if all nodes wish
to receive k stripes and they are willing to forward k stripes,
SplitStream will construct a forest such that the forwarding
load is evenly balanced across all nodes while achieving low
delay and link stress across the system.
Striping across multiple trees also increases the resilience
to node failures. SplitStream offers improved robustness to
node failure and sudden node departures like other systems
that exploit path diversity in overlays [4, 35, 3, 30]. Split-
Stream ensures that the vast majority of nodes are interior
nodes in only one tree. Therefore, the failure of a single
node causes the temporary loss of at most one of the stripes
(on average). With appropriate data encodings, applications can mask or mitigate the effects of node failures even
while the affected tree is being repaired. For example, applications can use erasure coding of bulk data [9] or multiple
description coding (MDC) of streaming media [27, 4, 5, 30].
The key challenge in the design of SplitStream is to construct a forest of multicast trees that distributes the forwarding load subject to the bandwidth constraints of the
participating nodes in a decentralized, scalable, efficient and
self-organizing manner. SplitStream relies on a structured
peer-to-peer overlay [31, 36, 39, 33] to construct and maintain these trees. We implemented a SplitStream prototype
and evaluated its performance. We show experimental results obtained on the PlanetLab [1] Internet testbed and
on a large-scale network simulator. The results show that
SplitStream achieves these goals.
The rest of this paper is organized as follows. Section 2
outlines the SplitStream approach in more detail. A brief description of the structured overlay is given in Section 3. We
present the design of SplitStream in Section 4. The results
of our experimental evaluation are presented in Section 5.
Section 6 describes related work and Section 7 concludes.
2.
THE SPLITSTREAM APPROACH
In this section, we give a detailed overview of SplitStream’s
approach to cooperative, high-bandwidth content distribution.
2.1 Tree-based multicast
In all multicast systems based on a single tree, a participating peer is either an interior node or a leaf node in the
tree. The interior nodes carry all the burden of forwarding multicast messages. In a balanced tree with fanout f
h
−1
and height h, the number of interior nodes is ff −1
and the
h
number of leaf nodes is f . Thus, the fraction of leaf nodes
increases with f . For example, more than half of the peers
are leaves in a binary tree, and over 90% of peers are leaves
in a tree with fanout 16. In the latter case, the forwarding
load is carried by less than 10% of the peers. All nodes have
equal inbound bandwidth, but the internal nodes have an
outbound bandwidth requirement of 16 times their inbound
bandwidth. Even in a binary tree, which would be impractically deep in most circumstances, the outbound bandwidth
required by the interior nodes is twice their inbound bandwidth. Deep trees are not practical because they are more
fault prone and they introduce larger delays, which is a problem for some applications.
2.2 SplitStream
SplitStream is designed to overcome the inherently unbalanced forwarding load in conventional tree-based multicast
systems. SplitStream strives to distribute the forwarding
load over all participating peers and respects different capacity limits of individual peers. SplitStream achieves this
by splitting the multicast stream into multiple stripes, and
using separate multicast trees to distribute each stripe.
Figure 1 illustrates how SplitStream balances the forwarding load among the participating peers. In this simple example, the original content is split into two stripes and mul-
Source
1
stripe 1
stripe 2
5
3
8
2
4
6
7
Figure 1: A simple example illustrating the basic
approach of SplitStream. The original content is
split into two stripes. An independent multicast tree
is constructed for each stripe such that a peer is an
interior node in one tree and a leaf in the other.
ticast in separate trees. For simplicity, let us assume that
the original content has a bandwidth requirement of B and
that each stripe has half the bandwidth requirement of the
original content. Each peer, other than the source, receives
both stripes inducing an inbound bandwidth requirement of
B. As shown in Figure 1, each peer is an internal node in
only one tree and forwards the stripe to two children, which
yields an outbound bandwidth of no more than B.
In general, the content is split into k stripes. Participating peers may receive a subset of the stripes, thus controlling
their inbound bandwidth requirement in increments of B/k.
Similarly, peers may control their outbound bandwidth requirement in increments of B/k by limiting the number of
children they adopt. Thus, SplitStream can accommodate
nodes with different bandwidths, and nodes with unequal
inbound and outbound network capacities.
This works well when the bandwidth bottleneck in the
communication between two nodes is either at the sender
or at the receiver. While this assumption holds in many
settings, it is not universally true. If the bottleneck is elsewhere, nodes may be unable to receive all desired stripes.
We plan to extend SplitStream to address this issue. For example, nodes could monitor the packet arrival rate for each
stripe. If they detect that the incoming link for a stripe
is not delivering the expected bandwidth, they can detach
from the stripe tree and search for an alternate parent.
2.3 Applications
SplitStream provides a generic infrastructure for highbandwidth content distribution. Any application that uses
SplitStream controls how its content is encoded and divided
into stripes. SplitStream builds the multicast trees for the
stripes while respecting the inbound and outbound bandwidth constraints of the peers. Applications need to encode
the content such that (i) each stripe requires approximately
the same bandwidth, and (ii) the content can be reconstructed from any subset of the stripes of sufficient size.
In order for applications to tolerate the loss of a subset of
stripes, they may provide mechanisms to fetch content from
other peers in the system, or may choose to encode content
in a manner that requires greater than B/k per stripe, in
return for the ability to reconstitute the content from less
than k stripes. For example, a media stream could be encoded using MDC so that the video can be reconstituted
from any subset of the k stripes with video quality proportional to the number of stripes received. Hence, if an interior
node in a stripe tree should fail then clients deprived of the
stripe are able to continue displaying the media stream at
reduced quality until the stripe tree is repaired. Such an encoding also allows low-bandwidth clients to receive the video
at lower quality by explicitly requesting less stripes.
Another example is the multicasting of file data with erasure coding [9]. Each data block is encoded using erasure
codes to generate k blocks such that only a (large) subset
of the k blocks is required to reconstitute the original block.
Each stripe is then used to multicast a different one of the k
blocks. Participants receive all stripes and once a sufficient
subset of the blocks is received the clients are able to reconstitute the original data block. If a client misses a number
of blocks from a particular stripe for a period of time (while
the stripe multicast tree is being repaired after an internal
node has failed) the client can still reconstitute the original
data blocks due to the redundancy. An interesting alternative is the use of rateless codes [24, 26], which provide
a simple approach to coordinating redundancy, both across
stripes and within each stripe.
Applications also control when to create and tear down a
SplitStream forest. Our experimental results indicate that
the maximum node stress to construct a forest and distribute
1 Mbyte of data is significantly lower than the node stress
placed on a centralized server distributing the same data.
Therefore, it is perfectly reasonable to create a forest to
distribute a few megabytes of data and then tear it down.
The results also show that the overhead to maintain a forest
is low even with high churn. Therefore, it is also reasonable
to create long-lived forests. The ideal strategy depends on
the fraction of time that a forest is used to transmit data.
2.4 Properties
Next, we discuss necessary and sufficient conditions for
the feasibility of forest construction by any algorithm and
relate them with what SplitStream can achieve.
Let N be the set of nodes and k be the number of stripes.
Each node i ∈ N wants to receive Ii (0 < Ii ≤ k) distinct
stripes and is willing to forward a stripe to up to Ci other
nodes. We call Ii the node’s desired indegree and Ci its
forwarding capacity. There is a set of source nodes (S ⊆ N )
whose elements originate one or more of the k stripes (i.e.,
1 ≤ |S| ≤ k). The forwarding capacity Cs of each source
node s ∈ S must at least equal the number of stripes that s
originates, Ts .
Definition 1. Given a set of nodes N and a set of sources
S ⊆ N , forest construction is feasible if it is possible to connect the nodes such that each node i ∈ N receives Ii distinct
stripes and has no more than Ci children.
The following condition is obviously necessary for the feasibility of forest construction by any algorithm.
Condition 1. If forest construction is feasible, the sum
of the desired indegrees cannot exceed the sum of the forwarding capacities:
∀i∈N
Ii ≤
Ci
(1)
∀i∈N
Condition 1 is necessary but not sufficient for the feasibility of forest construction, as the simple example in Figure 2
illustrates. The incoming arrows in each node in the figure
correspond to its desired indegree and the outgoing arrows
correspond to its forwarding capacity. The total forwarding
capacity matches the total desired indegree in this example
but it is impossible to supply both of the rightmost nodes
with two distinct stripes. The node with forwarding capacity three has desired indegree one and, therefore, it can only
provide the same stripe to all its children.
Sources
Figure 2: An example illustrating that condition 1
is not sufficient to ensure feasibility of a SplitStream
forest.
Condition 2 prevents this problem. It is sufficient to ensure feasibility because it prevents the concentration of forwarding capacity in nodes that are unable to forward all
stripes.
Condition 2. A sufficient condition for the feasibility of
forest construction is for Condition 1 to hold and for all
nodes whose forwarding capacity exceeds their desired indegree to receive or originate all k stripes, i.e.,
∀i : Ci > Ii ⇒ Ii + Ti = k.
(2)
This is a natural condition in a cooperative environment
because nodes are unlikely to spend more resources improving the quality of service perceived by others than on improving the quality of service that they perceive. Additionally, inbound bandwidth is typically greater than or equal
to outbound bandwidth in consumer Internet connections.
Given a set of nodes that satisfy Condition 2, the SplitStream algorithm can build a forest with very high probability provided there is a modest amount of spare capacity
in the system. The probability of success increases with
the minimum number of stripes that nodes receives,
Imin ,
and
the
total
amount
of
spare
capacity,
C
=
∀i∈N Ci −
∀i∈N Ii . We derive the following rough upper bound on
the probability of failure in Section 4.5:
C
Imin k−1
)
(3)
k
As indicated by the upper bound formula, the probability
of success is very high even with a small amount of spare
capacity in the system. Additionally, we expect Imin to be
large for most applications. For example, erasure coding for
reliable distribution of data and MDC for video distribution perform poorly if peers do not receive to most stripes.
Therefore, we expect configurations where all peers receive
all stripes to be common. In this case, the algorithm can
guarantee efficient forest construction with probability one
even if there is no spare capacity.
In an open cooperative environment, it is important to
address the issue of free loaders, which appear to be prevalent in Gnutella [2]. In such an environment, it is desirable
to strengthen Condition 1 to require that the forwarding capacity of each node be greater than or equal to its desired
|N | × k × (1 −
indegree (i.e., ∀i ∈ N : Ci ≥ Ii ). (This condition may be unnecessarily strong in more controlled settings, for example,
in a corporate intranet.) Additionally, we need a mechanism to discourage free loading such that most participants
satisfy the stronger condition. In some settings, it may be
sufficient to have the SplitStream implementation enforce
the condition in the local node. Stronger mechanisms may
use a trusted execution platform like Microsoft’s Palladium
or a mechanism based on incentives [28]. This is an interesting area of future work.
3.
0 2128-1
nodeId
key
d46a1c
65a1fc route(m,d46a1c)
d462ba
d4213f
BACKGROUND
SplitStream is implemented using tree-based applicationlevel multicast. There are many proposals for how applicationlevel multicast trees can be built and maintained [8, 19, 40,
13, 32, 22, 6, 23]. In this paper, we consider the implementation of SplitStream using Scribe [13] and Pastry [33]. It
could also be implemented using a different overlay protocol
and group communication system; for example, Bayeux on
Tapestry [39, 40] or Scribe on CAN [15]. Before describing the SplitStream design, we provide a brief overview of
Pastry and Scribe.
3.1 Pastry
Pastry is a scalable, self-organizing structured peer-topeer overlay network similar to CAN [31], Chord [36], and
Tapestry [39]. In Pastry, nodes and objects are assigned random identifiers (called nodeIds and keys, respectively) from
a large id space. NodeIds and keys are 128 bits long and can
be thought of as a sequence of digits in base 2b (b is a configuration parameter with a typical value of 3 or 4). Given
a message and a key, Pastry routes the message to the node
with the nodeId that is numerically closest to the key, which
is called the key’s root. This simple capability can be used
to build higher-level services like a distributed hash table
(DHT) or an application-level group communication system
like Scribe.
In order to route messages, each node maintains a routing
table and a leaf set. A node’s routing table has about log2b N
rows and 2b columns. The entries in row r of the routing
table refer to nodes whose nodeIds share the first r digits
with the local node’s nodeId. The (r + 1)th nodeId digit of
a node in column c of row r equals c. The column in row
r corresponding to the value of the (r + 1)th digit of the
local node’s nodeId remains empty. At each routing step, a
node normally forwards the message to a node whose nodeId
shares with the key a prefix that is at least one digit longer
than the prefix that the key shares with the present node’s
id. If no such node is known, the message is forwarded to a
node whose nodeId shares a prefix with the key as long as
the current node’s nodeId but is numerically closer. Figure 3
shows the path of an example message.
Each Pastry node maintains a set of neighboring nodes in
the nodeId space (called the leaf set), both to ensure reliable
message delivery, and to store replicas of objects for fault
tolerance. The expected number of routing hops is less than
log2b N . The Pastry overlay construction observes proximity in the underlying Internet. Each routing table entry is
chosen to refer to a node with low network delay, among all
nodes with an appropriate nodeId prefix. As a result, one
can show that Pastry routes have a low delay penalty: the
average delay of Pastry messages is less than twice the IP
delay between source and destination [11]. Similarly, one
d13da3
Figure 3: Routing a message from the node with
nodeId 65a1f c to key d46a1c. The dots depict the
nodeIds of live nodes in Pastry’s circular namespace.
can show the local route convergence of Pastry routes: the
routes of messages sent to the same key from nearby nodes
in the underlying Internet tend to converge at a nearby intermediate node. Both of these properties are important for
the construction of efficient multicast trees, described below.
A full description of Pastry can be found in [33, 11, 12].
3.2 Scribe
Scribe [13, 14] is an application-level group communication system built upon Pastry. A pseudo-random Pastry key,
known as the groupId, is chosen for each multicast group. A
multicast tree associated with the group is formed by the
union of the Pastry routes from each group member to the
groupId’s root (which is also the root of the multicast tree).
Messages are multicast from the root to the members using
reverse path forwarding [17].
The properties of Pastry ensure that the multicast trees
are efficient. The delay to forward a message from the root
to each group member is low due to the low delay penalty of
Pastry routes. Pastry’s local route convergence ensures that
the load imposed on the physical network is small because
most message replication occurs at intermediate nodes that
are close in the network to the leaf nodes in the tree.
Group membership management in Scribe is decentralized and highly efficient, because it leverages the existing,
proximity-aware Pastry overlay. Adding a member to a
group merely involves routing towards the groupId until the
message reaches a node in the tree, followed by adding the
route traversed by the message to the group multicast tree.
As a result, Scribe can efficiently support large numbers of
groups, arbitrary numbers of group members, and groups
with highly dynamic membership.
The latter property, combined with an anycast [14] primitive recently added to Scribe, can be used to perform distributed resource discovery. Briefly, any node in the overlay
can anycast to a Scribe group by routing the message towards the groupId. Pastry’s local route convergence ensures
that the message reaches a group member near the message’s sender with high probability. A full description and
evaluation of Scribe multicast can be found in [13]. Scribe
anycast is described in [14].
Source
M
M
StripeId 0x
M
Stripe Id 1x
StripeId Fx
NodeIds starting 0x
NodeIds starting Fx
NodeIds starting 1x
NodeIds starting 2x ..Ex
Figure 4: SplitStream’s forest construction. The
source splits the content and multicasts each stripe
in its designated tree. Each stripe’s stripeId starts
with a different digit. The nodeIds of interior nodes
share a prefix with the stripeId, thus they must be
leaves in the other trees, e.g., node M with a nodeId
starting with 1 is an interior node in the tree for
the stripeId starting with 1 and a leaf node in other
trees.
4.
SPLITSTREAM DESIGN
In this section, we describe the design of SplitStream. We
begin with the construction of interior-node-disjoint trees
for each of the stripes. Then, we discuss how SplitStream
balances the forwarding capacity across nodes, such that the
bandwidth constraints of each node are observed.
4.1 Building interior-node-disjoint trees
SplitStream uses a separate Scribe multicast tree for each
of the k stripes. A set of trees is said to be interior-nodedisjoint if each node is an interior node in at most one
tree, and a leaf node in the other trees. SplitStream exploits the properties of Pastry routing to construct interiornode-disjoint trees. Recall that Pastry normally forwards a
message towards nodes whose nodeIds share progressively
longer prefixes with the message’s key. Since a Scribe tree
is formed by the routes from all members to the groupId,
the nodeIds of all interior nodes share some number of digits with the tree’s groupId. Therefore, we can ensure that k
Scribe trees have a disjoint set of interior nodes simply by
choosing groupIds for the trees that all differ in the most
significant digit. Figure 4 illustrates the construction. We
call the groupId of a stripe group the stripeId of the stripe.
We can choose a value of b for Pastry that achieves the
value of k suitable for a particular application. Setting
2b = k ensures that each participating node has an equal
chance of becoming an interior node in some tree. Thus,
the forwarding load is approximately balanced. If b is chosen such that k = 2i , i < b, it is still possible to ensure this
fairness by exploiting certain properties of the Pastry routing table, but we omit the details due to space constraints.
Additionally, it is fairly easy to change the Pastry implementation to route using an arbitrary base that is not a power
of 2. Without loss of generality, we assume that 2b = k in
the rest of this paper.
4.2 Limiting node degree
The resulting forest of Scribe trees is interior-node-disjoint
and satisfies the nodes’ constraints on the inbound bandwidth. To see this, observe that a node’s inbound bandwidth is proportional to the desired indegree, which is the
number of stripes that the node chooses to receive. It is
assumed that each node receives and forwards at least the
stripe whose stripeId shares a prefix with its nodeId, because the node may have to serve as an interior node for
that stripe.
However, the forest does not necessarily satisfy nodes’
constraints on outbound bandwidth; some nodes may have
more children than their forwarding capacity. The number
of children that attach to a node is bounded by its indegree
in the Pastry overlay, which is influenced by the physical
network topology. This number may exceed a node’s forwarding capacity if the node does not limit its outdegree.
Scribe has a built-in mechanism (called “push-down”) to
limit a node’s outdegree. When a node that has reached
its maximal outdegree receives a request from a prospective child, it provides the prospective child with a list of
its current children. The prospective child then seeks to be
adopted by the child with lowest delay. This procedure continues recursively down the tree until a node is found that
can take another child. This is guaranteed to terminate
successfully with a single Scribe tree provided each node is
required to take on at least one child.
However, this procedure is not guaranteed to work in
SplitStream. The reason is that a leaf node in one tree may
be an interior node in another tree, and it may have already
reached its outdegree limit with children in this other tree.
Next, we describe how SplitStream resolves this problem.
4.3 Locating parents
The following algorithm is used to resolve the case where
a node that has reached its outdegree limit receives a join
request from a prospective child. First, the node adopts the
prospective child regardless of the outdegree limit. Then,
it evaluates its new set of children to select a child to reject. This selection is made in an attempt to maximize the
efficiency of the SplitStream forest.
First, the node looks for children to reject in stripes whose
stripeIds do not share a prefix with the local node’s nodeId.
(How the node could have acquired such a child in the first
place will become clear in a moment.) If the prospective
child is among them, it is selected; otherwise, one is chosen
randomly from the set. If no such child exists, the current
node is an interior node for only one stripe tree, and it selects
the child whose nodeId has the shortest prefix match with
that stripeId. If multiple such nodes exist and the prospective child is among them, it is selected; otherwise, one is
chosen randomly from the set. The chosen child is then notified that it has been orphaned for a particular stripeId.
This is exemplified in Figure 5.
The orphaned child then seeks to locate a new parent
in up to two steps. In the first step, the orphaned child
examines its former siblings and attempts to attach to a
random former sibling that shares a prefix match with the
stripeId for which it seeks a parent. The former sibling
either adopts or rejects the orphan, using the same criteria
as described above. This “push-down” process continues
recursively down the tree until the orphan either finds a new
parent or no children share a prefix match with the stripeId.
If the orphan has not found a parent the second step uses
the spare capacity group.
4.4 Spare capacity group
If the orphan has not found a parent, it sends an anycast
message to a special Scribe group called the spare capacity
080*
001*
0800
0800
0800 0800
089*
08B*
1800
081*
(1)
9*
001*
0800
080*
0800
0800
0800 0800
orphan
085*
0800
on 1800
089* 08B* 081*
9*
(2)
089*
0800
080*
0800 0800
0800
08B* 081*
085*
001*
0800
089*
080*
0800 0800
orphan
on 0800
08B* 081*
001*
(4)
(3)
Figure 5: Handling of prospective children by a node that has reached its outdegree limit. Circles represent
nodes and the numbers close to them are their nodeIds (* is a wildcard). Solid lines indicate that the bottom
node is a child of the top node and the number close to the line is the stripeId. Dashed lines represent
requests to join a stripe. The node with id 080* has reached its outdegree limit of 4. (1) Node 001* requests
to join stripe 0800. (2) Node 080* takes 001* as a child and drops 9*, which was a child in stripe 1800 that
does not share the first digit with 080*. (3) Then node 085* requests to join stripe 0800. (4) Node 080*
takes 085* as a child and drops 001*, which has a shorter prefix match with stripe 0800 than other children.
group. All SplitStream nodes that have less children in stripe
trees than their forwarding capacity limit are members of
this group. Scribe delivers this anycast message to a node
in the spare capacity group tree that is near the orphan in
the physical network. This node starts a depth-first search
(DFS) of the spare capacity group tree by forwarding the
message to a child. If the node has no children or they have
all been checked, the node checks whether it receives one
of the stripes which the orphaned child seeks to receive (in
general, this is the set of stripe groups that the orphan has
not already joined). If so, it verifies that the orphan is not
an ancestor in the corresponding stripe tree, which would
create a cycle. To enable this test, each node maintains its
path to the root of each stripe that it receives.
If both tests succeed, the node takes on the orphan as a
child. If the node reaches its outdegree limit as a result, it
leaves the spare capacity group. If one of the tests fails, the
node forwards the message to its parent and the DFS of the
spare capacity tree continues until an appropriate member
is found. This is illustrated in Figure 6.
The properties of Scribe trees and the DFS of the spare
capacity tree ensure that the parent is near the orphan in
the physical network. This provides low delay and low link
stress. However, it is possible for the node to attach to a
parent that is already an interior node in another stripe tree.
If this parent fails, it may cause the temporary loss of more
than one stripe for some nodes. We show in Section 5 that
only a small number of nodes and stripes are affected on
average.
Anycasting to the spare capacity group may fail to locate
an appropriate parent for the orphan even after an appropriate number of retries with sufficient timeouts. If the spare
capacity group is empty, the SplitStream forest construction
is infeasible because an orphan remains after all forwarding
capacity has been exhausted. In this case, the application
on the orphaned node is notified that there is no forwarding
capacity left in the system.
Anycasting can fail even when there are group members
with available forwarding capacity in the desired stripe. This
can happen if attaching the orphan to receive the stripe from
any of these members causes a cycle because the member is
the orphan itself or a descendant of the orphan. We solve
this problem as follows. The orphan locates any leaf in the
desired stripe tree that is not its descendant. It can do this
by anycasting to the stripe tree searching for a leaf that is
anycast
for 6
0
2
in: {0,3,A}
spare: 2
4
1 spare: 0 5
3
in: {1,…,16}
spare: 4
Figure 6: Anycast to the spare capacity group.
Node 0 anycasts to the spare capacity group to find
a parent for the stripe whose identifier starts with
6. The request is routed by Pastry towards the root
of the spare capacity group until it reaches node 1,
which is already in the tree. Node 1 forwards the
request to node 2, one of its children. Since 2 has no
children, it checks if it can satisfy node 0’s request.
In this case, it cannot because it does not receive
stripe 6. Therefore, it sends the request back to
node 1 and node 1 sends it down to its other child.
Node 3 can satisfy 0’s request and replies to 0.
not its descendant. Such a leaf is guaranteed to exist because
we require a node to forward the stripe whose stripeId starts
with the same digit as its nodeId. The orphan replaces the
leaf on the tree and the leaf becomes an orphan. The leaf
can attach to the stripe tree using the spare capacity group
because this will not cause a cycle.
Finally, anycasting can fail if no member of the spare capacity group provides any of the desired stripes. In this case,
we declare failure and notify the application. As we argue
next, this is extremely unlikely to happen when the sufficient
condition for forest construction (Condition 2) holds.
4.5 Correctness and complexity
Next, we argue informally that SplitStream can build a
forest with very high probability provided the set of nodes N
satisfies the sufficient condition for feasibility (Condition 2)
and there is a modest amount of spare capacity in the system. The analysis assumes that all nodes in N join the forest
at the same time and that communication is reliable to ensure that all the spare capacity in the system is available in
the spare capacity group. It also assumes that nodes do not
leave the system either voluntarily or due to failures. SplitStream includes mechanisms to deal with violations of each
of these assumptions but these problems may block some
parents that are available to forward stripes to orphans,
e.g., they may be unreachable by an orphan due to communication failures. If these problems persist, SplitStream
may be unable to ensure feasibility even if Condition 2 holds
at every instant. We ignore these issues in this analysis but
present simulation results that show SplitStream can cope
with them in practice.
The construction respects the bounds on forwarding capacity and indegree because nodes reject children beyond
their capacity limit and nodes do not seek to receive more
stripes than their desired indegree. Additionally, there are
no cycles by construction because an orphan does not attach
to a parent whose path to the root includes the orphan. The
issue is whether all nodes can receive as many distinct stripes
as they desire.
When node i joins the forest, it selects Ii stripes uniformly
at random. (The stripe whose stripeId starts with the same
digit as i’s nodeId is always selected but the nodeId is selected randomly with uniform probability from the id space.)
Then i joins the spare capacity tree advertising that it will
be able to forward the selected stripes and attempts to join
the corresponding stripe trees. We will next estimate the
probability that the algorithm leaves an orphan that cannot
find a desired stripe.
There are two ways for a node i to acquire a parent for
each selected stripe s: (1) joining the stripe tree directly
without using the spare capacity group, or (2) anycasting to
the spare capacity group. If s is the stripe whose stripeId
starts with the same digit as i’s nodeId, i is guaranteed to
find a parent using (1) after being pushed down zero or more
times and this may orphan another node. The algorithm
guarantees that i never needs to use (2) to locate a parent
on this stripe. The behavior is different when i uses (1) to
locate a parent on another stripe; it may fail to find a parent
but it will never cause another node to become an orphan.
When a node i first joins a stripe s, it uses (1) to find a
parent. If the identifiers of i and s do not share the first
digit, i may fail to find a parent for s after being pushed
down at most hs times (where hs is the height of s’s tree)
but it does not cause any other node to become an orphan.
If the trees are balanced we expect that hs is O(log|N |).
If the identifiers of i and s share the same digit, i is guaranteed to find a parent using (1) but it may orphan another
node j on the same stripe or on a different stripe r. In this
case, j attempts to use (1) to acquire a parent on the lost
stripe. There are three sub-cases: (a) j looses a stripe r
(r = s), (b) j looses stripe s and the identifiers of j and s
do not share the first digit, and (c) j looses stripe s and the
identifiers of j and s share the first digit. The algorithm
ensures that in case (a), the first digit in j’s nodeId does
not match the first digit in r’s stripeId. This ensures that
this node j does not orphan any other node when it uses (1)
to obtain a parent for r. Similarly, j will not orphan any
other node in case (b). In cases (a) and (b), j either finds a
parent or fails to find a parent after being pushed down at
most hr or hs times. In case (c), we can view j as resuming
the walk down s’s tree that was started by i.
Therefore, in all cases, i’s first join of stripe s results in at
most one orphan j (not necessarily i = j) that uses anycast
to find a parent for a stripe r (not necessarily r = s) after
O(log|N |) messages. This holds even with concurrent joins.
If an orphan j attempts to locate a parent for stripe r by
anycasting to the spare capacity group, it may fail to find
a node in the spare capacity group that receives stripe r.
We call the probability of this event Pf . It is also possible
that all nodes in the spare capacity group that receive r
are descendants of j. Our construction ensures that the
identifiers of j and r do not share the first digit. Therefore,
the expected number of descendants of j for stripe r should
be O(1) and small if trees are well balanced. The technique
that handles this case succeeds in finding a parent for j with
probability one and leaves an orphan on stripe r that has no
descendants for stripe r. In either case, we end up with a
probability of failure Pf and an expected cost of O(log|N |)
messages on success.
We will compute an upper bound on Pf . We start by
assuming that we know the set 1, ..., l of nodes in the spare
capacity group when the anycast is issued and their desired
indegrees I1 , ..., Il . We can compute an exact value for Pf
with this information:
I2
Il
I1
)(1 − )...(1 − )
k
k
k
If all nodes join at least Imin stripes, we can compute an
upper bound on Pf that does not require knowledge of the
desired indegrees of nodes in the spare capacity group:
Pf = (1 −
Imin l
)
k
We can assume that each node i in the spare capacity
group has spare capacity less than k; otherwise, Condition 2
implies that Ii = k and i can satisfy the anycast
request.
Since the spare capacity in the system C =
∀i∈N Ci −
I
is
the
minimum
capacity
available
in
the spare
i
∀i∈N
capacity group at any time, l ≥ C/(k − 1) and so
Pf ≤ (1 −
C
Imin k−1
)
k
This bound holds even with concurrent anycasts because we
use the minimum spare capacity in the system to compute
the bound.
There are at most |N | node joins and each node joins at
most k stripes. Thus the number of anycasts issued during
forest construction that may fail is bounded by |N | × k.
Since the probability of A or B occurring is less than or
equal to the probability of A plus the probability of B, the
following is a rough upper bound on the probability that the
algorithm fails to build a feasible forest
Pf ≤ (1 −
C
Imin k−1
)
k
The probability of failure is very low even with a modest amount of spare capacity in the system. For example,
the predicted probability of failure is less than 10−11 with
|N | = 1, 000, 000, k = 16, Imin = 1, and C = 0.01 × |N |.
The probability of failure decreases when Imin increases, for
example, it is 10−13 in the same setting when Imin = 8 and
C = 0.001 × |N |. When the desired indegree of all nodes
|N | × k × (1 −
equals the total number of stripes, the algorithm never fails.
In this case, it is guaranteed to build a forest if the sum of
the desired indegrees does not exceed the sum of the forwarding capacities even when there is no spare capacity.
Next, we consider the algorithmic complexity of the SplitStream forest construction. The expected amount of state
maintained by each node O(log|N |). The expected number
of messages to build the forest is O(|N |log|N |) if the trees
are well balanced or O(|N |2 ) in the worst case. We expect
the trees to be well balanced if each node forwards the stripe
whose identifier shares the first digit with the node’s identifier to at least two other nodes.
5.
EXPERIMENTAL EVALUATION
This section presents results of experiments designed to
evaluate both the overhead of forest construction in SplitStream and the performance of multicasts using the forest.
We ran large-scale experiments on a network simulation environment and live experiments on the PlanetLab Internet
testbed [1]. The results support our hypothesis that the
overhead of maintaining a forest is low and that multicasts
perform well even with high churn in the system.
5.1 Experimental setup
We start by describing the experimental setup.
Network simulation: We used a packet-level, discreteevent network simulator. The simulator models the propagation delay on the physical links but it does not model
queuing delay, packet losses, or cross traffic because modeling these would prevent large-scale network simulations.
In the simulations we used three different network topology
models: GATech, Mercator and CorpNet. Each topology has
a set of routers and we ran SplitStream on end nodes that
were randomly assigned to routers with uniform probability.
Each end node was directly attached by two LAN links (one
on each direction) to its assigned router. The delay on LAN
links was set to 1ms.
GATech is a transit-stub topology model generated by the
Georgia Tech [38] random graph generator. This model has
5050 routers arranged hierarchically. There are 10 transit
domains at the top level with an average of 5 routers in each.
Each transit router has an average of 10 stub domains attached, and each stub has an average of 10 routers. The link
delays between routers are computed by the graph generator
and routing is performed using the routing policy weights of
the graph generator. We generated 10 different topologies
using the same parameters but different random seeds. All
GATech results are the average of the results obtained by
running the experiment in each of these 10 topologies. We
did not attach end nodes to transit routers.
Mercator is a topology model with 102,639 routers, obtained
from measurements of the Internet using the Mercator system [21]. The authors of [37] used measured data and some
simple heuristics to assign an autonomous system to each
router. The resulting AS overlay has 2,662 nodes. Routing
is performed hierarchically as in the Internet. A route follows the shortest path in the AS overlay between the AS of
the source and the AS of the destination. The routes within
each AS follow the shortest path to a router in the next AS
of the AS overlay path. We use the number of IP hops as a
proxy for delay because there is no link delay information.
CorpNet is a topology model with 298 routers and was gener-
ated using measurements of the world-wide Microsoft corporate network. Link delays between routers are the minimum
delay measured over a one month period.
Due to space constraints, we present results only for the
GATech topology for most experiments but we compare
these results with those obtained with the other topologies.
SplitStream configuration: The experiments ran Pastry
configured with b = 4 and a leaf set with size l = 16. The
number of stripes per SplitStream multicast channel was
k = 2b = 16.
We evaluated SplitStream with six different configurations
of node degree constraints. The first four are designed to
evaluate the impact on overhead and performance of varying the spare capacity in the system. We use the notation
x × y to refer to these configurations where x is the value
of the desired indegree for all nodes and y is the forwarding
capacity of all nodes. The four configurations are: 16 × 16,
16×18, 16×32 and 16×N B. The 16×16 configuration has a
spare capacity of only 16 because the roots of the stripes do
not consume forwarding capacity for the stripes they originate. The 16 × 18 and 16 × 32 configurations provide a
spare capacity of 12.5% and 100%, respectively. Nodes do
not impose any bound on forwarding capacity in the 16×N B
configuration. SplitStream is able to build a forest in any
of these configurations with probability 1 (as shown by our
analysis).
The last two configurations are designed to evaluate the
behavior of SplitStream when nodes have different desired
indegrees and forwarding capacities. The configurations are
d × d and Gnutella. In d × d, each node has a desired indegree equal to its forwarding capacity and it picks stripes to
receive as follows: it picks the stripe whose stripeId has the
same first digit as its nodeId with probability 1 and it picks
each of the other stripes with probability 0.5. The analysis
predicts a low probability of success when building a forest
with the d × d configuration because there is virtually no
spare capacity in the system and nodes do not receive all
stripes. But SplitStream was able to build a forest successfully in 9 out of 10 runs.
The Gnutella configuration is derived from actual measurements of inbound and outbound bandwidth of Gnutella
peers [34]. The CDF of these bandwidths is shown in Figure 7. This distribution was sampled to generate pairs of inbound (bin ) and outbound (bout ) bandwidths for each SplitStream node. Many nodes have asymmetric bandwidth as
is often the case with DSL or cable modem connections.
We assumed a total bandwidth for a stream of 320Kbps
with 20Kbps per stripe. The desired indegree of a node was
set to max(1, min(bin /20Kbps, 16)) and the forwarding capacity to min(bout/20Kbps, 32). Approximately, 90% of the
nodes have a desired indegree of 16. The spare capacity in
the system is 6.9 per node. The analysis predicts a success probability of almost 1 when building a forest with this
configuration.
SplitStream Implementation: The SplitStream implementation used in the simulation experiments has three optimisations that were omitted in Section 4 for clarity.
The first optimisation reduces the overhead of cycle detection during forest construction. As described in Section 4,
each node maintains the path to the root of each stripe that
it receives. Maintaining this state incurs a considerable communication overhead because updates to the path are multi-
100
Cumulative proportion of nodes
1
Percentage of Hosts
80
60
40
Outbound
Inbound
20
0.9
0.8
0.7
0.6
16 x NB
0.5
16 x 32
0.4
16 x 18
0.3
16 x 16
0.2
0.1
0
0
1
10
100
1,000
10,000
100,000
1
1,000,000
10
100
cast to all descendants. We can avoid maintaining this state
by taking advantage of the prefix routing properties of Pastry. Cycles are possible only if some parent does not share
a longer prefix with a stripeId than one of its children for
that stripe. Therefore, nodes need to store and update path
information only in such cases. This optimisation reduces
the overhead of forest construction by up to 40%.
The second optimisation improves anycast performance.
When a node joins the SplitStream forest, it may need to
perform several anycasts to find a parent for different stripes.
Under the optimization, these anycasts are batched; the
node uses a single anycast to find parents for multiple stripes.
This optimization can reduce the number of anycasts performed during forest construction by up to a factor of eight.
The third optimization improves the DFS traversal of the
anycast tree. A parent adds the list of its children to an
anycast message before forwarding the message to a child. If
the child is unable to satisfy the anycast request, it removes
itself from the list and sends the message to one of its siblings
(avoiding another visit to the parent).
5.2 Forest construction overhead
The first set of experiments measured the overhead of forest construction without node failures. They started from
a Pastry overlay with 40,000 nodes and built a SplitStream
forest with all overlay nodes. All the nodes joined the spare
capacity and the stripe groups at the same time. The overheads would be lower with less concurrency.
We used two metrics to measure the overhead: node stress
and link stress. Node stress quantifies the load on nodes.
A node’s stress is equal to the number of messages that it
receives. Link stress quantifies the load on the network. The
stress of a physical network link is equal to the number of
messages sent over the link.
Node stress: Figures 8 and 9 show the cumulative distribution of node stress during forest construction with different
configurations on the GATech topology. Figure 8 shows results for the 16×y configurations and Figure 9 shows results
for d × d and Gnutella. A point (x, y) in the graph indicates
that a fraction y of all the nodes in the topology has node
stress less than or equal to x. Table 1 shows the maximum,
mean and median node stress for these distributions. The
results were similar on the other topologies.
Figure 8 and Table 1 show that the node stress drops as
10000
Figure 8: Cumulative distribution of node stress
during forest construction with 40,000 nodes on
GATech.
the spare capacity in the system increases. With more spare
capacity, nodes are orphaned less often and so there are less
pushdowns and anycasts. The 16 × N B configuration has
the lowest node stress because there are no pushdowns or
anycasts. The 16 × 16 configuration has the highest node
stress because each node uses an anycast to find a parent for
8 stripes on average. The nodes with the maximum node
stress in all configurations (other than 16 × N B) are those
with nodeIds closest to the identifier of the spare capacity
group. Table 1 shows that increasing the spare capacity of
the 16 × 16 configuration by only 12.5% results in a factor
of 2.7 decrease in the maximum node stress.
Conf.
Max
Mean
Median
16 × 16
2971
57.2
49.9
16 × 18
1089
52.6
47.4
16 × 32
663
35.3
30.9
16 × N B
472
16.9
12
d×d
2532
42.1
36.6
Gnut.
1054
56.7
54.2
Table 1: Maximum, mean and median node stress
during forest construction with 40,000 nodes on
GATech.
Figure 9 shows that the node stress is similar with Gnutella
and 16 × 16. Gnutella has a significant amount spare capacity but not all members of the spare capacity group receive
all stripes, which increases the length of the DFS traversals
of the anycast tree. d × d has the same spare capacity as
16 × 16 but it has lower node stress because nodes join only
9 stripe groups on average instead of 16.
1
Cumulative proportion of nodes
Figure 7: Cumulative distribution of bottleneck
bandwidth for both inbound and outbound network
links of Gnutella peers.
1000
Node Stress
Bandwidth (Kbps)
0.9
0.8
0.7
0.6
dxd
0.5
Gnutella
0.4
16 x 16
0.3
0.2
0.1
0
1
10
100
1000
10000
Node Stress
Figure 9: Cumulative distribution of node stress
during forest construction with 40,000 nodes on
GATech.
70
Average node stress
60
50
1
Cumulative proportion of links
We also ran experiments to evaluate the node stress during forest construction for overlays with different sizes. Figure 10 shows the mean node stress with the 16×x configurations. The maximum and median node stress show similar
trends as the number of nodes increases.
0.9
0.8
0.7
16 x NB
0.6
16 x 32
0.5
0.4
16 x 18
0.3
16 x 16
0.2
0.1
0
40
1
10
30
100
1000
10000
Link stress
20
16 x NB
16 x 18
10
Figure 11: Cumulative distribution of link stress
during forest construction with 40,000 nodes on
GATech.
16 x 32
16 x 16
0
0
5000
10000
15000
20000
25000
30000
35000
40000
Number of nodes in SplitStream
Figure 10: Mean node stress during forest construction with varying number of nodes on GATech.
From the analysis, we would expect the mean node stress
to be O(logn), where n is the number of nodes. But there
is a second effect that is ignored in the analysis; the average
cost of performing an anycast and joining a stripe group
decreases with the group size. The first effect dominates
when n is small and the second effect compensates the first
for large n. This suggests that our complexity analysis is
too pessimistic.
The results demonstrate that the node stress during forest construction is low and is largely independent of the
number of nodes in the forest. It is interesting to contrast
SplitStream with a centralized server distributing an s-byte
file to a large number of clients. With 40,000 clients, the
server will have a node stress of 40,000 handling requests
and will send a total of s × 40, 000 bytes. The maximum
node stress during SplitStream forest construction with the
16 × 16 configuration is 13.5 times lower, and the number of
bytes sent by each node to multicast the file over the forest
is bounded by s.
Link stress: Figure 11 shows the cumulative distribution
of link stress during forest construction with different configurations on GATech. A point (x, y) in the graph indicates
that a fraction y of all the links in the topology has link
stress less than or equal to x. Table 2 shows the maximum,
mean and median link stress for links with non-zero link
stress. It also shows the fraction of links with non-zero link
stress (links). Like node stress, the link stress drops as the
spare capacity in the system increases and the reason is the
same. The links with the highest stress are transit links.
The results were similar on the other topologies: the medians were almost identical and the averages were about 10%
lower in CorpNet and 10% higher in Mercator. The difference in the averages is explained by the different ratio of the
number of LAN links to the number of router-router links
in the topologies. This ratio is highest in CorpNet and it is
lowest in Mercator.
We conclude that the link stress induced during forest
construction is low on average. The maximum link stress
across all configurations is at least 6.8 times lower than the
maximum link stress in a centralized system with the same
number of nodes.
Conf.
Max
Mean
Med.
Links
16 × 16
5893
74.1
52.6
.99
16 × 18
4285
65.2
48.8
.99
16 × 32
2876
43.6
30.8
.99
16 × N B
1804
21.2
17
.94
d×d
5405
57.5
38
.99
Gnut.
5058
70.22
53
.99
Table 2: Maximum, mean, and median link stress
for used links and fraction of links (Links) used during forest construction with 40,000 nodes on GATech.
5.3 Forest multicast performance
We also ran experiments to evaluate the performance of
multicast over a SplitStream forest without failures. To put
this performance in perspective, we compared SplitStream,
IP multicast, and Scribe. IP multicast represents the best
that can be achieved with router support and Scribe is a
state-of-the-art, application-level multicast system that uses
a single tree. We used three metrics to evaluate multicast
performance in the comparison: node stress, link stress, and
delay penalty relative to IP.
The experiments ran on the 40,000-node Pastry overlay
that we described in the previous section. Our implementation of IP multicast used a shortest path tree formed by
the merge of the unicast routes from the source to each recipient. This is similar to what could be expected in our
experimental setting using protocols like Distance Vector
Multicast Routing Protocol (DVMRP) [18]. We created a
single group for IP multicast and Scribe that all overlay
nodes joined. The tree for the Scribe group was created
without the bottleneck remover [13].
To evaluate SplitStream, we multicast a data packet to
each of the 16 stripe groups of a forest with 40,000 nodes
(built as described in the previous section). For both Scribe
and IP multicast, we multicast 16 data packets to the single
group.
Node stress: During this multicast experiment, the node
stress of each SplitStream node is equal to its desired indegree, for example, 16 in the 16 × x configurations or less in
others. Scribe and IP multicast also have a node stress of 16.
The number of messages sent by each node in SplitStream
is also bounded by the forwarding capacity of each node, for
example, it is 16 in the 16 × 16 configuration. This is important because it enables nodes with different capabilities
to participate in the system.
500
17.6
16
131
0.13
1k
18.3
16
233
0.23
3k
17.7
16
509
0.52
10k
17.9
16
845
0.89
20k
18.7
16
1055
0.96
30k
20.22
16
1281
0.97
40k
20.4
16
1411
0.98
Table 3: Maximum, mean and median link stress for
used links and fraction of links (Links) used during
multicast with the 16 × 16 configuration on GATech
with varying number of nodes.
The next set of experiments compared the link stress during multicast with different SplitStream configurations and
40,000 nodes on GATech. Table 4 shows the maximum,
mean and median link stress for used links, and the fraction
of links used in these experiments. The results show that
the link stress tends to decrease when the spare capacity
increases. However, the absence of bounds on forwarding
capacity in (16 × N B) causes a concentration of stress in a
smaller number of links, which results in increased average
and maximum stress for used links. The average link stress
in d × d and Gnutella is lower because nodes receive less
stripes on average.
Conf.
Max
Mean
Med.
Links
16 × 16
1411
20.5
16
.98
16 × 18
1124
19
16
.98
16 × 32
886
19
16
.97
16 × N B
1616
20
16
.94
d×d
982
11.7
9
.97
Gnut.
1032
18.2
16
.97
centralized
639984
128.9
16
.43
Scribe
3990
39.6
16
.47
16 × 16
1411
20.5
16
.98
IP
16
16
16
.43
Table 5: Maximum, mean, and median link stress
for used links and fraction of links (Links) used by
centralized unicast, Scribe, IP, and SplitStream multicast with 40,000 nodes on GATech.
1
Cumulative proportion of links
Num.
Mean
Med.
Max
Links
Conf.
Max
Mean
Median
Links
0.9
0.8
0.7
0.6
16 x 16
0.5
IP Multicast
0.4
0.3
0.2
0.1
0
1
10
100
1000
10000
Link stress
(a) SplitStream vs IP
1
Cumulative proportion of links
Link stress: We start by presenting results of experiments
that measured link stress during multicast with different
SplitStream forest sizes. Table 3 shows the results of these
experiments with the 16×16 configuration in GATech. When
a SplitStream node is added to the system, it uses two additional LAN links (one on each direction) and it induces
a link stress of 16 in both. Adding nodes also causes an
increase on the link stress of router-router links because the
router network remains fixed. Since the majority of links
for the larger topologies are LAN links, the median link
stress remains constant and the mean link stress grows very
slowly. The maximum link stress increases because the link
stress in router-router links increases. This problem affects
all application-level multicast systems.
0.9
0.8
0.7
0.6
16 x 16
0.5
Scribe
0.4
0.3
0.2
0.1
0
1
10
100
1000
10000
Link stress
(b) SplitStream vs Scribe
Table 4: Maximum, mean, and median link stress
for used links and fraction of links (Links) used during multicast with different SplitStream configurations and 40,000 nodes on GATech.
Figure 12: Cumulative distribution of link stress
during multicast with 40,000 nodes on GATech.
We picked the SplitStream configuration that performs
worst (16 × 16) and compared its performance with Scribe,
IP multicast, and a centralized system using unicast. Figure 12 shows the cumulative distribution of link stress during
multicast for the different systems on GATech with 40,000
nodes. A point (x, y) in the graph indicates that a fraction
y of all the links in the topology has link stress less than or
equal to x. Table 5 shows the maximum, mean and median
link stress for used links, and the fraction of links used.
The results show that SplitStream uses a significantly
larger fraction of the links in the topology to multicast messages than any of the other systems: SplitStream uses 98%
of the links in the topology, IP multicast and the centralized unicast use 43%, and Scribe uses 47%. This is mostly
because SplitStream uses both outbound and inbound LAN
links for all nodes whereas IP multicast and the centralized
unicast only use inbound LAN links. Scribe uses all inbound
LAN links but it only uses outbound LAN links for a small
fraction of nodes (the interior nodes in the tree). We observed the same behavior on the other topologies.
SplitStream loads the links it uses less than Scribe. Table 5 shows that the average stress in links used by SplitStream is close to the average stress in links used by IP
multicast (28% worse). The average link stress in links used
by Scribe is 247% worse than that achieved by IP multicast. SplitStream also achieves a maximum link stress that
is almost a factor of 3 lower than Scribe’s. The comparison would be even more favorable to SplitStream with a
configuration with more spare capacity.
We also observed this behavior in the other topologies.
The average stress in links used by SplitStream is at most
13% worse than the average stress in links used by IP mul-
Delay penalty: Next, we quantify the delay penalty of
SplitStream relative to IP multicast. We computed two metrics of delay penalty for each SplitStream stripe: RMD and
RAD. To compute these metrics, we measured the distribution of delays to deliver a message to each member of a stripe
group using both the stripe tree and IP multicast. RMD is
the ratio between the maximum delay using the stripe tree
and the maximum delay using IP multicast, and RAD is the
ratio between the average delay using the stripe tree and the
average delay using IP multicast.
Figures 13 and 14 show RAD results for SplitStream multicast with different configurations with 40,000 nodes. They
present the cumulative RAD distribution for the 16 stripes.
A point (x, y) in the graph indicates that a fraction y of the
16 stripes has RAD less than or equal to y. The results for
RMD were qualitatively similar and the maximum RMD for
the configurations in the two figures was 5.4 in GATech and
4.6 in CorpNet.
16
Cumulative stripes
14
12
RAD (d x d)
10
RAD (Gnutella)
8
RAD (16 x 16)
6
4
2
0
0
2
3
4
5
(a) GATech
16
14
12
RAD (d x d)
10
RAD (Gnutella)
8
RAD (16 x 16)
6
4
2
0
0
16
1
Delay penalty
Cumulative stripes
ticast on CorpNet and at most 37% worse in Mercator. The
average link stress in links used by Scribe is 203% worse
than that achieved by IP multicast in CorpNet and 337%
worse in Mercator.
We conclude that SplitStream can deliver higher bandwidth than Scribe by using available bandwidth in node access links in both directions. This is a fundamental advantage of SplitStream relative to application level multicast
systems that use a single tree.
1
2
3
4
5
Delay penalty
Cumulative stripes
14
(b) CorpNet
12
RAD (16 x NB)
RAD (16 x 32)
RAD (16 x 18)
RAD (16 x 16)
10
8
Figure 14: Cumulative distribution of delay penalty
on GATech and CorpNet with 40,000 nodes.
6
4
2
0
0
0.5
1
1.5
2
2.5
Delay penalty
Figure 13: Cumulative distribution of delay penalty
with 16 × x configurations on the GATech topology
with 40,000 nodes.
Figure 13 shows that the delay penalty increases when the
spare capacity in the system decreases. The 16 × N B configuration provides the lowest delay because nodes are never
orphaned. The mechanisms to deal with orphaned nodes
(push down and anycast) increase the average depth of the
stripe trees. Additionally, the bounds on outdegree may
prevent children from attaching to the closest prospective
parent in the network. To put these results into context, if
the stripe trees were built ignoring physical network proximity, the average RAD would be approximately 3.8 for the
16 × N B configuration and significantly higher for the other
configurations.
Figure 14 shows that the RAD distribution is qualitatively
similar in GATech and CorpNet for three representative configurations. We do not present results for Mercator because
we do not have delay values for the links in this topology.
The delay penalty tends to be lower in CorpNet because
Pastry’s mechanism to exploit proximity in the network is
more effective in CorpNet than in GATech [12]. The figure
also shows that the delay penalty with Gnutella and with
16 × 16 is similar for most stripes. However, the variance
is higher in Gnutella because nodes with a very small forwarding capacity can increase the average depth of a stripe
tree significantly if they are close to the top of the tree. The
delay penalty is higher with d × d than with the other two
configurations because the average forwarding capacity is
lower (only 9), which results in deeper stripe trees.
We conclude that SplitStream achieves delay that is within
a small factor of optimal. This performance should be sufficient even for demanding applications that have an interactive component, e.g., large virtual class rooms.
5.4 Resilience to node failures
Previous experiments evaluated the performance of SplitStream without failures. This section presents results to
quantify performance and overhead with node failures. The
performance metric is the fraction of the desired stripes received by each node, and the overhead metric is the number
of control messages sent per second by each node (similar to
node stress).
Path diversity: The first set of experiments analyzed the
paths from each node i to the root of each stripe that i re-
Conf.
Max
Mean
Median
16 × 16
6.8
2.1
2
16 × 32
6.6
1.7
2
d×d
5.3
1.5
1
16 × N B
1
1
1
Gnut.
7.2
2.4
2
16
14
Number of Stripes
ceives. If all these paths are node-disjoint, a single node failure can deprive i of at most one stripe (until the stripe tree
repairs). SplitStream may fail to guarantee node-disjoint
paths when nodes use anycast to find a parent but this is
not a problem as the next results show.
12
10
8
6
Maximum
Average
Minimum
4
2
0
In a 40,000-node SplitStream forest on GATech, the mean
and median number of lost stripes when a random node fails
is 1 for all configurations. However, nodes may loose more
than one stripe when some nodes fail. Table 6 shows the
max, median, and mean number of stripes lost by a node
when its worst case ancestor fails. The number of stripes
lost is very small for most nodes, even when the worst case
ancestor fails. This shows that SplitStream is very robust
to node failures.
Catastrophic failures: The next experiment evaluated
the resilience of SplitStream to catastrophic failures. We
created a 10,000-node SplitStream forest with the 16 × 16
configuration on GATech and started multicasting data at
the rate of one packet per second per stripe. We failed 2,500
nodes 10s into the simulation.
Both Pastry and SplitStream use heartbeats and probes
to detect node failures. Pastry used the techniques described
in [25] to control probing rates; it was tuned to achieve 1%
loss rate with a leaf set probing period of 30s. SplitStream
nodes send heartbeats to their children and to their parents.
The heartbeats sent to parents allow nodes to detect when
a child fails so they can rejoin the spare capacity group. We
configured SplitStream nodes to send these hearbeats every
30s. In both Pastry and SplitStream, heartbeats and probes
are suppressed by other traffic.
Figure 15 shows the maximum, average, and minimum
number of stripes received by each node during the experiment. Nodes loose a large number of stripes with the large
scale failure but SplitStream and Pastry recover quickly.
Most nodes receive packets on at least 14 stripes after 30s
(one failure detection period) and they receive all stripes after 60s. Furthermore, all nodes receive all stripes after less
than 3 minutes.
Figure 16 breaks down the average number of messages
sent per second per node during the experiment. The line
labeled Pastry shows the Pastry overhead and the line labeled Pastry+SplitStream represents the total overhead, i.e.,
the average number of Pastry and SplitStream control messages. The figure also shows the total number of messages
including data packets (labeled Pastry+SplitStream+Data).
The results show that nodes send only 1.6 control messages per second before the failure. This overhead is very
low.
The overhead increases after the failure while Pastry and
SplitStream repair. Even after repair, the overhead is higher
than before the failure because Pastry uses a self-tuning
mechanism to adapt routing table probing rates [25]. This
mechanism detects a large number of failures in a short pe-
0
20
40
60
80
100
120
140
160
180
200
220
Time (seconds)
Figure 15: Maximum, average, and minimum number of stripes received when 25% out of 10,000 nodes
fail on GATech.
25
Number of messages per second
per node
Table 6: Worst case maximum, mean, and median
number of stripes lost at each node when a single
node fails.
20
Pastry
15
Pastry + SplitStream
Pastry + SplitStream + Data
10
5
0
0
20
40
60
80 100 120 140
Time (seconds)
160
180
200
220
Figure 16: Number of messages per second per node
when 25% out of 10,000 nodes fail on GATech.
riod and increases the probing rate (to the maximum in this
case). Towards the end of the trace, the overhead starts to
dip because the self-tuning mechanism forgets the failures it
registered.
High churn: The final simulation experiment evaluated the
performance and overhead of SplitStream with high churn
in the overlay. We used a real trace of node arrivals and
departures from a study of Gnutella [34]. The study monitored 17,000 unique nodes in the Gnutella overlay over a
period of 60 hours. It probed each node every seven minutes to check if it was still part of the Gnutella overlay. The
average session time over the trace was approximately 2.3
hours and the number of active nodes in the overlay varied
between 1300 and 2700. Both the arrival and departure rate
exhibit large daily variations.
We ran the experiment on the GATech topology. Nodes
joined a Pastry overlay and failed according to the trace.
Twenty minutes into the trace, we created a SplitStream
forest with all the nodes in the overlay at that time. We used
the 16 × 20 configuration. From that time on, new nodes
joined the Pastry overlay and then joined the SplitStream
forest. We sent a data packet to each stripe group every 10
seconds. Figure 17 shows the average and 0.5th percentile of
the number of stripes received by each node over the trace.
The results show that SplitStream performs very well even
under high churn: 99.5% of the nodes receive at least 75%
of the stripes (12) almost all the time. The average number
16
14
14
12
12
Number of stripes
Number of stripes
16
10
8
6
4
0.5th percentile
2
Average
10
8
6
4
Average
2
0
Minimum
0
0
10
20
30
40
50
60
0
20
40
60
Sequence number
Time (hours)
Figure 17: Number of stripes received with the
Gnutella trace on GATech.
80
100
Figure 19: Number of stripes received versus sequence number.
100000
Number of messages per second per
node
Minimum
Average
Maximum
10000
Absolute delay (msec)
of stripes received by each node is between 15 and 16 most
of the time.
Figure 18 shows the average number of messages per second per node in the Gnutella trace. The results show that
nodes send less than 1.6 control messages per second most
of the time. The amount of control traffic varies mostly
because Pastry’s self-tuning mechanism adjusts the probing
rate to match the observed failure rate. The number of control messages never exceeds 4.5 per second per node in the
trace. Additionally, the vast majority of these messages are
probes or heartbeats, which are small (50B on the wire).
Therefore, the overhead is very low, for example, control
traffic never consumes more than 0.17% of the total bandwidth used with a 1Mb/s data stream.
1000
100
10
1
0
20
40
60
Sequence number
80
100
Figure 20: Packet delays versus sequence number.
7
Pastry
6
Pastry + SplitStream
5
Pastry + SplitStream + Data
4
3
2
1
0
0
10
20
30
40
50
60
Time (hours)
Figure 18: Number of messages per second per node
with the Gnutella trace on GATech.
5.5 PlanetLab results
Finally, we present results of live experiments that evaluated SplitStream in the PlanetLab Internet testbed [1]. The
experiments ran on 36 hosts at different PlanetLab sites
throughout the US and Europe. Each host ran two SplitStream nodes, which resulted in a total of 72 nodes in the
SplitStream forest. We used the 16 × 16 configuration with
a data stream of 320Kbits/sec. A 20Kbit packet with a sequence number was multicast every second on each stripe.
Between sequence numbers 32 and 50, four hosts were randomly selected and the two SplitStream nodes running on
them were killed. This caused a number of SplitStream
nodes to loose packets from one or more stripes while the
affected stripe trees were repaired.
Figure 19 shows the average and minimum number of
stripe packets received by any live SplitStream node with
a particular sequence number. The effect of the failed nodes
can be clearly seen. The repair time is determined primarily
by SplitStream’s failure detection period, which triggers a
tree repair when no heartbeats or data packets have been
received for 30 seconds. As can be seen in Figure 19, once a
failure has been detected SplitStream is able to find a new
parent rapidly.
Figure 20 shows the minimum, average and maximum delay for packets received with each sequence number at all
SplitStream nodes. The delay includes the time taken to
send the packet from a source to the root of each stripe
through Pastry. Finally, Figure 21 shows the CDF of the
delays experienced by all packets received independent of
sequence number and stripe.
The delay spikes in Figure 20 are caused by congestion
losses in the Internet1 . However, Figure 21 shows that 90%
of packets experience a delay of under 1 second. Our results show that SplitStream works as expected in an actual
deployment, and that it recovers from failures gracefully.
1
TCP is used as the transport protocol; therefore, lost packets cause retransmission delays. A transport protocol that
does not attempt to recover packet losses could avoid these
delays.
1
nodes. However, it is possible to add this capability to CoopNet.
FCast [20] is a reliable file transfer protocol based on IP
multicast. It combines a Forward Error Correction [9] encoding and a data carousel mechanism. Instead of relying on
IP multicast, FCast could be easily built upon SplitStream,
for example, to provide software updates cooperatively.
In [10, 26], algorithms and content encodings are described
that enable parallel downloads and increase packet loss resilience in richly connected, collaborative overlay networks
by exploiting downloads from multiple peers.
0.9
Fraction of packets
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
200
400
600
800
1000 1200 1400 1600 1800 2000
Absolute delay (msec)
Figure 21: Cumulative distribution of packet delays.
5% of the packets experience a delay of greater then
2 seconds and the maximum observed delay is 11.7
seconds.
6.
RELATED WORK
Many application-level multicast systems have been proposed [16, 22, 32, 40, 13, 6, 23]. All are based on a single
multicast tree per sender. Several systems use end-system
multicast for video distribution, notably Overcast [22] and
SpreadIt [7]. SplitStream differs in that it distributes forwarding load over all participants using multiple multicast
trees, thereby reducing the bandwidth demands on individual peers.
Overcast organizes dedicated servers into a source-rooted
multicast tree using bandwidth estimation measurements to
optimize bandwidth usage across the tree. The main differences between Overcast and SplitStream are (i) that Overcast uses dedicated servers while SplitStream utilises clients;
(ii) Overcast creates a single bandwidth optimised multicast
tree, whereas SplitStream assumes that the network bandwidth available between peers is limited by their connections
to their ISP rather than the network backbone. This scenario is typical because most backbone links are over provisioned.
Nguyen and Zakhor [29] propose streaming video from
multiple sources concurrently, thereby exploiting path diversity and increasing tolerance to packet loss. They subsequently extend the work in [29] to use Forward Error Correction [9] encodings. The work assumes that the client is
aware of the set of servers from which to receive the video.
SplitStream constructs multiple multicast trees in a decentralized fashion and is therefore more scalable.
Apostolopoulos [4, 5] originally proposed utilising striped
video and MDC to exploit path diversity for increased robustness to packet loss. They propose building an overlay
composed of relays, and having each stripe delivered to the
client using a different source. The work examines the performance of the MDC, but does not describe an infrastructure to actually forward the stripes to the clients. CoopNet [30] implements such a hybrid system, which utilises
multiple trees and striped video using MDC. When the video
server is overloaded, clients are redirected to other clients,
thereby creating a distribution tree routed at the server.
There are two fundamental differences between CoopNet
and SplitStream: (i) CoopNet uses a centralised algorithm
(running on the server) to build the trees while SplitStream
is completely decentralised; and (ii) CoopNet does not attempt to manage the bandwidth contribution of individual
7. CONCLUSIONS
We presented the design and evaluation of SplitStream,
an application-level multicast system for high-bandwidth
data dissemination in cooperative environments. The system stripes the data across a forest of multicast trees to balance forwarding load and to tolerate faults. It is able to distribute the forwarding load among participating nodes while
respecting individual node bandwidth constraints. When
combined with redundant content encoding, SplitStream offers resilience to node failures and unannounced departures,
even while the affected multicast tree is repaired. The overhead of forest construction and maintenance is modest and
well balanced across nodes and network links, even with
high churn. Multicasts using the forest do not load nodes
beyond their bandwidth constraints and they distribute the
load more evenly over the network links than applicationlevel multicast systems that use a single tree.
The simulator and the versions of Pastry and SplitStream
that ran on top of it are available upon request from Microsoft Research. The version of Pastry and SplitStream
that ran on PlanetLab is available for download from: http:
//www.cs.rice.edu/CS/Systems/Pastry/FreePastry
Acknowledgements
We thank Manuel Costa, Alan Mislove and Ansley Post for useful discussions and help with implementation and experimentation; Steven Gribble, Krishna Gummadi and Stefan Saroiu for the
data from [34]; and Hongsuda Tangmunarunkit, Ramesh Govindan and Scott Shenker for the Mercator topology ([37]). We
would also like to thank Mayank Bawa, Amin Vahdat (our shepherd) and the anonymous reviewers for their comments on earlier
drafts.
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