Detecto | 6029 | Improved Intersection Operations during Detector Failures

Improved Intersection Operations during Detector Failures
1. Report No.
2. Government Accession No.
Technical Report Documentation Page
3. Recipient's Catalog No.
FHWA/TX-10/0-6029-1
4. Title and Subtitle
5. Report Date
IMPROVED INTERSECTION OPERATIONS DURING DETECTOR
FAILURES
November 2009
Published: March 2010
6. Performing Organization Code
7. Author(s)
8. Performing Organization Report No.
Srinivasa Sunkari, Praprut Songchitruksa, Hassan Charara, and Xiaosi
Zeng
Report 0-6029-1
9. Performing Organization Name and Address
10. Work Unit No. (TRAIS)
Texas Transportation Institute
The Texas A&M University System
College Station, Texas 77843-3135
11. Contract or Grant No.
12. Sponsoring Agency Name and Address
13. Type of Report and Period Covered
Texas Department of Transportation
Research and Technology Implementation Office
P.O. Box 5080
Austin, Texas 78763-5080
Technical Report:
September 2007–August 2009
Project 0-6029
14. Sponsoring Agency Code
15. Supplementary Notes
Project performed in cooperation with the Texas Department of Transportation and the Federal Highway
Administration.
Project Title: Fully Adaptive Detection-Control System for Isolated Intersections
URL: http://tti.tamu.edu/documents/0-6029-1.pdf
16. Abstract
The objective of this project was to develop three modules that would improve the efficiency of
intersection operations at isolated signalized intersections. The motivation for these modules was to use the
existing detectors more efficiently. This would in turn reduce the number of detectors required at the
intersection and also improve operations in case of detector failures. The adaptive variable initial module
(Module 1) can improve the typical variable initial feature available in most signal controllers by factoring
the turning movements at the intersections in real time along with queue distribution, and activity on
driveways between the detectors and stop bar. The detector failure module (Module 2) develops a rolling
database of phase utilizations of all phases at the intersections. The module uses this database to determine
the appropriate phase time when a detector failure is identified. The variable detector module (Module 3)
monitors the phase utilizations on the major-street phase and the volume on the right-turn and left-turn
detectors to vary the delay programmed on detectors to further improve the intersection operations.
Researchers evaluated Module 1 and Module 2 and found them improving the intersection operations.
However, initial implementations of Module 3 showed limited benefits and only under very rare conditions.
Thus, researchers did not develop Module 3 further. Modules 1 and 2 require data that are easily available
within the controller and can be incorporated into the signal controller firmware.
17. Key Words
18. Distribution Statement
Variable Initial, Detector Failure, Intersection
Efficiency, Detector Delay, D-CS
No restrictions. This document is available to the
public through NTIS:
National Technical Information Service
Springfield, Virginia 22161
http://www.ntis.gov
19. Security Classif.(of this report)
20. Security Classif.(of this page)
21. No. of Pages
Unclassified
Unclassified
86
Form DOT F 1700.7 (8-72) Reproduction of completed page authorized
22. Price
IMPROVED INTERSECTION OPERATIONS DURING DETECTOR
FAILURES
by
Srinivasa Sunkari
Research Engineer
Texas Transportation Institute
Praprut Songchitruksa
Associate Research Scientist
Texas Transportation Institute
Hassan Charara
Research Scientist
Texas Transportation Institute
and
Xiaosi Zeng
Research Associate
Texas Transportation Institute
Report 0-6029-1
Project 0-6029
Project Title: Fully Adaptive Detection-Control System for Isolated Intersections
Performed in cooperation with the
Texas Department of Transportation
and the
Federal Highway Administration
November 2009
Published: March 2010
TEXAS TRANSPORTATION INSTITUTE
The Texas A&M University System
College Station, Texas 77843-3135
DISCLAIMER
This research was performed in cooperation with the Texas Department of Transportation
(TxDOT) and the Federal Highway Administration (FHWA). The contents of this report reflect
the views of the authors, who are responsible for the facts and the accuracy of the data presented
herein. The contents do not necessarily reflect the official view or policies of the FHWA or
TxDOT. This report does not constitute a standard, specification, or regulation.
This report is not intended for construction, bidding, or permit purposes. The engineer in
charge of the project was Srinivasa Sunkari, P.E. (Texas) #87591. The United States
Government and the State of Texas do not endorse products or manufacturers. Trade or
manufacturers’ names appear herein solely because they are considered essential to the object of
this report.
v
ACKNOWLEDGMENTS
This research was conducted during a one-year study under a cooperative research
program with TxDOT and FHWA. Kelli Williams of the Odessa District was the project director.
Other TxDOT members of the project monitoring committee included, Larry Colclasure,
Noberto Aguirre, Don Baker, Adam Chodkeiwicz, Ted Copeland, Gordon Harkey, Ed
Kloboucnik, Rebecca Wells, and Wade Odell.
Texas Transportation Institute (TTI) researchers specifically thank signal technicians
from the Waco District, Houston District, and the City of Bryan for assisting us in the installation
of the equipment for this project. This project would not have been implemented without their
assistance.
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TABLE OF CONTENTS
Page
List of Figures ............................................................................................................................. viii List of Tables ................................................................................................................................ ix Introduction ................................................................................................................................... 1 Background ................................................................................................................................. 1 Advance Safety Strategies at Isolated Traffic Signals ............................................................ 1 Efficiency Issues at Isolated Signals ....................................................................................... 4 Existing Controller Features to Implement Improvements ..................................................... 4 Module Development .................................................................................................................... 9 Variable Initial ............................................................................................................................ 9 Queue Length Estimation ..................................................................................................... 10 Simplified Case ..................................................................................................................... 15 Adaptive Control ................................................................................................................... 16 Detector Failure ........................................................................................................................ 16 Detector Delay .......................................................................................................................... 18 Module Methodology .................................................................................................................. 23 Variable Initial .......................................................................................................................... 23 Scope ..................................................................................................................................... 23 Methodology ......................................................................................................................... 23 Detector Failure ........................................................................................................................ 25 Scope ..................................................................................................................................... 26 Methodology ......................................................................................................................... 26 Variable Delay .......................................................................................................................... 29 Scope ..................................................................................................................................... 30 Methodology ......................................................................................................................... 30 Module Implementation ............................................................................................................. 33 Site Selection ............................................................................................................................ 33 Waco District ........................................................................................................................ 33 Bryan District ........................................................................................................................ 33 Houston District .................................................................................................................... 33 Software Configuration ............................................................................................................. 37 Variable Initial ...................................................................................................................... 39 Detector Failure .................................................................................................................... 42 Variable Delay ...................................................................................................................... 44 Field Implementation ................................................................................................................ 45 Evaluation and Conclusion ........................................................................................................ 49 Module 1 ................................................................................................................................... 49 Module 2 ................................................................................................................................... 53 Measures of Effectiveness .................................................................................................... 53 Evaluation Scenarios............................................................................................................. 55 Evaluation Results ................................................................................................................ 55 Conclusions ............................................................................................................................... 72 References .................................................................................................................................... 75 vii
LIST OF FIGURES
Page
Figure 1. Typical Dilemma Zone Detector Layout for TxDOT (4). ............................................... 2 Figure 2. Potential Detector Layouts Used for D-CS, PIA, and AWEGS Type of Strategies. ...... 3 Figure 3. Variable Initial Timing. ................................................................................................... 5 Figure 4. Input-Output Technique for Queue and Delay Estimation............................................ 12 Figure 5. Hybrid Technique for Queue and Delay Estimation. .................................................... 13 Figure 6. Factors Influencing RTOR Capacity. ............................................................................ 20 Figure 7. Turn Bay, Driveway, and Detector Locations. .............................................................. 25 Figure 8. Detector Failure (Module 2) Architecture. .................................................................... 28 Figure 9. Illustration of Database Format. .................................................................................... 29 Figure 10. Flow Chart of the Factors Affecting Variable Delay Module. .................................... 32 Figure 11. Site Location in Waco District. ................................................................................... 34 Figure 12. Detector and Intersection Configuration at the Site in Waco District. ........................ 34 Figure 13. Site Location in Bryan District. ................................................................................... 35 Figure 14. Intersection and Detector Configuration at the Site in Bryan District. ....................... 35 Figure 15. Site Location in Houston District. ............................................................................... 36 Figure 16. Intersection and Detector Configuration at the Site in Houston District..................... 36 Figure 17. Phase Setting Configuration. ....................................................................................... 38 Figure 18. Detector Mapping Configuration. ............................................................................... 39 Figure 19. Variable Initial Setting Screen..................................................................................... 40 Figure 20. Driveway Setting Screen for Variable Initial. ............................................................. 41 Figure 21. Variable Initial Prediction. .......................................................................................... 42 Figure 22. Detector Failure Log.................................................................................................... 43 Figure 23. Green Prediction Log. ................................................................................................. 44 Figure 24. Right-Turn Delay Module Settings. ............................................................................ 45 Figure 25. D-CS Implementation Architecture. ............................................................................ 47 Figure 26. Installation of Adaptive D-CS in the Houston District near Conroe. .......................... 48 Figure 27. Accuracy of Predicted Initial Green (Phase 2). ........................................................... 50 Figure 28. Accuracy of Predicted Initial Green (Phase 6). ........................................................... 51 Figure 29. Relationship between Predicted Green and Queue Clearance (Phase 2). ................... 51 Figure 30. Relationship between Predicted Green and Queue Clearance (Phase 6). ................... 52 Figure 31. Error in Predicting the Initial Green. ........................................................................... 53 Figure 32. Example Comparison of Algorithms (Waco, Phase 2, 50% Failure). ......................... 59 Figure 33. Example Comparison of Algorithms (Waco, Phase 4, 50% Failure). ......................... 60 Figure 34. Example Comparison of Algorithms (Waco, Phase 5, 50% Failure). ......................... 60 Figure 35. Example Comparison of Algorithms (Conroe, Phase 2, 50% Failure). ...................... 64 Figure 36. Example Comparison of Algorithms (Conroe, Phase 4, 50% Failure). ...................... 64 Figure 37. Example Comparison of Algorithms (Conroe, Phase 5, 50% Failure). ...................... 65 Figure 38. Example Comparison of Algorithms (Bryan, Phase 2, 50% Failure). ........................ 69 Figure 39. Example Comparison of Algorithms (Bryan, Phase 4, 50% Failure). ........................ 69 Figure 40. Example Comparison of Algorithms (Bryan, Phase 5, 50% Failure). ........................ 70 Figure 41. Comparison of Algorithm Performance by Site (RMSE). .......................................... 72 viii
LIST OF TABLES
Page
Table 1. Modules Deployed at Each Site in This Project. ............................................................ 48 Table 2. Root Mean Square Error Comparison. ........................................................................... 53 Table 3. Waco―Mean and Variance of Green Durations (Mondays). ........................................ 56 Table 4. Waco―Mean and Variance of Change in Green Durations (Mondays). ....................... 57 Table 5. Naïve Prediction versus Ground Truth by Phase (Waco, 50% Failure). ........................ 58 Table 6. Advanced Algorithm versus Ground Truth by Phase (Waco, 50% Failure). ................. 58 Table 7. Comparison of Algorithm Performance by Phase (Waco, 50% Failure). ...................... 58 Table 8. Comparison of Performance for All Phases (Waco, 50% Failure). ................................ 59 Table 9. Conroe―Mean and Variance of Green Durations (Mondays). ...................................... 61 Table 10. Conroe―Mean and Variance of Change in Green Durations (Mondays).................... 62 Table 11. Naïve Prediction versus Ground Truth by Phase (Conroe, 50% Failure). .................... 63 Table 12. Advanced Algorithm versus Ground Truth by Phase (Conroe, 50% Failure). ............. 63 Table 13. Comparison of Algorithm Performance by Phase (Conroe, 50% Failure). .................. 63 Table 14. Comparison of Algorithm Performance for All Phases (Conroe, 50% Failure). .......... 64 Table 15. Bryan―Mean and Variance of Green Durations (Mondays). ...................................... 66 Table 16. Bryan―Mean and Variance of Change in Green Durations (Mondays)...................... 67 Table 17. Naïve Prediction versus Ground Truth by Phase (Bryan, 50% Failure). ...................... 68 Table 18. Advanced Algorithm versus Ground Truth by Phase (Bryan, 50% Failure). ............... 68 Table 19. Comparison of Algorithm Performance by Phase (Bryan, 50% Failure). .................... 68 Table 20. Comparison of Algorithm Performance for All Phases (Bryan, 50% Failure). ............ 69 Table 21. Overall Performance Comparison at Varying Rates of Detector Failure. .................... 71 Table 22. Detector Failure Rate and Average Length of Failure Time. ....................................... 71 ix
INTRODUCTION
BACKGROUND
Improving operations at signalized intersections is an important objective for the Texas
Department of Transportation (TxDOT). TxDOT has been proactively tackling the issue of
improving safety by using alternative signal control strategies over the past few years. The Texas
Transportation Institute (TTI) with support from TxDOT has developed a number of strategies to
address the issue of improving safety at high-speed isolated signalized intersections. These
include Detection-Control System (D-CS) (1), Platoon Identification Algorithm (PIA) (2), and
Advance Warning of End-of-Green System (AWEGS) (3). These advance strategies improve the
safety at the intersections and enhance the signal operations.
Along with improving safety, there is a need to improve the overall efficiency of the
intersection operations. The implementation of the above-mentioned advance strategies has
highlighted the importance of detection at the intersection for efficient operations. There are
many controller features available to improve the efficiency of intersections. However, these
features are deployed without considering existing volume conditions. Therefore, this project
developed an adaptive system that considers the current traffic and historical traffic conditions in
order to improve the intersection efficiency. Such a system is not only applicable at intersections
utilizing advance safety strategies like D-CS but also at non-D-CS intersections, thereby
significantly increasing the utility of this system. It is also anticipated that signal controller
vendors will be interested in incorporating this system into the signal controller firmware,
making it very easy to implement by TxDOT.
Advance Safety Strategies at Isolated Traffic Signals
TxDOT typically uses two to three detectors per lane on high-speed approaches to
improve safety by reducing dilemma zone conflicts (4). TxDOT’s configuration is illustrated in
Figure 1. The detector locations are based on approach speeds and operate in pulse mode with an
extension ranging from 1.2 to 2.0 seconds. The configuration also calls for a stop-bar detector,
which is configured as a queue discharge detector.
1
Extension
350
6 x 40
475
600
1.2
Detector Placement, 70 mph
320
430
540
Detector Placement, 65 mph
6 x 40
375
475
275
Detector Placement, 60 mph
6 x 40
6 x 40
225
320
415
Detector Placement, 55 mph
1.2
1.4
1.2
2.0
6 x 40
220
350
Detector Placement, 50 mph
2.0
6 x 40
175
290
Detector Placement, 45 mph
2.0
6 x 40
110/90
240/190
Detector Placement, 40/35 mph
Figure 1. Typical Dilemma Zone Detector Layout for TxDOT (4).
Over the past few years, TxDOT and TTI have developed three advance strategies to
further improve safety on high-speed approaches to isolated signalized intersections. These are
the D-CS, PIA, and AWEGS. All three strategies use advance detection on the high-speed
approaches. The advance detection is in the form of two detectors per lane at a distance of
between 750 feet to 1200 feet and depends on the approach speeds. The objective of the advance
detectors is to detect high-speed vehicles, their speeds, and their classification. Even though the
detector configuration in Figure 1 includes a stop-bar detector, some TxDOT districts do not
2
install stop-bar detectors. This is primarily because detectors at stop bars typically have higher
failure rates due to the rigors of vehicles braking/stopping and accelerating on them. The
function of stop-bar detectors is to improve intersection efficiency by clearing the queue at the
start of green, and the districts modify the controller parameters to account for the absence of
stop-bar detectors. Figure 2 illustrates a typical detector layout being used at locations.
PIA and AWEGS strategies use the existing TxDOT detector configuration illustrated in
Figure 2 along with the advance detectors, even though stop-bar detectors are not required for the
PIA and AWEGS algorithms. On the other hand, the D-CS strategy does not require dilemma
zone detectors for its operation but does require stop-bar detectors.
Dilemma Zone
Detectors
Minor Street
Stop Bar
Detectors
Advance Detectors
Major Street
Figure 2. Potential Detector Layouts Used for D-CS, PIA, and AWEGS Type of Strategies.
Strategies like D-CS (1), PIA (2), and AWEGS (3) have proved to significantly improve
safety at signalized intersections by reducing red-light running by over 35 to 60 percent.
Moreover, the same infrastructure can be used to enhance operational efficiency at intersections.
These improvements to efficiency can further improve the functionality of intersections where
strategies like D-CS, PIA, and AWEGS are deployed. These improvements to operational
efficiency are also applicable to typical intersections across the state.
3
Efficiency Issues at Isolated Signals
There are a number of techniques to improve operational efficiency at signalized
intersections. This project developed three strategies of using both historical and real-time
detector information to improve intersection efficiency. Two of the strategies are:

to use detection from advance detectors to efficiently customize and determine the
minimum green required in the absence of stop-bar detectors, and

to operate the intersection during detector failures without relying on a constant call
on the phase(s) resulting in a max out.
A third strategy for varying the detector delay for right-turn detectors and left-turn
detectors was developed. Researchers, however, found that the strategy had very limited
applicability and the benefits from the strategy were limited. Therefore, researchers did not
incorporate this strategy into the system. Still, this report will discuss TTI researcher’s efforts in
developing this strategy.
Existing Controller Features to Implement Improvements
Traffic signal controllers have numerous features (5) to improve intersection operations.
Some of these features can specifically be applied to improve the intersection efficiency for the
strategies mentioned earlier. These are discussed in this section.
Variable Initial (6)
Under variable initial timing, the duration of the initial portion of the green (the first
timed portion of the green interval) can increase depending on the number of vehicle actuations
stored on the phase while its signal is displaying yellow or red. The variable initial timing period
can be thought of as a “variable minimum green” and is determined by the following three
parameters:

minimum green time, which determines the minimum variable initial time period;

seconds per actuation, which determines the time by which the variable initial time
will be increased (starting from zero) with each vehicle actuation received during the
yellow and red intervals of the phase; and

maximum initial, which is the maximum of the variable initial timing period.
4
Figure 3 shows the effect of these parameters on the variable initial timing period. The
figure shows how the initial timing starts with the minimum green time. Once the number of
vehicle actuations multiplied by the seconds per actuation becomes larger than the minimum
green time, the initial timing takes on the former value, until it reaches the maximum initial
value, which acts as an upper limit.
Variable initial timing is most effectively used when setback detectors are provided such
that in the absence of stop-bar detection, the initial timing can be incremented to the appropriate
value required to service vehicles that queue between the stop line and the setback detector.
Variable initial timing requires point detection to operate, so it may not be appropriate to use
with the zone detection provided by video detection.
Variable initial can be very easily applied for a single lane approaching an intersection
that has low turning movement volumes and where there are no driveways between the advance
detector and intersection stop bar. However, programming the variable initial becomes more
complicated for multi-lane approaches and at locations where a common lead-in wire is used for
multiple detectors.
Initial Timing (seconds)
Maximum initial
Initial timing
Added initial range
Seconds per actuation
Minimum green
Number of vehicle actuations
multiplied by the seconds per
actuation value
Number of Vehicle Actuations
Figure 3. Variable Initial Timing.
Detector Failure
One of the causes of inefficient intersection control is due to detector failure. It is
reported that about 50 percent of the inductive loops are malfunctioning at any given time. The
5
National Traffic Signal Report Card (7), which surveyed 378 agencies across the country,
indicates that the detection system received a grading of F for detector systems. Failure of
detectors results in the controller receiving a continuous call for that particular phase. This
results in a significantly inefficient operation.
Over the years, a number of fully adaptive systems have been developed with the
objective of predicting the traffic demand based on historical volumes. The Smart Diamond
Project (8) conducted by TTI in the mid-1990s looked at predicting volumes by populating a
database of measured traffic volumes. The objective was to mine historical patterns of traffic
data and make strategic and tactical decisions about future traffic demands. The Smart Diamond
study developed a database of four-week traffic demand. The system used the observed traffic
demands combined with historical demands to produce forecast demands that were to be used to
generate new signal timings. The same philosophy can be used to predict traffic demand during
detector failures. Current controllers have the capability to log the green utilization for each
phase. This parameter can be an indicator of the traffic demand at the intersection and can
potentially be used to predict the traffic demand due to malfunction of detectors.
Delay on Detectors
Currently, traffic engineers using National Electrical Manufacturers Association (NEMA)
controllers (5) have the capability to program a specific amount of delay into the controller for a
specific detector. Historically, engineers programmed the same delay into the detector amplifier.
According to NEMA TS-2 specifications (5), a delay is defined as the ability of a detector to
delay its output for a predetermined length of time after a vehicle has entered its zone of
detection. When selected, the detector output is delayed for the time set. If the vehicle departs
before the time set, an output does not occur and the timer is reset. The delay time is adjustable
over the range of 0 to 30 seconds and remains a constant value.
A detector delay is typically used to permit the left-turning vehicles on the permitted
portion of the protected-permitted left-turn phase along the arterial to find gaps in the opposing
through movements. This delay reduces the unnecessary terminations of the opposing arterial
phase. A similar strategy is used to allow the right-turning vehicles on minor streets to find gaps
in the major-street through movements. A variable call delay based on traffic volumes at the
intersections can improve intersection efficiency.
6
The controller features currently employed to improve efficiency operate in a static
manner. They also do not react to detector failures. The adaptive system proposed in this project
can make the features more efficient and allow these improvements to be incorporated into the
signal controller software.
7
MODULE DEVELOPMENT
Researchers developed and evaluated three modules in this project to improve
intersection operations. The first module’s objective is to improve the use of variable initial
features in the absence of stop-bar detection. Such a system is adaptive in nature and accounts
for various detector configurations, the number of lanes, and the number, location, and use of
driveways. The objective of the second module is to improve intersection operations during
detection failure. Currently during a detector failure for a particular phase, the phase gets a
continuous call, resulting in inefficient operation. However, in this module, when a detector
failure is identified, the system relies upon historical traffic demand data to assign appropriate
phase time to improve intersection operations. The third module applies an appropriate delay for
the right-turn detector and/or left-turn detector to minimize phase terminations for the major
movements. This feature can improve intersection efficiency and safety.
VARIABLE INITIAL
The variable initial (VI) is a timing feature in a controller designed to allocate a varying
amount of initial green based on traffic demand as observed by the number of non-green
actuations at respective phases. The VI time is a computed value that is at least as large as the
minimum green time and not more than the maximum initial time.
The VI timing period is determined by the following time settings (9):

The minimum green setting determines the minimum VI time period.

The added initial setting determines the time by which the VI time period will be
increased from zero with each vehicle actuation received during the associated phase
yellow and red intervals.

The maximum initial setting determines the maximum VI time period. The maximum
initial setting is subordinate to the minimum green time setting. Therefore, the
minimum green time must be satisfied regardless of the maximum initial setting.
The VI time period can be expressed as follows:
)
;
9
The following section provides an overview of past research on queue length estimation.
In a variable initial module, queue length is a key variable in determining how the initial green
should be configured. This section summarizes methodology and results of past research
attempts on this issue.
Queue Length Estimation
Li (10) proposed an online queue length estimation algorithm using the flow conservation
law. The algorithm requires both stop-bar and advance detectors to work properly. Let m(t+1),i be
the number of vehicles stored between stop-bar and advance detectors at the end of (t+1)th green
for the subject lane i; then, m(t+1),i can be calculated as
mt 1,i  mt ,i  mat ,i  nat ,i  md t ,i Where:
mt,i = number of vehicles between two detectors at the end of tth green for lane i,
mat,i = new arrivals observed by the advance detector until the end of tth red,
nat,i = vehicle arrivals observed by the advance detector during the next (t+1)th green, and
mdt,i = departures observed by the stop-bar detector during the (t+1)th green.
While Li’s algorithm can theoretically track the number of vehicles in the queue, its
performance is subject to uncontrollable cumulative errors stemmed from detector malfunctions.
Xu et al. (11) proposed an online algorithm to estimate queue length at isolated signalized
intersections. The algorithm uses the vehicle arrival information from stop-bar and advance
detections to estimate queue length. The proposed algorithm consists of two parts. First, the
algorithm tries to identify the first vehicle in the queue after the amber onset. Then, the algorithm
estimates the physical queue lengths using the following parameters: (a) the average distance
from the front bumper of the first vehicle in the queue to the stop bar, (b) the average intervehicle spacing of vehicles in the queue, and (c) the vehicle lengths. The vehicles are considered
joining the queue if their speed drops below a pre-specified threshold.
This algorithm was tested only in a simulated environment. It considered only a
simplified case of a single-lane approach with no turn lanes. No specific discussions on how it
could be extended to multi-lane approaches were provided. Several parameters required for the
algorithm must be properly calibrated, but no guidelines were provided on how these parameters
10
should be configured. A sensitivity analysis of the parameters in the algorithm was also not
studied.
Sharma et al. (12) proposed a hybrid algorithm using real-time advance and stop-bar
detections to estimate queue length and delay at a signalized intersection. Traffic engineers
commonly use three types of delay to evaluate intersection performance:

stopped delay: delay incurred when a vehicle stops completely;

approach delay: delay incurred when a vehicle decelerates, stops, and then accelerates
again until it crosses a stop bar; and

control delay: delay incurred when a vehicle decelerates, stops, and then accelerates
until it resumes the desired travel speed.
This paper described two approaches for estimating delay and maximum queue length.
The input-output technique uses advance detector actuations, phase change data, and parametric
data (e.g., saturation headway, storage capacity, etc.) as model inputs. The advance detector
actuations are used to track arrivals at intersection approach over time. The phase status and
saturation headway data are used to estimate the number of departures from the stop bar over
time. These two profiles are combined to estimate the queue accumulation at the intersection
approach. The second approach, the hybrid technique, incorporates stop-bar actuations as
additional model inputs. In comparison with the first approach, the stop-bar actuations and phase
statuses are used to estimate real-time vehicle departures instead of saturation headway. The
inductive loop detector (ILD) vehicle signature identification techniques are used to count
vehicles crossing the stop bar. Both techniques estimate delay and maximum queue length once
each cycle. The techniques were developed based on the assumptions that the vehicles do not
change lanes after passing the advance detectors and that the vehicles in the queue will follow
the first-in-first-out (FIFO) principle. Figure 4 and Figure 5 depict the profiles obtained from
input-output and hybrid algorithms, respectively.
11
7
Arrival
Departure
6
Number of Vehicles
5
4
3
2
1
0
0
10
20
30
40
50
60
40
50
60
Tim e (sec)
4.5
Queue
4
Number of Vehicles
3.5
3
2.5
2
1.5
1
0.5
0
0
10
20
30
Time (sec)
Figure 4. Input-Output Technique for Queue and Delay Estimation.
12
7
Arrival
Departure
6
Number of Vehicles
5
4
3
2
1
0
0
10
20
30
40
50
60
40
50
60
Tim e (sec)
4.5
Queue
4
Num ber of Vehicles
3.5
3
2.5
2
1.5
1
0.5
0
0
10
20
30
Time (sec)
Figure 5. Hybrid Technique for Queue and Delay Estimation.
From the queue polygon, the maximum queue length of six vehicles occurs at 28 seconds.
The delay can be accumulated for each vehicle arrival and departure. The total delay, which is
the sum of delays from all vehicles, is equal to the area under the queue profile. The average
vehicular delay is equal to the total delay divided by the number of vehicle arrivals/departures
during a cycle.
Both input-output and hybrid techniques consist of three modules:

Arrival profile module. Advance detector actuations are used to determine shifted
arrival times, which are adjusted arrival times from advance detectors to stop bars.
13
Maximum queue length is determined by the number of detector actuations prior to
the end of red plus the start-up loss time. If the queue length reaches the storage
capacity, a linear extrapolation based on historical arrival flow rate is used to extend
the profile.

Departure profile module. For the input-output technique, the queue is discharged at
the rate of saturation headway after the end of red plus start-up loss time. For the
hybrid technique, the stop-bar actuations are used to determine the departure profile.
The vehicle headway is used to determine when the queue is cleared, i.e., when the
headway is greater than the pre-specified “queue clearance headway.”

Delay estimation module. For the input-output technique, the total delay is the
difference of departure from arrival profile. For the hybrid technique, the algorithm
will first check the balance between the number of arrivals and departures and then
apply appropriate adjustment prior to delay calculation.
The study (12) found that the hybrid technique did not perform better than the inputoutput technique, mainly because of the stop-bar detection performance and the presence of long
left-turn and right-turn bays at the studied site. The hybrid technique, however, may be more
beneficial at intersections where there is significant driveway traffic between the advance
detectors and the stop bar. The sites with large variability in saturation flow rate due to changing
weather conditions may benefit from the hybrid technique as well.
Gard (13) developed models for estimating maximum queue lengths at two-way stopcontrolled intersections using regression equations. The data used for model calibration were
collected from 15 two-way stop-controlled intersections in Sacramento, California. The
developed models predict the maximum vehicle queue for subject movement during a one-hour
observation period. The author chose to opt for the maximum queue length rather than the 95th
percentile queue length in this study in order to simplify the data collection process. The
explanatory variables found to be statistically significant in the models include:

hourly traffic volume divided by peak-hour factor (PHF) for subject movement,

hourly traffic volume divided by PHF that conflicts with subject movement,

presence of a traffic signal located on the major street within one-quarter mile of the
subject intersection,

number of through lanes occupied by conflicting traffic,
14

posted speed limit on major street, and

percentage of right-turn vehicles on shared minor-street approach.
While the empirical regression equations proposed in this study may be suitable for
engineering design applications, they are not meant for real-time intersection control applications
where queue lengths must be estimated at regular intervals in response to changes in traffic
conditions. Transferability of the models could potentially be another issue for empirical
equations. The models developed using specific data sets may not be readily applicable to other
locations without necessary modifications.
Geroliminis and Skabardonis (14) proposed an analytical methodology for predicting
platoon arrival profiles and queue length along signalized arterials. The proposed model was
evaluated using CORSIM simulation. The simulation output was first compared with field data
(delays and travel times) to verify that the model reasonably replicates field conditions at the test
sites. Then, the simulated queue lengths predicted by the proposed model and the simulation
were compared and found to be in agreement.
To predict the queue length at a traffic signal, the proposed model predicts the time that
the traffic signal starts serving the groups of uninterrupted vehicles, i.e., it predicts the effective
extension of the red time because of the discharge of the queued vehicles.
Simplified Case
The simplified case is used as a basis for further algorithm modifications to account for
various factors that could affect the queue length and thus the appropriate setting for variable
initial. The algorithm for variable initial estimates the queue length on a cycle-by-cycle basis.
The simplified case assumes the following:

There is no remaining queue from the previous cycle.

The through-traffic lanes are not shared by any turning movements.

There are no driveway activities between the advance detectors and the stop bar.

Through-traffic vehicles are distributed equally across all lanes.

There are no trucks in the composition of queued vehicles.

Non-green traffic demand does not exceed the storage capacity, i.e., the number of
vehicles that can be stored between the advance detectors and the stop bar.
15
The estimated queue length for this case is:
Where:
Na = number of actuations during yellow and red periods and n = number of through lanes.
Adaptive Control
Liu et al. (15) proposed an adaptive signal control system with an online signal
performance measure. The proposed method uses a real-time delay estimation technique based
on vehicle re-identification using an algorithm that matches individual vehicle waveforms or
signatures obtained from advanced inductive loop detectors. The two objectives considered in
signal optimization algorithm are system efficiency and system fairness. For system efficiency,
three measures of effectiveness (MOEs) are evaluated: total intersection delay, total throughput,
and average delay. The fairness of the system is measured via standard deviation of movement
delays. A multi-objective signal control technique was used to compromise these two conflicting
objectives.
The proposed system was evaluated in a simulation environment for a single intersection
using Paramics microscopic simulation software. The system was applied to both pre-timed and
actuated controllers for evaluation. The simulation experiments indicated that the proposed
adaptive control system could be an efficient method even under the application of a simple
algorithm for adapting the signal timing plan.
DETECTOR FAILURE
Detector failure is the primary cause of inefficient operations at signalized intersections.
It is reported that about 50 percent of the inductive loops are malfunctioning at any given time.
The National Traffic Signal Report Card (7), which surveyed 378 agencies across the country,
indicates that the detection system received a grade of F for detector systems. Failure of detectors
results in the controller receiving a continuous call for that particular phase. This results in a
significantly inefficient operation. If the traffic demand at intersections can be predicted, and a
detector failure identified, a system can be developed to provide appropriate green times for
phases with detector failures. Such a system will reduce the wastage of green and minimize
intersection delay.
16
The primary challenge in this module is the identification of a detector failure. TS-2
controllers have some detector diagnostics features that can be used to identify various types of
detector failures. The EPAC (9) and Naztec (16) controllers usually use three parameters to
identify a detector failure. The maximum presence limit diagnostic specifies the maximum
interval a detector is occupied (in minutes) prior to being considered a fault. This type of failure
is most common due to an open loop fault. However, an open loop fault is diagnosed by the
detector amplifier and results in a constant call, which is very inefficient. If the value set for
maximum presence failure is not very high, such a failure can also be triggered during some
unique circumstances where a vehicle is stationary on a detector for an extended period of time,
like during preemption, during manual control of the intersection, or due to a vehicle breakdown
over a detector. Upon diagnosing the maximum presence fault, the controller will provide the
larger of the minimum green or the specified fail time. The detector starts functioning normally
when the detector is reset.
The no activity limit diagnostic, on the other hand, specifies the maximum time between
detector actuations (in minutes) before the detector is considered to be faulty. Care should be
taken when programming this parameter to ensure that the controller does not diagnose the
detector to be faulty during light traffic conditions (like late at night). Upon diagnosing the no
activity fault, the controller will provide the larger of the minimum green or the specified fail
time. The detector starts functioning normally when the detector receives a call and resets the no
activity failure. The third diagnostic is the erratic count diagnostic, which establishes the
maximum actuations per minute that can occur prior to being considered a fault. According to
the Naztec controller manual (16), typical values of the range of erratic counts are from 40 to 70
per minute. Current controllers have the capability to log the green utilization for each phase.
This parameter can be an indicator of the traffic demand at the intersection and can potentially be
used to predict the traffic demand due to malfunction of detectors.
There have been a few studies that developed methods for short-term traffic volume
forecasting. These methods function as a key component in many intelligent transportation
systems (ITS). However, the stochastic nature of traffic flows makes it a challenging task to
consistently and accurately forecast traffic volumes.
Forecasting algorithms can be categorized as neural networks, dynamic wavelets neural
networks, non-parametric regression, time series models, pattern recognition, spectral analysis,
17
Kalman filtering techniques, adaptive predictive system, and Gaussian maximum likelihood
models (17). Most short-term forecasting studies use data aggregated over 5 to 15 minute
intervals to forecast traffic volumes. However, some studies have used intervals as small as
3 minutes or as large as 30 minutes. Larger intervals like 15 minutes to 30 minutes average out
local fluctuations and smooth out predictable traffic volume data, while smaller intervals can
capture some of the smaller fluctuations in the traffic patterns. However, traffic patterns can get a
bit noisy, thus reducing the confidence in the prediction of volumes.
These short-term forecasting studies were designed to observe traffic patterns and
forecast traffic volumes in the short term. However, the application for detector failure would
require a methodology that uses traffic patterns over a long-term time period to predict traffic
volumes in the absence of detections. Moreover, the algorithm may need to perform this function
for an extended period of time till the detectors are fixed. Hence, the methodologies developed
for short-term prediction are of limited use. A statistically robust approach that considers traffic
patterns both over a long-term period as well as in the immediate past would be more appropriate
to forecast traffic demand.
DETECTOR DELAY
Delay is sometimes used for stop-bar detectors in exclusive turn lanes. Delay can be used
either for left-turn lanes or right-turn lanes as long as permitted operation is used. The primary
purpose of using the detector delay function is to minimize unnecessary terminations of a major
movement (major-street through) to service a minor movement (major-street left turn and minorstreet right turn). National Transportation Communication for ITS Protocol (NTCIP), defines
detector delay as the ability of a detector to delay its output for a predetermined length of time
after a vehicle has entered its zone of detection (5). Delaying the detector output gives the
turning vehicle an opportunity to find a gap in the conflicting traffic stream, thus removing the
need to terminate the conflicting phase. Detector delay can be implemented in either the detector
or the controller. A delay programmed in the detector will delay the detector output to the
controller for the predetermined amount of time, irrespective of the traffic signal status. This
means that the delay is applied every time a vehicle actuates the detector. However, a detector
delay programmed in the controller delays the actuation only when the signal phase the detector
18
is tied to is not green. Hence, the delay is applied only when the signal indication is yellow or red
to give an opportunity for the turn vehicle to find a gap.
Detector delay is applied to right-turn movements on the minor road when an exclusive
right-turn lane is available and Right-Turn-on-Red (RTOR) is allowed. Typically, a delay of 8 to
14 seconds is used (18). This delay facilitates a right-turn vehicle to find a gap in the through
movement of the major road. If the vehicle finds a gap, the delay timer is reset and the controller
does not receive the call from that vehicle. If the right-turning vehicle does not find a gap, the
signal controller receives a call and responds accordingly. The controller at an appropriate time
will terminate the major-street movement and service the right-turn vehicle if the vehicle still has
not found a gap.
Detector delay can also be applied to a left-turn phase if an exclusive left-turn lane is
available and protected-permitted phasing is used. Typically, a delay of 5 to 12 seconds is used
for protected-permitted left-turn phasing (18) and is particularly useful during low volume
conditions. Before the controller registers the vehicle call, delay gives an opportunity to left-turn
vehicles arriving during the permitted portion of the phase to find gaps in the opposing through
movement. Under low volume conditions, this delay will minimize the termination of opposing
through movements, thus avoiding stopping through vehicles to service a single left-turning
vehicle. Frequently, the left-turn vehicle may just find a gap as the opposing through gaps out,
resulting in an unnecessary phase termination. Minimizing terminating the opposing through
phase becomes more critical if the approach speeds are high and/or if the approach volumes are
higher than the left-turn volumes.
The selection of the detector delay value depends on numerous factors. Detector delay
will increase delay to the turning movements for which the detector delay is applied. For RTOR
vehicles, the delay incurred depends on the ability to find gaps in the main-street through
movements and the right-turn volume. The ability to find gaps in the main-street through traffic
depends on the through-traffic volume, sight distance, and approach speed. There have been a
few studies that investigated the capacities of RTOR for right turns and permitted left-turn
movement for left turns. Factors influencing the capacity of RTOR from an exclusive right turn
are as follows (19) and are illustrated in Figure 6:

volume of conflicting traffic, which includes:
o through traffic in the right-most lane from the left (VT),
19
o protected left-turn traffic from the opposite direction (VL), and
o a proportion of the right-turn traffic from the left that is proportionate to the
drivers that do not turn the right-turn indicator (VR);

pedestrian volume (VP); and

red duration in the cycle (TR).
Left‐turn movement (VL)
Right‐turn under consideration
Through movement (VT)
Pedestrian Movement (VP)
Right‐turn movement (VR)
Figure 6. Factors Influencing RTOR Capacity.
Longer red duration on an approach can potentially increase the number of vehicles
serviced by RTOR. However, the time available by RTOR vehicles is the red duration less the
saturation green time for the conflicting movements and is known as the unsaturated red time.
During the unsaturated red time, RTOR vehicles will have to come to a stop at the stop bar and
select a gap when it is available to complete the maneuver. The delay for the detector should be
large enough that an RTOR vehicle will have an opportunity to complete these maneuvers during
the unsaturated red time. Numerous studies have investigated the methodology used to estimate
the capacity of right-turn movement at stop-controlled signs. According to the Highway Capacity
Manual (HCM) (20), a right-turn vehicle will accept a critical gap of 5.5 seconds to make a right
turn at a stop sign. It is expected that RTOR drivers will accept similar gaps to complete the
maneuver. The same methodology refers to a follow-up gap of 2.6 seconds. This means that a 5.5
second or greater gap allows the first vehicle turning right to accept the gap. If the gap is
20
8.1 seconds (5.5 + 2.6) or greater, both first and second vehicles in the queue can make the right
turn (21). A gap of 10.7 seconds can provide for three vehicles.
The utility of detector delay for right-turn movement thus depends on the ability of rightturning vehicles to find gaps in conflicting movements. However, adequate gaps are difficult to
find under high-volume conditions, so under such conditions, detector delay actually increases
the delay experienced by right-turn traffic. Thus, detector delay tends to be beneficial only under
the following conditions:

low to moderate volumes of conflicting traffic, and

low to moderate right-turn volumes.
21
MODULE METHODOLOGY
TTI researchers developed three modules during this project. This section describes the
scope and methodology used to develop the module.
VARIABLE INITIAL
Traffic signal controllers have numerous features (5) to improve intersection operations.
This section summarizes the variable initial methodology developed in this project. This
module’s objective is to estimate the initial green time required at the onset of the green on a
cycle by cycle basis for clearing the through-traffic queue up to the location of advanced
detectors (typically dilemma zone detectors). If the queue extends beyond the advanced
detectors, subsequent actuations will extend the green time in the same manner as those
registered at stop-bar detectors.
Scope
This methodology was developed for the following conditions:

signalized intersections without stop-bar detectors, and

signalized intersections with advanced detectors.
Methodology
Under variable initial (6) timing, the duration of the initial portion of the green (the first
timed portion of the green interval) can increase depending on the number of vehicle actuations
stored on the phase while its signal is displaying yellow or red. The variable initial timing period
which is also known as a “variable minimum green” is determined by the following three
parameters:

minimum green time, which determines the minimum variable initial time period;

seconds per actuation, which determines the time by which the variable initial time
will be increased (starting from zero) with each vehicle actuation received during the
yellow and red intervals of the phase; and

maximum initial, which is the maximum of the variable initial timing period.
Variable initial timing is effectively when stop-bar detectors are absent and only setback
detectors are present. In such cases, the initial timing is incremented to the appropriate value that
23
is required to service vehicles queued up between the stop line and the setback detector. Variable
initial timing requires point detection to operate, so it may not be appropriate to use with the
zone detection provided by video detection.
For a single lane approaching an intersection with low turning movement volumes and no
driveways between the advance detector and intersection stop bar variable initial can be very
easily applied. However, programming the variable initial becomes more complicated for multilane approaches and at locations where a common lead-in wire is used for multiple detectors.
The proposed methodology estimates the number of through vehicles waiting during the
cycle based upon the number of actuations observed at the advanced detectors. Since the
configurations of advanced detectors also depend on site-specific factors such as number of lanes
and operating speed, site-specific equations must be established to relate the number of
actuations to actual vehicle arrivals. The method first estimates the number of vehicles based on
observed actuations under assumed ideal conditions, which are:

no exclusive left-turn and right-turn lanes,

no driveways, and

no heavy vehicles.
Once methodology estimates the number of vehicles under ideal conditions, the
adjustment factors are then applied to account for any departures from ideal conditions. Once the
adjusted number of through vehicles is calculated, a proper initial green time can be allocated for
that cycle. Figure 7 illustrates the factors impacting the estimation of the through vehicles on an
intersection approach. It will not be possible to get an approach in the real world that is ideal,
i.e., without any exclusive turn lanes, driveways, and heavy vehicles. However, some sites that
had very few of the factors were identified to generate field data to develop adjustment factors.
TTI researchers collected data from two AWEGS (3) sites in Waco and College Station that do
not have any driveways on one or both approaches to generate adjustment factors from almost
ideal field sites.
24
Stop Line to the Center of the Driveway (LD)
Stop Line to the Beginning of Dilemma Zone Detectors (L1)
Stop Line to the End of Dilemma Zone Detectors (L2)
LDZ=L1-L2
Effective Length of Turn Bay (LB)
LC is first approximated by LB.
Figure 7. Turn Bay, Driveway, and Detector Locations.
Researchers used the data in the field to generate equations for estimating the through
vehicles on an approach when no stop-bar detection is present. These equations were based on
the number of detector actuations, which in turn will be based on the number of upstream
detectors, the number of lanes, and the location of the detectors with respect to the stop bar.
Equations also considered the percentage of left-turning vehicles based on left-turn phase
utilization. Since it was difficult to estimate the percentage of right-turn traffic, users were
prompted to estimate the percentage right-turn traffic. These turning percentages were then taken
into consideration to develop their impact on the number of through vehicles at the intersections.
The impact of driveways, their location, and their use on the estimation of through vehicles were
estimated in an analytical manner. Similarly, the impact of heavy vehicles on the number of
through vehicles was incorporated. These equations will be developed using both simulation as
well as analytical techniques.
DETECTOR FAILURE
This section documents the methodology used to develop the detector failure module.
The objective of the detector failure model is two-fold. First is to identify a detector failure either
for a particular movement or for the entire intersection, and second is to operate the intersection
in a more efficient manner. During detector failure, the signal controller typically receives a
continuous detection for the detector that has failed. Such an operation is very inefficient. The
detector failure model would develop a rolling four-week historical operational log. In case of a
25
detector failure, either for a phase or the entire intersection, this historical log will be used to
determine the expected intersection operations and implement those operations. Such an
operation, while not truly representative of existing traffic demand, is more efficient than
operations with a faulty detector.
Scope
The scope of the module is limited to providing a mode of operations that would be
appropriate for normal, average traffic conditions. This means that during a detector failure, the
module would determine the expected demand from historical data and provide the appropriate
phase duration for the expected demand. However, the module will not be able to account for
unexpected surges in traffic demand due either to special events or incidents. This system will
improve operations during detector(s) failures.
Methodology
The methodology of the detector failure module primarily consists of three parts. The
first part is to identify a detector failure. Once the detector failure is identified, the module
should determine the traffic demand for the movement(s) served by the detector that has failed.
This determination would be based on a historical log of either traffic demand or a parameter that
is a surrogate of traffic demand. Finally, the appropriate phase time would be implemented in the
controller.
Identifying Detector Failure
Traffic signal controllers have detector diagnostics features. These features allow users to
specify the criteria to be used to diagnose detectors and identify a failure. The typical criteria
available are maximum presence, no call, and erratic count. Maximum presence criteria are used
to identify a detector failure when a constant call is seen on a specific detector for a user
specified time. Typically, a detector amplifier places a constant call when a fault is identified in
an inductive loop. In the case of video detection, sometimes due to a fault in the video processor,
a constant call is seen. If the duration of a constant call exceeds the user-specified threshold (in
minutes) within the detector diagnostics in the controller, a failure is identified. On a similar
note, if for some reason the controller does not receive a call or does not see any activity for a
duration exceeding the user-specified threshold (in minutes) within the detector diagnostics
26
parameter in the controller, the controller diagnoses the detector as a failure. Finally, if the
controller sees an unreasonably large number of detections within a very short period of time
(number of calls per minute) and exceeds the user-specified threshold, the detector is diagnosed
as a failure. The user specifies the thresholds for the three diagnostics criteria, and those
thresholds depend on the traffic patterns at the intersections.
When a controller identifies a detector failure, usually the controller places a constant call
on that detector. This causes the phase mapped to the failed detector maxing out every time,
resulting in very inefficient operations during off-peak timings. Some controllers, however, give
an option to the user to specify how long the phase should be on during a detector failure. This
can result in a more efficient operation during off-peak timings but can be inefficient during the
peak timings.
The detector failure module (Module 2) will monitor detector activity through the
detector Bus Interface Unit (BIU). The module will identify the detector failure if the criteria
programmed in the controller are used. However, the module will monitor the controller’s
response to the detector failure and use that as a criterion to implement a more appropriate phase
time. Figure 8 illustrates the architecture of the detector failure module.
27
Detector Activity
1. Maximum presence
2. No activity
3. Erratic count
Detector diagnostics in
Controller
Yes
Controller places a
constant call
No
D-CS Module
Monitor phase
times
Implement revised
phase timings
Detector failure
diagnosed
Normal
operations
Four weeks
phase duration
database
Traffic Signal
Controller
Figure 8. Detector Failure (Module 2) Architecture.
Determining the Expected Traffic Demand
Once the detector failure is identified, the detector failure module determines the
appropriate phase time for the phase mapped to the detector that has failed from a phase
durations database consisting of the previous four weeks. These phase durations are logged for
each 15-minute period starting at midnight. The database consists of the phase durations of each
and every separate phase that is complete (i.e., start and complete) within each 15-minute
interval. Thus, each 15-minute interval consists of the number of phases complete within that
interval as well as the average of the complete phases. These two pieces of information are
logged for each phase for each 15-minute interval of the day. An example of a slice of data for
one time interval in the database is illustrated in Figure 9.
28
Figure 9. Illustration of Database Format.
The database consists of such data for all 15-minute intervals of the day for all 28 days.
At the end of each day, at midnight, the data for that particular day replaces the data from a
similar day at the beginning of the database. For example, at the end of a Monday, the data from
that day will replace the data for Monday 1 of the database. Thus, a rolling four-week database
of phase durations is maintained in the database.
Implementing the Detector Failure Module
Upon identifying a detector failure, the detector failure module will extract for the
appropriate phase the phase durations and the number of complete phases for the appropriate
time slice. This extraction of data will be conducted from each of the weekdays for a weekday
scenario or from the weekend days for a weekend scenario. The module will then calculate the
average of the phase durations from the database and implement the phase duration in the
controller and implement it.
Implementation of the phase duration is accomplished using the force-off function. Upon
diagnosis of a detector failure, the controller will place a constant call on a phase. The detector
failure module then terminates the phase by applying a “ring force off” once the phase duration
has exceeded the optimum duration determined by the module. This force off ends the phase and
brings on the next phase. Thus, maxing out of the phase is avoided and intersection operations
are more efficient.
VARIABLE DELAY
Traffic engineers using NEMA controllers (5) have the capability to program a specific
amount of delay into the controller for a specific detector. Historically, the same delay was
programmed into the detector amplifier. According to NEMA TS-2 specifications (5), a delay is
29
defined as the ability of a detector to delay its output for a predetermined length of time after a
vehicle has entered its zone of detection. When selected, the detector output is delayed for the
time set. If the vehicle departs before the time set, an output does not occur and the timer is reset.
The delay time is adjustable over the range of 0 to 30 seconds and remains a constant value.
The delay feature, when used for protected-permissive left-turn phases, reduces the
number of times the opposing arterial phase is terminated due to left-turning vehicles. A similar
strategy is used to allow the right-turning vehicles on minor streets to find gaps in the majorstreet through movements. The existing configuration uses a constant delay throughout the day.
A variable call delay based on traffic volumes at the intersections has the potential to further
improve the efficiency of the intersection operations.
Scope
The scope of the module is limited to left-turn movements with protected-permissive
phasing and right-turn movements with exclusive turn bays with detectors coming on separate
channels.
Methodology
Use of detector delay is a well-established practice to improve the efficiency at fully
actuated traffic signals. Detector delay on arterial left-turn phases using protected-permitted
phasing will minimize unnecessary termination of the major-street through movement. This is
particularly the case during low volume conditions when major-street traffic has many
acceptable gaps in the traffic stream and a left-turning vehicle will most likely find a gap without
stopping. Similarly, a right-turning vehicle on the minor street can easily find gaps in the majorstreet movement during light volume conditions and not call the minor-street phase. However,
fewer gaps are available for turning vehicles when major-street volume increases, requiring the
turning vehicles to wait past the delay time before placing a call on the respective phase. These
turning vehicles will then be serviced either when they find a gap or when the phase is serviced.
However, when the major-street volumes get very high, the only way to service these turning
vehicles is by calling a phase. In such cases, these turning vehicles may have to wait longer than
the maximum time to be serviced. Under such circumstances, use of the constant delay value
increases delay to the arterial left-turn and minor-street right-turn movements.
30
There are numerous factors that the variable delay module will consider to determine the
appropriateness of using detector delay functions as well as the duration of the detector delay.
Following is a description of the factors primarily influencing the use of detector delay. Figure
10 illustrates these factors, as well.

Major-street volumes: It is expected that as the major-street volumes increase, there
will be fewer acceptable gaps in the traffic stream, resulting in fewer vehicles taking
these gaps. So, the higher the volume, the more the turning vehicles will be delayed.

Gap acceptance characteristics: Gap acceptance characteristics vary among motorists.
More aggressive drivers will accept smaller gaps, and less aggressive drivers will
accept only larger gaps. Hence, the type of drivers in an area will influence the gap
acceptance characteristics.

Turning movement volumes: In case the major-street volumes are very high (they do
not gap out), turning movements with higher volumes will experience greater delay at
the intersections. This delay experienced will increase if detector delay is employed.
If the vehicle has to wait to be served by its phase, it has to wait for the duration of
the delay (d seconds) as well as the duration of the conflicting phase (major-street
movement) (P seconds). If, however, the phase serving the turning movement has a
v/c ratio of less than one (i.e., the phase serves all the vehicles in the queue), the
detector delay is reset and is applied again for the next set of vehicles and, hence, they
have to wait for d+P seconds till they are serviced. If, on the other hand, the v/c ratio
of the turning movement phase is greater than 1 (i.e., some of the vehicles in the
queue are not cleared), the detector delay is not reset and the next set of vehicles will
have to wait for P seconds to be serviced. Thus, from this discussion, detector delay
can be eliminated when the following conditions are met:
o Major-street volumes are high enough that gaps are not available.
o Turning movement volumes are low enough that the minor phase can clear all the
vehicles.
Previous research (18) on the duration of detector delay provided the following
guidelines:

right-turn detector delay―8 to 14 seconds, and

left-turn detector delay―5 to 12 seconds.
31
Figure 10. Flow Chart of the Factors Affecting Variable Delay Module.
These settings have been accepted across the industry and are applied appropriately. The
methodology will refer to the local agency’s preferences to determine the duration of detector
delay.
32
MODULE IMPLEMENTATION
SITE SELECTION
Based on the criteria set for each module, three sites were selected for deploying the
modules. These sites are located in the Waco District, Bryan District, and Houston District. Not
all modules were applicable at all sites. The modules deployed depended on the intersection as
well as detection configuration. Module 2 was, however, deployed at all intersections. The
system deployment required an intersection operating with a TS-2 cabinet and enough space in
the cabinet to place an industrial personal computer.
Waco District
The site in Waco is located at the intersection of US 84 and Aviation Parkway (Figure
11). This site has setback detectors with inductive loops at over 960 feet from the stop bar on US
84. The intersection, however, has video detection for detection at the stop bar (Figure 12). The
variable initial module, the detector failure module, and the variable delay module were
deployed at this site.
Bryan District
The site in Bryan is located at the intersection of SH 21 and Business 6 (Figure 13). This
site has only video detection on all four approaches at the stop bars (Figure 14). Only the
detector failure module was deployed at this site.
Houston District
The site in the Houston District is located at the intersection of SH 105 and FM 3083 in
Conroe (Figure 15). The intersection uses only inductive loops on all four approaches at the
intersection. This includes the dilemma zone detectors at 475 feet, 375 feet, and 275 feet from
the stop bar on the SH 105 approaches and stop-bar detectors in all lanes (Figure 16). The
variable initial module and the detector failure module were deployed at this site.
33
Aviation
Parkway
Figure 11. Site Location in Waco District.
Figure 12. Detector and Intersection Configuration at the Site in Waco District.
34
Business 6
Business 6
Figure 13. Site Location in Bryan District.
Figure 14. Intersection and Detector Configuration at the Site in Bryan District.
35
Figure 15. Site Location in Houston District.
475', 375' and 275'
(Trailing edge)
All detectors are
inductive loops
SH 105
475', 375' and 275'
(Trailing edge)
Figure 16. Intersection and Detector Configuration at the Site in Houston District.
36
SOFTWARE CONFIGURATION
Once the algorithms for the three modules were developed with simulation and analytical
methods, TTI researchers developed the modules for field implementation. This included a
graphical user interface (GUI) for configuring the modules as well as developing the appropriate
output files to log the various processes both within the controller as well as within the three
modules. Every effort was made to minimize user input requirements. When the input was
required from the user, it was made to be as simple as practical. The three modules were
developed sequentially. They were tested in the TransLink® Laboratory using a cabinet in the
loop simulation. The GUI and the output files were fine-tuned.
Figure 17 and Figure 18 illustrate the general configuration required for all the three
modules. This configuration is all that is needed for the detector failure module. Once this
configuration is completed, configuration screens specific for variable initial and variable delay
will be available to the user if these modules are applicable and if the user chooses to implement
them. The detector failure module is applicable under all circumstances. The user can specify the
configuration of phase numbering schemes, phasing sequences, number of lanes per approach,
and basic phase setting in the phase configuration screen.
The detector mapping to various phases, the type of detector, and the detector diagnostics
are configured in the detector mapping configuration screen. Sixteen detectors can be configured
in this screen.
37
Figure 17. Phase Setting Configuration.
38
Figure 18. Detector Mapping Configuration.
Variable Initial
Configuration of the variable initial feature requires information about location of
upstream detectors, type of detectors, traffic arrival type, and other information illustrated in
Figure 19. Information regarding the location of driveways including location and type of use
can be configured in a screen, as illustrated in Figure 20.
Once the module is operational, the algorithm will count the vehicles arriving on the
detectors on yellow and red and estimate the variable initial. The module logs this information in
a log file, as illustrated in Figure 21. Based on a count on red (COR), a value of initial green (IG)
is predicted.
39
Figure 19. Variable Initial Setting Screen.
40
Figure 20. Driveway Setting Screen for Variable Initial.
41
Figure 21. Variable Initial Prediction.
Detector Failure
The screens illustrated in Figure 17 and Figure 18 are used to configure the detector
failure module. The module is constantly monitoring the health of the detectors according to the
stated detector diagnostics. Detector diagnostic results are logged in a file, as illustrated in Figure
22. A detector failure due to a max presence at 23:59:47 hours on phase 5 in detector 10 is
logged.
The module also predicts the expected green at the beginning of each phase. The
predicted green time (in milliseconds) is also logged and is illustrated in Figure 23. The log
illustrates the predicted green, the actual green, and the difference between the two values.
42
Figure 22. Detector Failure Log.
43
Figure 23. Green Prediction Log.
Variable Delay
The variable delay module is applicable for right-turning vehicles from right-turn bays
with an exclusive right-turn detector and left-turning vehicles from left-turn bays with protectedpermissive operations. The module requires some configuration, like conflicting volumes, to
disable the detector delay. Additional information like size of the detector, speeds of turning
vehicles, and percentage trucks can also be configured to implement the variable delay module.
Figure 24 illustrates the configuration screen for right-turn delay settings.
44
Figure 24. Right-Turn Delay Module Settings.
FIELD IMPLEMENTATION
Project 0-6029 developed three modules for improving signal operations at isolated
signals. These modules were deployed at three sites in TS-2 cabinets. In a TS-2 cabinet, the
signal controller communicates with the detector’s rack and the back panel using BIUs with
Synchronous Data Link Communication (SDLC). The adaptive D-CS system operates in an
industrial PC in the cabinet. This industrial PC communicates with the cabinet using a special set
45
of BIUs called enhanced BIUs. These enhanced BIUs have a serial port in addition to an SDLC
port. The BIUs communicate with the signal controller using SDLC communication. The
industrial PC communicates with the BIUs using the serial communication through the serial
port. The implementation architecture is illustrated in Figure 25. These enhanced BIUs replace
the detector BIU (BIU-D) and BIU # 1 (BIU-1) so that the adaptive D-CS can monitor the
detector activity and signal status and also have the capability to place calls and force-offs.
Figure 26 illustrates the system deployed at the site near Conroe. Table 1 also summarizes the
modules implemented at each of the sites in Texas.
46
Signal Controller Cabinet
Serial Port
Detector Rack
Signal Controller
BIU-D
SDLC Port
Industrial PC
Serial
Ports
BIU-1
BIU-2
Figure 25. D-CS Implementation Architecture.
47
Figure 26. Installation of Adaptive D-CS in the Houston District near Conroe.
Table 1. Modules Deployed at Each Site in This Project.
Module 1―Variable
Module 2―Detector
Module 3―Variable
Initial
Failure
Detector Delay
Site 1―Waco
Yes
Yes
Yes
Site 2―Bryan
No
Yes
No
Site 3―Conroe
Yes
Yes
No
48
EVALUATION AND CONCLUSION
Researchers evaluated three modules in this project. The variable initial module (Module
1) and the detector failure module (Module 2) had numerous applications. Module 1 was
applicable in many cases where stop-bar detection was not installed. In many cases, it eliminates
the need for stop-bar detectors, thereby reducing installation and maintenance costs. Module 1
can be used at D-CS type installations or any other intersection having only upstream detectors.
These include intersections with dilemma zone detectors. Module 2 is applicable at all
intersections that are operating fully actuated, including D-CS type intersections. The module
can provide significant benefits when a few detectors either fail or malfunction for a period of
time. Variable detector delay (Module 3), however, was found to have very little use. A static
value of detector delay provides some benefits by minimizing unnecessary terminations for the
major-street movement. However, the benefits of variable delay were very limited and under rare
circumstances. Hence, researchers did not deploy Module 3 after a preliminary deployment in
Waco and did not evaluate it further.
MODULE 1
Researchers calibrated the adaptive variable initial module at the site in Waco. The Waco
site was a four-lane highway with two lanes in each direction approaching the intersection. The
Waco site had a D-CS installed and hence had a pair of detectors in each lane over 950 feet from
the intersection. There were no driveways between the detectors and the stop bar. However, there
was a significant variation in the turning percentage at the intersection. Researchers observed a
significant imbalance in the queue distribution. The intersection, though, did have video
detection and hence stop-bar detection. The occupancy in stop-bar detection is therefore a good
measure to validate the methodology for the adaptive variable initial.
Module 1 was then implemented at site 3 near Conroe. As mentioned earlier, the site in
Conroe is a six-lane highway with three lanes in each direction. The site has dilemma zone
detectors in each lane at 475 feet, 375 feet, and 275 feet from the stop bar. Thus, the intersection
in Conroe has significantly different characteristics compared to the intersection in Waco where
the model was calibrated. The Conroe site also had stop-bar detectors. These stop-bar detectors
facilitated a thorough evaluation of the adaptive variable initial module. The module logged the
parameters used to determine the variable initial as well as the recommended initial green. These
49
included the detector counts during the red portion, the predicted initial green, and the time taken
to clear the queue for each cycle. Figure 27 and Figure 28 illustrate the relationship between the
counts on red and the predicted initial green for phase 2 and phase 6, respectively. The same
graph also illustrates the actual queue clearance for the same counts. The graph clearly illustrates
a strong correlation between counts on red and initial green. The upper and lower limits of queue
clearance values straddle the predicted initial green values for the number of detector actuations.
This is an indication that the predicted initial green values are close to the time required for the
queue to clear. To further evaluate this aspect, researchers compared the predicted initial greens
with the observed queue clearance times for both phase 2 and phase 6, as illustrated in Figure 29
and Figure 30. A line was drawn with a slope of 1 in each of these graphs. These figures
illustrate that the predicted initial green values in general are close to the queue clearance values.
Figure 27. Accuracy of Predicted Initial Green (Phase 2).
50
Figure 28. Accuracy of Predicted Initial Green (Phase 6).
Figure 29. Relationship between Predicted Green and Queue Clearance (Phase 2).
51
Figure 30. Relationship between Predicted Green and Queue Clearance (Phase 6).
To further evaluate the accuracy of the predicted initial green, the error in predicting the
initial green with respect to the queue clearance was calculated. A histogram of this error for
phase 2 and phase 6 is illustrated in Figure 31. A key issue to understand in this error is the error
experienced during low volume conditions. Frequently during low volume conditions, there may
be a queue of just one or two vehicles. The time taken to clear this small queue of one or two
vehicles is smaller than the minimum green for phase 2 and phase 6. This fact is represented as
an error in the estimation of the initial green where the minimum value of the predicted initial
green is the minimum green. It can be seen from Figure 31 that a significant portion of the error
in predicting the initial green is between 0 and 3 seconds. This is the minimum green factor. The
error in prediction was then compared for phase 2 and phase 6 and also for the error for
weekdays and weekends. Table 2 illustrates the root mean square error (RMSE) for the
prediction of the initial green. It is seen that phase 6 has a slightly higher RMSE compared to
phase 2, and RMSE on a weekday appears to be slightly higher than for the weekend. However,
all these errors are very marginal and are usually greater than the queue clearance time.
52
Minimum
green effect
Minimum
green effect
Figure 31. Error in Predicting the Initial Green.
Table 2. Root Mean Square Error Comparison.
All data
Phase 2 only
Phase 6 only
Weekday only
Weekend only
RMSE (Seconds)
2.740
2.522
3.056
2.817
2.580
Sample Size
7,853
4,829
3,024
5,235
2,618
MODULE 2
Researchers evaluated the performance of both naïve and advanced prediction algorithms
proposed in this study. Three signalized intersections in Waco, Bryan, and Houston Districts
were selected as study sites for the evaluation. For each study site, data collection software was
deployed in a field-hardened computer installed inside a signal cabinet to collect the historical
green durations for all the phases. A minimum of four weeks of historical data were collected at
each site for the evaluation.
Measures of Effectiveness
The evaluation procedure considers the actual green duration observed for the interval as
a ground truth data. Therefore, the differences between the predicted and actual green durations
53
are the prediction errors. The desirable prediction algorithms should minimize these errors. For
the purpose of evaluation, researchers assumed that certain percentages of the detectors failed
and therefore required the prediction. Then, we quantified the differences between the predicted
values and what we actually observed from the data. The following MOEs were calculated to
quantify the performance of the two algorithms (naïve and advanced predictions) with respect to
the ground truth durations:

root mean square of errors (RMSE),

mean absolute errors (MAE),

mean absolute percentage of errors (MAPE),

mean error,

standard deviation of error,

percentage of comparison intervals, and

percentage of incalculable historical input data.
Let gi be the ground truth data for the interval i and gˆ i be the predicted values for the
corresponding interval i, where i = 1, 2,…, n. The n is the total number of intervals considered in
the comparison.
RMSE is expressed as
n
  gˆ
RMSE 
i 1
 gi 
i
2
. n
MAE is expressed as
n
MAE 
 gˆ
i 1
i
 gi
n
MAPE is expressed as
n
MAPE 

i 1
gˆ i  gi
100
gi
n
54
Evaluation Scenarios
For each study site, the researchers varied different rates of detector failure ranging from
10 percent to 100 percent. Researchers did not consider zero percent failure because that would
imply the detector is functioning 100 percent of the time and thus would require no prediction.
Failure intervals were randomly assigned to the evaluation data. For each failure interval, two
prediction algorithms―naïve and advanced prediction―were applied and the predicted values
were recorded for comparison. Naïve prediction simply utilizes the historical means from the
same time of day and the same day of week as a predictor. Researchers evaluated the
performance measures by phase and by the intersection (all phases combined).
For the purpose of evaluation, the data set used to populate the input tables is referred to
as calibration data. The data set used to test the performance of the algorithm is the validation
data. Ideally, calibration data and validation should be two separate data sets. However, due to
the limited amount of resources for the data collection, only the Waco site had sufficient data for
splitting into calibration and validation data sets. The other two sites in Bryan and Conroe relied
on the same set of data for both calibration and validation tasks.
Evaluation Results
This section documents the evaluation results from each of the three study sites evaluated
in this study. Researchers compared results from the two predication algorithms at each site. The
percentages of detector failure scenarios evaluated are 10 percent, 25 percent, 50 percent, 75
percent, 90 percent, and 100 percent.
Waco
Below are the dates of data used for the evaluation of the algorithms at the Waco site:

calibration data: 04/15/2009 – 07/05/2009;

validation data: 07/23/2009 – 08/23/2009; and

observed phases: 2, 4, 5, and 6.
Table 3 and Table 4 show examples of input data tables for the advanced prediction
algorithm. These tables show the input data calculated for Mondays using 15-minute intervals
from interval #25 to #88. There are 96 intervals in one day; interval #1 represents 12:00AM –
12:15AM, and thus intervals #25 to #88 would be equivalent to 6:00AM – 10:00PM.
55
Table 3. Waco―Mean and Variance of Green Durations (Mondays).
Monday
Interval
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
Mean Green Duration (sec)
4
5
6
2
9.0
57.6
182.3 10.0
295.3 10.1
9.2
75.5
279.9 10.9
9.8
45.8
269.2 10.5 10.8 38.4
188.7 10.3 10.6 36.7
153.8 11.3 14.3 33.4
161.3 10.6 15.4 36.6
167.9 10.2 11.8 37.5
9.7
44.5
249.4 11.0
200.1 10.1
9.9
43.7
138.7 10.2
9.8
58.4
240.4 10.1
9.7
61.4
236.4 10.3
9.5
62.9
237.7 10.1 10.3 68.3
151.1 10.2
9.9
61.7
185.1 10.0 10.4 52.7
149.2 10.5 10.5 54.1
169.4 10.2 10.0 58.0
170.2 10.1
9.9
60.8
171.0 10.2 10.3 51.4
137.0 10.1
9.7
61.2
168.2 10.2 10.5 56.1
141.6 10.6
9.7
56.2
128.0 10.2 11.1 56.5
9.6
58.1
176.8 10.4
176.4 10.5 10.4 55.1
9.6
44.3
196.2 10.4
236.8 10.5 10.2 42.4
215.7 10.1 10.0 40.6
258.6 10.0 11.3 38.5
231.3 10.5 11.5 35.7
180.5 10.1 10.0 41.4
9.9
54.5
138.8 10.4
166.7 10.5 10.2 51.8
66.1 10.3 11.4 39.8
143.2 10.5
9.9
49.6
155.3 10.2 10.3 47.8
156.3 10.4 10.4 42.3
135.1 10.3 10.6 37.1
180.1 10.6 12.0 34.2
203.2 10.1 13.5 31.1
139.4 10.5 11.5 34.3
64.0 10.5 10.8 35.0
96.8 10.3
9.7
45.9
9.6
47.4
101.5 10.4
107.2 10.1 10.0 45.9
9.8
62.5
162.5 10.0
68.1
142.8 10.6
9.4
143.1 10.2 10.0 75.8
163.1 10.1
9.5
94.9
190.0 10.6
9.5
72.5
221.8 10.2
8.9
82.4
150.1 10.2 10.4 91.4
198.8 10.3
8.9 101.7
9.0
96.5
234.9 10.0
267.0 10.3 10.1 103.6
9.3 101.4
222.4 10.0
123.3 10.1
9.1
93.3
168.5 10.1
8.9 103.4
144.8 10.0
8.6
86.8
8.5
82.1
150.9 10.0
206.1 10.5
8.7
74.3
8.8
59.1
254.9 10.4
9.4
57.1
345.5 10.0
56
2
Variance of Green Durations (sec )
2
4
5
6
29274.3
0.0
4.4
1194.4
0.2
4.8
7347.7
27699.0
20516.1
3.1
7.1
579.2
41722.4
3.4
9.6
219.4
12579.5
0.7
8.9
228.1
9333.1 11.6
19.4
64.0
2.2
19.9
118.8
17053.0
0.7
17.0
207.8
17124.0
17092.6
6.1
7.4
897.5
34060.3
0.4
8.7
383.5
11569.6
1.0
9.3
2332.7
25940.8
0.2
5.8
1908.1
46360.2
0.7
7.9
1864.3
30129.3
0.1
9.5
2782.9
1446.3
14233.3
0.2
10.4
15051.7
0.0
15.1
1349.7
2.6
15.0
2114.4
15621.0
11618.2
0.3
11.6
1455.4
15642.8
0.1
9.9
1741.9
11110.1
0.5
13.0
1102.2
2271.6
14250.2
0.2
7.0
1036.0
25007.8
0.6
13.0
11915.2
2.7
9.7
1340.0
6231.7
0.7
13.6
1794.5
12701.7
1.0
7.8
1967.7
14571.2
2.1
12.0
1379.3
27000.5
1.0
8.0
574.6
34942.6
3.6
10.8
409.4
22024.8
0.1
10.1
535.8
47650.6
0.0
14.4
333.5
23885.3
0.9
12.5
124.6
22553.7
0.2
10.7
559.6
14390.6
1.5
10.6
2149.2
2.4
11.7
1424.5
14072.4
1512.0
1.3
14.1
449.9
9571.1
1.8
10.3
761.9
17261.2
0.4
12.2
722.8
17329.2
1.4
10.2
515.9
9342.2
1.0
14.5
511.9
11652.0
1.6
18.4
123.4
0.3
20.9
51.4
13524.0
192.9
12880.7
1.3
13.0
1787.5
1.9
13.6
158.9
6494.6
0.6
6.2
1164.6
7330.5
2.0
7.4
771.4
7605.4
0.4
17.4
910.2
8368.5
0.0
9.2
2302.7
12561.1
5.4
7.2
2287.4
0.7
9.4
5879.1
15273.4
16284.8
0.2
10.4 11489.2
2786.7
23095.2
3.3
14.4
27279.7
0.3
3.3
3366.0
22802.9
1.8
16.5
8457.7
30574.9
1.0
5.8
8443.9
28614.5
0.0
4.1
8755.1
30144.3
1.0
11.9 11912.0
11719.4
0.0
6.0
7228.8
0.2
6.6
4788.7
10469.4
0.4
3.5
9937.2
17020.4
7579.2
0.0
2.5
3758.0
7690.3
0.0
3.2
6521.0
1.3
2.4
3955.3
19621.0
41513.9
2.4
4.0
2451.8
61417.9
0.0
7.7
1659.5
Table 4. Waco―Mean and Variance of Change in Green Durations (Mondays).
Monday
Interval
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
Average Change (sec)
4 5
6
2
‐175.9 ‐0.1 ‐0.3 15.7
96.1 0.1 0.2 33.8
‐11.0 0.7 0.6 ‐45.7
124.7 0.4 1.0 ‐8.8
‐66.7 ‐0.6 ‐0.2 ‐1.4
‐3.0 0.8 3.7 ‐3.7
‐3.6 ‐0.7 1.1 3.5
12.2 ‐0.4 ‐3.6 0.8
136.5 1.2 ‐2.1 8.1
‐93.8 ‐1.0 0.1 ‐1.6
‐92.4 0.0 ‐0.2 21.2
99.0 0.0 0.0 ‐2.1
55.5 0.2 ‐0.2 1.2
‐108.5 ‐0.2 1.0 6.6
‐113.1 0.0 ‐0.7 ‐5.0
7.2 ‐0.2 0.7 ‐11.8
4.0 0.6 0.2 3.9
‐16.2 ‐0.4 ‐0.9 2.7
13.6 ‐0.1 ‐0.1 2.9
‐10.4 0.1 0.5 ‐10.8
‐43.6 ‐0.1 ‐0.5 12.7
77.4 0.4 0.8 ‐7.0
‐38.1 0.0 ‐0.9 ‐1.0
‐25.0 ‐0.2 1.6 1.7
42.4 0.1 ‐1.7 ‐0.3
‐5.6 0.2 0.8 ‐1.7
43.6 ‐0.1 ‐0.7 ‐12.6
53.7 0.0 0.6 ‐2.3
13.0 ‐0.4 ‐0.2 ‐1.7
119.3 ‐0.1 1.2 ‐1.0
‐134.7 0.5 0.4 ‐4.0
‐77.3 ‐0.3 ‐1.5 5.7
‐54.3 0.9 ‐0.2 18.2
50.3 ‐0.7 0.3 ‐7.1
‐130.4 ‐0.1 1.2 ‐12.4
61.6 0.3 ‐1.4 10.1
78.0 ‐0.4 0.3 ‐1.7
‐13.7 0.2 0.0 ‐5.5
‐39.5 ‐0.2 0.3 ‐5.2
78.6 0.3 1.4 ‐3.5
19.5 ‐0.4 1.5 ‐3.1
‐81.2 0.5 ‐2.0 3.4
‐71.8 0.0 ‐0.7 0.5
50.3 ‐0.3 ‐1.2 12.6
‐9.7 0.1 ‐0.1 0.3
4.1 ‐0.3 0.4 ‐0.6
53.2 ‐0.1 0.0 17.2
‐6.1 0.5 ‐0.6 9.5
‐28.4 ‐0.3 0.6 7.6
‐11.7 0.0 0.0 40.3
44.0 0.4 ‐0.8 ‐46.5
‐19.6 ‐0.4 0.0 15.6
‐19.2 0.0 2.6 24.3
8.3 0.1 ‐2.8 ‐8.6
‐153.6 ‐0.4 1.0 ‐5.0
‐22.6 0.2 ‐0.5 35.7
76.8 ‐0.2 ‐0.2 ‐16.4
‐107.9 0.1 0.4 ‐24.5
77.6 0.0 ‐1.2 50.7
‐47.2 ‐0.1 ‐0.4 ‐59.8
‐22.7 0.0 0.1 ‐2.9
29.7 0.4 0.1 ‐4.3
20.7 0.3 0.1 ‐20.5
178.8 ‐0.6 0.6 ‐3.9
2
Variance of Change in Green (sec )
2
4
5
6
74022.3 0.2
0.5
81.3
1.8
2145.2
22376.9 0.0
22887.2 0.9
0.8
2453.1
90882.3 10.5 1.1
180.3
2.7
68.9
78237.8 6.0
20784.5 2.8
2.6
37.5
15992.9 3.3
2.7
16.5
7660.0
0.8
2.1
38.6
26391.5 1.5
2.5
125.7
56513.9 1.8
1.7
115.9
589.8
51751.6 0.5
2.4
17074.5 0.0
2.8
308.3
1.3
218.3
64223.4 0.5
79977.8 0.1
2.1
623.6
4.6
163.6
32545.4 0.3
13919.3 0.1
3.2
309.7
19732.5 1.7
6.3
244.6
23103.8 1.1
6.9
330.6
18547.1 0.1
0.5
371.1
19862.2 0.1
2.3
173.2
279.5
14298.5 0.1
2.0
10799.4 1.8
2.6
357.5
9117.8
2.8
5.2
135.5
5668.2
0.9
8.6
475.5
17629.3 0.9
9.0
234.5
15947.9 1.4
6.7
200.7
24870.9 2.3
3.8
218.9
9392.0
1.8
1.2
29.1
65237.0 1.1
0.1
12.7
42746.9 0.0
1.5
174.0
79963.1 0.4
2.4
130.5
6047.2
0.5
1.3
22.0
25673.8 5.3
1.7
685.0
13104.7 5.8
2.8
544.3
9621.4
0.6
2.3
137.5
5067.4
0.6
4.9
8.2
29429.2 0.8
1.7
86.2
35732.5 0.5
2.3
65.8
1.6
154.3
5574.8
0.4
5573.0
0.5
2.3
62.2
7741.9
0.3
1.9
6.6
14146.9 0.8
1.2
14.4
2455.6
1.0
3.5
27.7
4025.3
0.5
2.2
248.4
5039.2
0.5
1.4
157.4
3749.0
0.4
1.3
164.0
3303.1
0.1
3.7
467.9
893.8
5532.0
0.9
3.0
17737.7 1.1
1.8
638.7
16469.5 0.1
5.5
6568.2
20358.6 1.7
9.2
8633.8
4879.0
1.5
6.8
1012.8
48441.0 0.4 12.8 2515.4
129961.3 0.7 10.8 8353.4
85792.7 0.4
4.1
1023.1
44.7
0.1
9.8
17621.0
8019.9
0.1
3.9
21344.1
8431.4
0.0
7.0
6256.7
2.6
16431.6
13046.4 0.1
17083.7 0.0
1.1
18974.5
0.8
417.2
3446.6
0.0
19404.8 0.7
1.2
2110.7
23729.8 3.5
0.8
1723.4
20352.3 1.8
1.7
378.0
57
Table 5 through Table 8 summarize the performance evaluation results by phase and by
intersection (all phases). The results indicated that phase 4 will benefit most from the proposed
algorithm. This is because phase 4 is a side-street phase with no recall; therefore, the green times
observed from both the historical and immediate past are more likely to reflect the true demand
for the green times.
Table 5. Naïve Prediction versus Ground Truth by Phase (Waco, 50% Failure).
Phase
2
4
5
6
Number of Compared Intervals 2236 2726 2975 3005
RMSE (sec)
125.4 1.9
1.0 71.1
MAE (sec)
82.0 1.1
0.6 33.0
MAPE
50.0% 9.0% 6.6% 27.4%
Mean Error (Bias)
‐27.9 0.3
0.0 ‐14.0
SD of Error
122.2 1.9
1.0 69.7
Table 6. Advanced Algorithm versus Ground Truth by Phase (Waco, 50% Failure).
Phase
2
4
5
6
Number of Compared Intervals 2236 2726 2975 3005
RMSE
124.7 1.6
1.1 68.4
MAE
84.4 0.9
0.7 34.2
MAPE
52.8% 7.5% 7.5% 30.6%
Mean Error (Bias)
‐21.8 0.2
0.0 ‐9.4
SD of Error
122.8 1.6
1.1 67.8
Table 7. Comparison of Algorithm Performance by Phase (Waco, 50% Failure).
Comparison by Phase
2
4
5
6
RMSE Improvement
0.5% 13.7% ‐12.1% 3.8%
MAE Improvement
‐2.9% 16.5% ‐14.4% ‐3.6%
MAPE Improvement
‐2.8% 1.6% ‐0.9% ‐3.2%
Bias Improvement
21.6% 37.1% ‐79.5% 33.2%
Error Variance Improvement ‐0.4% 13.2% ‐12.1% 2.8%
* Base: Naïve prediction using historical means.
** Advanced: Proposed algorithm using means and variances.
*** Difference = Advanced ‐ Base
58
Table 8. Comparison of Performance for All Phases (Waco, 50% Failure).
All Phases
Base Advanced Difference
RMSE Improvement
67.8
66.8
1.5%
MAE Improvement
26.3
27.1
‐3.0%
MAPE Improvement
21.8%
23.1%
‐1.3%
Bias Improvement
‐9.5
‐7.0
26.3%
Error Variance Improvement 4388.6
4342.3
1.1%
* Base: Naïve prediction using historical means.
** Advanced: Proposed algorithm using means and variances.
Figure 32 through Figure 34 display the selected comparison of the prediction algorithms.
Phase 2 is difficult to predict, as expected, because the phase is operating in the recall mode and
the demand from the conflict movements needed to terminate the green times are intermittent.
Phases 4 and 5 are relatively predictable with more consistent demand from the conflicting
phases.
Phase 2
904.0
804.0
704.0
604.0
504.0
404.0
304.0
204.0
104.0
1
5
9
13
17
21
25
29
33
37
41
45
49
53
57
61
65
69
73
77
81
85
89
93
97
101
105
109
113
117
121
125
129
133
137
141
145
149
153
157
161
165
169
173
177
181
185
189
4.0
Actual
Base Prediction
Proposed Algorithm
Figure 32. Example Comparison of Algorithms (Waco, Phase 2, 50% Failure).
59
Phase 4
20.0
18.0
16.0
14.0
12.0
10.0
8.0
6.0
1
5
9
13
17
21
25
29
33
37
41
45
49
53
57
61
65
69
73
77
81
85
89
93
97
101
105
109
113
117
121
125
129
133
137
141
145
149
153
157
161
165
169
173
177
181
185
189
4.0
Actual
Base Prediction
Proposed Algorithm
Figure 33. Example Comparison of Algorithms (Waco, Phase 4, 50% Failure).
Phase 5
16.0
14.0
12.0
10.0
8.0
6.0
1
5
9
13
17
21
25
29
33
37
41
45
49
53
57
61
65
69
73
77
81
85
89
93
97
101
105
109
113
117
121
125
129
133
137
141
145
149
153
157
161
165
169
173
177
181
185
189
4.0
Actual
Base Prediction
Proposed Algorithm
Figure 34. Example Comparison of Algorithms (Waco, Phase 5, 50% Failure).
Houston District
Below are the data descriptions used for the performance evaluation of the algorithms at
the Conroe site:

calibration and validation data: 07/23/2009 – 08/23/2009; and

observed phases: 1 to 8.
Table 9 and Table 10 show the examples of input data used for the calculation of the
advanced algorithm on Mondays from 6:00AM to 10:00PM.
60
Table 9. Conroe―Mean and Variance of Green Durations (Mondays).
Monday
Interval
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
1
10.3
12.4
12.5
12.7
14.3
19.3
19.9
16.6
14.6
13.1
15.3
14.1
13.2
13.9
15.0
13.7
12.4
13.9
14.5
15.2
16.1
14.3
14.6
15.2
18.1
17.5
18.6
16.7
17.6
17.0
19.0
15.0
17.4
16.6
14.9
15.3
18.6
17.8
18.6
16.3
18.3
19.2
20.0
22.3
24.4
21.4
20.8
19.2
16.4
14.5
13.3
11.9
12.6
9.7
8.9
10.6
9.1
9.8
9.5
9.8
8.9
7.5
8.0
7.9
Mean Green Duration (sec)
2
3
4 5
6
7
25.6 7.3 8.0 6.1 83.0 9.3
30.2 8.1 6.9 5.9 63.0 7.2
29.5 9.3 7.9 6.2 54.3 8.3
29.1 8.5 7.8 6.6 60.7 7.2
33.5 8.7 6.1 6.9 62.9 9.1
33.7 10.1 5.8 6.5 65.1 8.3
32.3 10.9 6.9 6.8 61.8 9.4
33.7 10.9 7.8 6.8 58.2 5.7
36.7 10.2 7.5 6.8 51.4 NA
33.2 10.1 6.9 7.2 56.9 9.9
34.3 10.2 6.7 7.1 48.7 9.2
32.8 10.8 7.7 6.3 59.2 19.2
34.9 9.7 5.5 6.7 68.2 7.7
33.0 8.7 7.3 6.5 72.8 5.8
33.9 9.4 6.4 6.1 63.6 5.7
38.5 10.1 6.9 6.2 55.4 5.6
32.9 8.8 6.0 7.2 52.8 13.7
42.5 10.5 6.5 7.0 67.6 17.5
35.6 9.8 6.6 7.1 62.9 13.9
35.3 9.8 8.1 7.3 54.5 10.4
44.2 10.9 7.8 7.1 69.7 9.4
38.3 10.9 6.1 7.4 63.9 12.5
36.9 10.1 6.8 6.3 61.4 14.5
41.5 12.0 7.7 6.5 63.7 10.1
48.8 11.6 6.6 6.9 66.7 15.9
40.1 12.3 6.5 7.4 61.0 9.5
37.9 11.5 6.5 7.4 55.8 8.9
40.9 10.4 6.4 6.3 57.0 13.1
42.1 10.8 6.2 7.4 67.0 7.2
41.0 9.5 7.4 6.4 63.0 12.6
39.8 10.6 8.7 6.6 65.5 14.0
39.2 11.6 11.5 6.4 64.9 11.8
42.5 10.4 6.7 7.0 66.4 12.1
43.5 11.2 5.8 6.2 61.1 12.6
42.0 10.8 5.9 7.9 63.5 12.4
39.2 10.0 7.6 7.3 62.1 9.5
45.8 11.0 9.3 7.3 58.4 12.4
46.3 12.3 16.6 7.9 74.3 7.8
44.8 11.0 14.2 6.4 66.7 8.8
46.9 11.8 7.0 6.9 67.9 11.8
46.6 11.4 7.6 7.0 63.5 11.8
47.7 12.2 7.0 7.2 70.7 14.1
44.2 13.7 8.9 7.1 64.2 8.4
48.4 12.9 7.0 7.4 74.2 9.8
55.6 12.5 6.8 6.9 78.8 8.6
49.2 12.4 10.1 7.4 71.7 13.0
49.8 12.7 6.5 6.6 70.3 8.7
45.5 10.8 7.6 8.1 73.5 9.8
39.1 9.8 9.8 6.2 68.7 11.8
35.3 10.1 8.9 7.0 51.4 8.6
34.2 9.8 9.4 6.4 55.0 6.2
32.7 7.9 8.1 7.8 54.4 9.0
31.5 8.2 6.8 7.5 67.9 8.3
33.1 7.7 7.1 7.3 64.8 7.3
29.1 8.2 7.4 6.1 63.4 6.5
28.4 7.1 7.7 6.0 52.7 11.1
28.7 8.4 7.4 6.5 82.9 6.1
30.9 7.2 7.6 6.3 54.9 7.9
31.1 7.2 6.0 6.5 60.0 6.8
30.1 7.1 7.2 6.7 58.9 7.6
31.2 7.6 7.3 6.3 76.3 5.7
32.6 6.8 5.8 6.5 71.8 6.0
35.5 7.8 7.0 7.1 101.8 5.0
35.2 6.8 5.4 6.3 82.0 NA
2
8
7.4
8.4
10.1
9.5
11.3
11.2
15.5
13.0
12.8
11.8
12.7
12.1
9.8
9.6
11.8
11.1
11.4
13.4
12.2
10.4
10.1
10.7
13.1
13.8
15.5
12.9
13.8
14.6
14.2
12.3
11.0
15.1
13.6
15.0
11.0
11.9
14.0
18.8
17.6
13.0
14.5
13.3
14.0
14.3
15.8
14.2
15.1
13.0
11.4
9.9
11.7
8.7
8.1
8.1
7.1
7.4
8.2
7.4
7.5
8.0
7.6
6.3
7.5
6.1
61
1
17.5
28.8
26.5
29.0
36.0
57.3
50.6
34.2
47.9
29.2
22.2
32.4
22.4
32.2
34.0
26.1
26.7
34.3
23.8
45.7
38.7
32.7
24.1
33.1
37.8
58.3
62.7
33.1
41.1
47.7
36.6
33.0
46.8
44.4
40.6
38.1
55.3
48.2
29.0
42.0
47.1
51.9
58.4
47.3
33.5
32.6
38.7
50.4
44.0
24.0
39.1
28.4
20.4
12.1
10.6
12.7
13.8
21.2
12.2
11.6
7.8
6.8
7.2
5.8
Variance of Green Durations (sec )
2
3
4
5
6
7
8
71.9 3.9 5.1 0.9 6616.8 NA 4.2
267.8 7.8 4.1 0.3 1487.8 0.0 12.5
147.4 9.1 13.1 1.8 1188.1 8.8 24.0
131.2 3.1 7.4 2.5 851.3 5.7 16.2
189.5 5.3 2.2 3.4 1178.5 22.8 41.3
209.5 8.7 0.7 1.4 713.7 10.0 23.4
154.2 14.0 1.6 1.4 611.8 16.5 62.5
167.5 13.9 5.7 2.6 559.2 NA 28.5
204.5 12.0 7.2 1.8 311.9 NA 41.4
141.0 11.4 2.4 3.5 697.9 21.6 32.6
259.7 10.7 3.9 3.8 349.9 8.9 40.0
204.5 10.5 12.7 1.3 385.7 143.4 29.4
221.5 14.4 0.5 1.9 2191.8 0.5 20.7
163.6 5.2 6.3 2.1 2232.4 1.3 18.5
189.6 7.7 1.9 0.4 987.2 NA 39.3
235.2 11.9 7.6 0.7 407.4 0.7 36.0
186.3 4.6 1.0 4.3 554.4 66.0 35.1
297.7 10.9 5.2 2.9 1901.5 263.1 59.7
153.7 7.1 1.4 2.1 1077.9 110.6 42.5
133.7 8.4 13.7 4.1 466.5 10.6 19.5
264.7 14.5 1.5 3.4 387.3 18.1 8.5
167.0 28.6 0.5 2.3 708.3 78.5 18.1
243.8 9.7 2.9 2.0 1163.7 17.1 43.2
158.6 10.4 5.7 1.0 340.7 91.3 44.8
225.6 10.7 2.9 5.7 334.8 107.9 47.8
192.8 21.1 2.1 4.1 406.0 7.5 31.6
196.4 16.3 3.2 4.5 365.3 10.4 68.4
235.1 12.9 1.6 1.0 589.0 43.6 61.6
213.2 9.9 1.2 4.8 902.4 1.2 49.5
182.5 10.3 3.9 1.1 656.4 33.5 42.4
244.3 8.6 43.9 1.5 690.7 64.0 18.3
200.3 19.7 34.7 1.0 1134.8 76.9 63.5
218.8 6.2 0.9 2.6 847.3 0.9 51.5
224.4 8.6 1.0 2.2 461.0 48.6 43.9
311.5 16.6 0.8 25.0 438.8 71.0 27.9
227.4 4.4 9.0 5.4 866.8 2.6 44.0
186.2 13.6 39.7 6.1 660.3 67.5 68.6
181.3 14.3 40.8 13.0 473.0 6.8 140.5
218.6 12.7 45.1 1.3 789.1 17.3 115.5
234.8 17.5 1.2 1.8 352.3 140.0 46.2
211.3 7.1 2.6 4.7 269.5 3.7 50.1
168.9 23.0 10.6 3.4 747.2 28.9 45.6
182.0 28.9 12.8 4.0 466.4 7.8 35.3
161.6 18.7 4.7 3.8 479.9 23.7 43.8
79.3 23.6 2.7 2.5 189.8 7.5 47.4
140.4 19.7 50.6 3.6 189.7 48.4 37.4
226.4 16.1 2.4 2.3 496.4 6.7 52.8
194.4 11.5 2.5 3.9 619.0 NA 37.2
190.4 20.0 53.5 1.1 556.9 63.4 39.1
177.7 16.6 31.5 4.9 621.6 11.0 24.5
123.6 14.5 60.9 1.6 1125.5 0.1 80.8
243.3 8.0 27.6 7.3 561.2 29.6 23.9
287.0 11.5 8.6 4.4 1723.6 25.4 18.6
293.1 4.1 2.1 4.4 2227.8 3.2 9.8
288.4 14.2 15.9 0.9 1070.9 0.7 3.8
134.4 3.4 14.5 0.3 1550.0 75.3 11.0
330.6 11.4 9.9 2.2 4343.4 1.0 17.6
212.5 2.7 7.9 0.4 1084.2 NA 4.7
470.9 2.8 1.0 2.1 1726.2 0.6 10.8
222.9 3.0 9.6 2.3 1531.1 NA 17.6
327.8 3.2 14.8 1.0 2974.5 1.0 11.6
615.2 1.3 3.1 1.4 4240.3 0.3 2.8
451.1 3.5 14.2 6.0 8742.2 NA 9.0
506.3 1.0 0.5 0.3 9218.3 NA 1.2
Table 10. Conroe―Mean and Variance of Change in Green Durations (Mondays).
Monday
Interval
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
1
1.8
2.0
0.1
0.2
1.6
5.1
0.7
‐3.6
‐1.7
‐1.8
2.2
‐1.2
‐1.0
0.9
0.9
‐1.2
‐1.4
1.5
0.5
1.0
0.6
‐1.7
0.3
0.7
2.8
‐0.6
1.1
‐2.0
0.9
‐0.7
2.0
‐4.0
2.4
‐0.8
‐1.6
0.3
3.6
‐0.7
0.6
‐2.3
1.9
1.2
0.5
2.5
1.9
‐2.9
‐0.8
‐1.2
‐2.9
‐2.2
‐1.1
‐1.4
0.6
‐2.9
‐0.8
1.9
‐1.7
0.7
‐0.4
0.3
‐0.8
‐1.4
0.5
0.0
2
‐1.5
4.7
‐0.8
‐0.3
4.5
0.1
‐1.3
1.2
3.1
‐3.3
1.5
‐1.9
1.8
‐1.9
0.9
5.4
‐5.7
9.0
‐6.7
‐0.5
9.1
‐5.8
‐1.6
4.5
7.3
‐8.6
‐2.2
2.8
1.4
‐1.4
‐1.1
‐0.7
3.3
1.1
‐1.3
‐2.9
6.4
0.7
‐1.7
2.3
‐0.4
1.4
‐3.8
4.3
7.1
‐6.6
0.5
‐3.8
‐5.8
‐4.8
‐0.5
‐1.9
‐1.5
1.9
‐4.0
‐0.7
0.6
1.7
0.6
‐1.2
1.0
1.8
3.2
‐0.9
Average Change (sec)
6
7
3 4 5
0.2 2.2 0.7 ‐6.3 NA
0.8 ‐0.8 ‐0.1 ‐20.0 NA
1.3 1.0 0.4 ‐8.4 3.1
‐0.9 ‐0.1 0.0 6.7 NA
0.3 ‐1.8 0.5 2.7 ‐1.4
1.4 ‐0.2 ‐0.5 1.9 ‐3.5
0.8 1.0 ‐0.1 ‐2.8 6.3
0.1 1.0 0.1 ‐4.4 ‐0.8
‐0.9 ‐0.2 0.0 ‐7.3 NA
0.0 ‐0.8 ‐0.1 6.2 NA
0.2 ‐0.7 ‐1.0 ‐8.2 ‐2.1
0.5 0.7 ‐0.8 10.1 10.0
‐1.0 ‐1.6 0.1 10.1 ‐20.4
‐1.2 1.6 0.3 4.5 ‐1.4
0.7 ‐0.4 ‐0.5 ‐10.4 NA
0.7 0.1 0.3 ‐7.7 ‐0.1
‐1.3 ‐0.7 0.7 ‐2.9 NA
1.8 0.4 0.0 17.6 5.8
‐0.7 0.9 ‐0.2 ‐7.1 15.3
0.1 1.0 0.5 ‐9.2 ‐3.9
0.9 ‐2.2 0.1 15.6 ‐2.3
0.1 ‐2.0 0.2 ‐6.0 3.8
‐0.9 0.6 ‐1.2 ‐0.7 4.5
2.0 0.6 0.0 0.3 ‐8.0
‐0.3 ‐0.7 0.3 3.2 8.5
0.7 ‐0.4 0.8 ‐4.9 ‐7.7
‐0.8 0.1 0.0 ‐5.7 ‐0.2
‐1.1 ‐0.4 ‐1.2 1.2 6.6
0.4 ‐0.1 1.2 9.7 ‐7.5
‐1.3 0.7 ‐1.0 ‐2.8 8.4
1.2 2.4 0.1 2.7 ‐6.4
1.0 3.2 ‐0.3 ‐1.6 0.3
‐1.3 ‐4.0 0.7 1.4 ‐3.4
0.9 ‐1.0 ‐1.1 ‐5.5 1.5
‐0.4 0.2 1.8 2.5 ‐0.4
‐1.0 1.5 ‐0.3 ‐1.3 ‐7.3
1.0 3.4 ‐0.3 ‐2.5 2.1
1.3 2.5 0.7 14.6 ‐5.0
‐1.2 3.3 ‐1.3 ‐7.0 ‐2.6
0.8 ‐6.9 0.4 1.0 ‐3.4
‐0.4 1.0 0.2 ‐4.2 ‐2.8
0.8 ‐0.8 0.3 6.2 5.4
1.5 3.1 ‐0.2 ‐6.5 ‐14.1
‐0.8 ‐1.0 0.2 10.0 3.5
‐0.4 ‐0.2 ‐0.4 5.6 ‐1.7
‐0.1 1.6 0.4 ‐8.2 5.0
0.4 ‐3.0 ‐0.8 ‐0.1 ‐5.0
‐2.0 0.5 1.6 2.6 ‐1.9
‐0.7 3.3 ‐2.0 ‐4.3 ‐2.7
‐0.1 ‐3.8 0.9 ‐18.4 ‐3.2
0.2 ‐0.2 ‐0.5 4.9 ‐1.8
‐2.2 ‐0.7 1.2 ‐1.6 1.5
0.2 ‐1.3 0.5 14.8 1.5
‐0.2 0.0 ‐1.1 ‐2.7 ‐6.2
0.0 0.3 ‐1.3 ‐3.0 ‐0.7
‐0.9 2.8 0.2 ‐9.6 8.4
1.3 ‐2.7 0.3 32.2 NA
‐1.3 ‐0.2 ‐0.1 ‐30.9 NA
0.2 ‐1.1 0.2 6.6 NA
‐0.3 1.3 0.4 ‐0.4 0.6
0.4 0.0 ‐0.1 15.5 NA
‐0.6 ‐1.6 ‐0.5 ‐0.9 0.7
0.9 1.2 1.3 34.6 NA
‐0.9 ‐1.6 ‐1.3 ‐19.7 NA
2
8
0.4
1.0
1.8
‐0.9
1.9
0.0
4.3
‐2.5
‐0.1
‐0.9
0.9
‐0.7
‐2.1
‐0.4
2.1
‐0.5
0.2
1.8
‐1.0
‐2.0
‐0.3
0.7
3.1
0.1
1.7
‐2.6
1.0
0.6
‐0.6
‐1.7
‐1.3
4.3
‐1.6
1.5
‐4.1
0.7
2.3
5.0
‐1.6
‐4.5
1.5
‐1.2
0.7
0.5
1.3
‐0.5
‐0.3
‐2.1
‐1.3
‐1.7
1.8
‐3.1
‐0.4
‐0.3
‐0.7
0.0
0.8
‐0.8
0.2
0.5
‐0.4
‐1.4
1.2
‐1.4
62
1
2.0
1.0
7.0
4.0
1.7
2.5
13.5
9.8
8.4
6.3
1.6
3.1
4.4
3.0
4.9
4.7
5.8
4.7
6.3
12.5
12.4
8.7
8.7
6.8
11.0
8.6
10.3
12.6
3.4
5.4
4.7
1.9
15.8
22.9
14.5
30.5
25.6
73.7
22.0
11.4
16.0
10.7
10.7
15.1
31.5
30.9
30.5
38.2
8.8
6.3
5.2
10.0
8.5
0.2
0.7
2.9
3.0
2.8
3.6
5.7
1.4
0.8
0.2
0.2
Variance of Change in Green (sec )
2
3
4
5
6
7
8
4.2 2.0 1.4 0.6 1640.6 NA 1.5
0.5 1.8 0.4 0.4 55.1 NA 4.8
7.4 1.4 5.8 0.5 150.8 NA 2.7
0.1 0.8 9.8 1.6 384.7 NA 5.7
8.2 2.5 3.3 0.2 95.7 NA 16.0
12.8 5.1 0.3 0.2 330.9 28.1 14.8
37.7 2.6 0.2 0.0 93.2 4.7 1.8
2.4 2.9 3.0 0.3 44.4 NA 3.3
57.1 4.3 11.8 0.7 47.5 NA 8.8
75.6 1.9 1.2 0.3 165.8 NA 6.5
100.4 3.2 1.5 8.7 396.6 NA 7.0
82.4 8.2 6.5 1.7 248.5 239.3 13.1
25.4 10.5 2.9 0.5 244.7 NA 10.1
5.0 6.3 2.7 1.1 1173.4 NA 2.6
2.9 0.2 1.5 2.6 304.0 NA 3.0
52.0 3.0 2.3 0.0 72.6 NA 7.5
140.1 0.5 1.6 2.4 93.5 NA 2.2
116.2 2.5 2.0 0.9 887.9 594.0 7.7
95.2 3.3 0.2 1.2 520.6 NA 12.0
51.4 3.0 12.8 2.2 170.5 108.7 11.9
80.2 2.9 32.2 0.3 71.9 4.0 3.8
77.5 1.3 3.3 3.3 42.2 72.8 2.8
62.1 2.5 0.0 1.4 100.1 42.4 8.0
36.5 1.5 2.3 1.6 240.2 16.4 5.9
9.7 2.7 1.0 0.4 45.8 220.9 8.0
74.6 0.9 1.9 1.0 201.1 141.1 1.6
10.7 8.8 1.3 6.8 55.9 6.7 14.4
26.1 1.6 0.7 2.7 66.8 38.2 8.7
18.4 3.5 0.6 1.4 281.6 88.6 0.7
41.7 0.4 2.1 1.2 243.5 46.7 12.5
19.4 1.5 23.0 0.9 124.9 127.7 3.0
1.3 1.3 8.6 1.6 301.8 240.2 26.5
1.1 1.1 25.0 0.8 431.2 157.5 25.5
42.4 0.6 1.7 0.1 130.9 40.2 1.8
57.3 0.7 1.0 2.3 59.7 23.8 12.1
48.6 1.0 0.4 4.6 26.1 123.2 8.3
29.0 1.5 2.5 6.6 73.7 28.9 3.4
31.7 1.2 17.0 2.8 158.4 67.5 111.8
64.0 0.5 16.8 1.2 99.7 NA 28.4
97.5 6.6 47.4 1.4 38.0 NA 34.7
45.8 7.1 4.8 0.3 317.5 221.3 18.2
39.4 4.4 2.6 0.2 40.4 48.1 12.1
82.6 13.8 10.9 2.0 13.6 NA 4.6
12.4 13.3 0.3 2.2 20.1 NA 1.6
13.6 2.6 3.6 1.4 18.3 8.1 11.7
60.2 1.3 20.3 0.4 106.8 59.0 30.0
74.1 2.2 19.9 1.8 107.7 102.5 20.7
18.9 2.7 3.3 1.4 207.7 NA 4.9
64.7 1.8 48.7 2.3 281.4 NA 0.3
113.7 3.1 53.7 1.8 207.1 27.4 2.1
40.8 4.5 21.7 2.9 277.2 6.2 8.1
80.8 5.6 7.7 6.2 210.6 1.6 21.4
23.1 3.5 9.4 12.1 110.4 19.9 10.3
36.6 8.5 1.4 5.2 718.3 77.0 5.1
9.7 2.1 3.2 1.0 316.3 4.3 2.2
4.7 0.4 46.9 0.6 220.2 185.9 2.4
111.2 3.0 72.6 0.4 214.7 NA 4.6
35.4 4.5 7.9 0.1 1101.3 NA 3.5
96.2 3.3 2.6 0.5 248.3 NA 1.5
149.3 2.7 0.4 2.0 274.7 NA 0.8
38.4 3.4 7.9 7.8 727.0 NA 2.3
17.3 3.0 4.8 2.9 491.8 NA 2.8
119.7 0.6 6.8 8.2 3524.1 NA 5.8
50.4 0.9 6.7 7.9 3326.4 NA 4.0
Table 11 through Table 14 summarize the performance evaluation results by phase and
by intersection (all phases). The results also indicated that phase 4 will benefit most from the
proposed algorithm. This is because phase 4 is a side-street phase with no recall; therefore, the
green times observed from both the historical and immediate past are more likely to reflect the
true demand for the green times.
Table 11. Naïve Prediction versus Ground Truth by Phase (Conroe, 50% Failure).
Phase
Number of Compared Intervals
RMSE (sec)
MAE (sec)
MAPE
Mean Error (Bias)
SD of Error
1
2
3
4
5
6
7
8
1412 1409 1231 1190 1116 1286 685 1341
1.7 37.1 1.2
2.4
1.1 61.8 4.0
2.0
1.1 12.7 0.9
1.4
0.7 27.5 2.6
1.3
9.3% 15.4% 9.3% 18.4% 9.7% 24.2% 27.6% 12.7%
0.0 ‐3.0 0.0
0.0
0.0 ‐6.8 0.2
0.0
1.7 37.0 1.2
2.4
1.1 61.5 4.0
2.0
Table 12. Advanced Algorithm versus Ground Truth by Phase (Conroe, 50%
Failure).
Phase
1
2
3
4
5
6
7
8
Number of Compared Intervals 1412 1409 1231 1190 1116 1286 685 1341
RMSE
1.8 37.8 1.3
2.3
1.1 60.0 3.9
2.1
MAE
1.3 14.8 1.0
1.4
0.7 28.3 2.6
1.5
MAPE
10.5% 18.7% 10.4% 18.2% 10.0% 26.5% 26.8% 14.1%
Mean Error (Bias)
‐0.1 ‐1.5 0.0
0.0
0.0 ‐4.3 0.1
0.0
SD of Error
1.8 37.8 1.3
2.3
1.1 59.9 3.9
2.1
Table 13. Comparison of Algorithm Performance by Phase (Conroe, 50%
Failure).
Comparison by Phase
1
2
3
4
RMSE Improvement
‐7.1% ‐1.8% ‐10.1% 1.7%
MAE Improvement
‐14.8% ‐16.5% ‐12.4% 1.1%
MAPE Improvement
‐1.2% ‐3.4% ‐1.1%
0.2%
Bias Improvement
‐22.5% 49.7% 290.4% ‐1908.2%
Error Variance Improvement
‐7.1% ‐2.1% ‐10.1% 1.7%
* Base: Naïve prediction using historical means.
** Advanced: Proposed algorithm using means and variances.
*** Difference = Advanced ‐ Base
63
5
5.2%
‐3.1%
‐0.3%
218.2%
5.2%
6
2.9%
‐2.8%
‐2.4%
37.5%
2.6%
7
1.2%
1.3%
0.8%
61.3%
1.1%
8
‐8.2%
‐11.4%
‐1.4%
151.8%
‐8.2%
Table 14. Comparison of Algorithm Performance for All Phases (Conroe, 50%
Failure).
All Phases
Base Advanced Difference
RMSE Improvement
26.7
26.3
1.5%
MAE Improvement
6.4
6.9
‐7.2%
Bias Improvement
‐1.3
‐0.8
40.8%
Error Variance Improvement
704.5
687.6
2.4%
* Base: Naïve prediction using historical means.
** Advanced: Proposed algorithm using means and variances.
Figure 35 through Figure 37 display the selected comparison of the prediction algorithms.
Similarly, phases on recall mode with intermittent demand from the conflicting movements, such
as phase 2, are difficult to predict with high accuracy. Phases 4 and 5 are relatively more
predictable, as they experience more consistent demand from the conflicting phases.
Phase 2
704.0
604.0
504.0
404.0
304.0
204.0
104.0
1
5
9
13
17
21
25
29
33
37
41
45
49
53
57
61
65
69
73
77
81
85
89
93
97
101
105
109
113
117
121
125
129
133
137
141
145
149
153
157
161
165
169
173
177
181
185
189
4.0
Actual
Base Prediction
Proposed Algorithm
Figure 35. Example Comparison of Algorithms (Conroe, Phase 2, 50% Failure).
Phase 4
22.0
20.0
18.0
16.0
14.0
12.0
10.0
8.0
6.0
1
5
9
13
17
21
25
29
33
37
41
45
49
53
57
61
65
69
73
77
81
85
89
93
97
101
105
109
113
117
121
125
129
133
137
141
145
149
153
157
161
165
169
173
177
181
185
189
4.0
Actual
Base Prediction
Proposed Algorithm
Figure 36. Example Comparison of Algorithms (Conroe, Phase 4, 50% Failure).
64
Phase 5
12.0
11.0
10.0
9.0
8.0
7.0
6.0
5.0
1
5
9
13
17
21
25
29
33
37
41
45
49
53
57
61
65
69
73
77
81
85
89
93
97
101
105
109
113
117
121
125
129
133
137
141
145
149
153
157
161
165
169
173
177
181
185
189
4.0
Actual
Base Prediction
Proposed Algorithm
Figure 37. Example Comparison of Algorithms (Conroe, Phase 5, 50% Failure).
Bryan
Below are the data descriptions used for the performance evaluation of the algorithms at
the Bryan site:

calibration and validation data: 07/03/2009 – 08/12/2009; and

observed phases: 1 to 8.
Table 15 and Table 16 show the examples of input data used for the calculation of the
advanced algorithm on Mondays from 6:00AM to 10:00PM.
65
Table 15. Bryan―Mean and Variance of Green Durations (Mondays).
Monday
Interval
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
1
11.7
11.5
7.4
8.4
8.5
8.6
8.1
8.6
8.3
8.2
8.9
7.8
7.7
8.4
8.5
8.3
8.9
8.8
8.9
8.7
9.4
10.2
9.2
8.9
9.7
9.9
10.1
9.4
9.4
9.2
9.4
9.0
9.6
9.6
9.1
9.5
9.8
10.4
10.2
9.6
9.7
10.8
9.8
10.4
11.5
10.3
11.2
9.9
9.1
9.1
9.2
9.2
8.8
8.8
8.8
10.7
8.6
9.3
8.2
8.5
9.4
8.5
8.3
8.0
Mean Green Duration (sec)
2
3
4
5
6
7
10.3 8.7 14.5 7.2 13.7 7.9
12.6 9.5 17.4 8.0 16.4 8.1
16.6 11.5 18.2 8.4 14.5 9.0
17.3 12.1 16.8 9.1 15.6 9.9
19.5 11.9 18.6 9.0 18.0 10.9
21.6 14.2 22.7 9.4 18.0 14.3
23.9 14.2 23.0 10.6 19.8 15.0
20.4 11.7 19.8 9.8 18.5 11.9
18.3 11.3 19.2 9.1 18.2 11.3
20.1 11.1 18.4 9.4 18.4 10.4
18.9 11.3 19.5 9.5 18.5 10.7
18.5 11.0 18.1 9.0 17.8 10.9
18.8 10.6 18.3 9.9 18.5 9.8
20.7 11.6 17.7 10.1 21.6 9.9
19.7 10.8 18.0 8.4 18.5 10.1
19.7 11.8 19.3 10.9 19.4 9.9
20.7 11.5 18.4 9.5 19.0 10.3
19.3 11.2 18.2 10.4 17.6 10.5
18.1 11.5 18.6 10.7 18.1 10.7
18.0 12.0 18.7 9.5 18.7 9.8
18.3 12.6 18.4 9.6 18.1 10.6
20.5 11.8 17.4 11.3 18.4 9.8
21.5 11.8 19.4 10.7 18.8 11.0
21.4 12.9 19.7 11.4 18.7 12.5
21.1 13.2 20.6 11.6 19.0 12.2
19.3 11.8 20.6 10.7 20.1 11.5
20.2 11.9 20.4 10.5 20.8 11.7
21.0 13.0 19.1 10.4 20.8 11.1
18.3 11.4 19.0 10.1 19.7 10.5
21.6 12.4 19.9 10.3 17.9 10.1
19.6 10.7 20.9 11.0 19.8 11.1
21.1 12.3 19.1 10.6 19.3 10.4
16.4 12.3 19.8 10.1 19.7 11.0
20.1 12.4 18.5 10.4 20.3 10.4
19.2 11.9 20.0 10.1 18.8 10.8
20.7 12.2 18.0 10.2 20.2 10.5
19.2 11.8 19.1 10.1 18.5 9.6
19.6 13.2 19.2 10.0 20.9 11.2
23.1 13.5 18.7 12.0 21.3 10.7
21.6 14.1 18.1 11.3 20.3 10.1
21.3 13.3 17.8 10.7 20.7 9.8
21.0 14.2 18.5 11.3 21.4 10.2
24.2 14.1 19.2 12.0 21.8 10.9
23.0 16.1 20.0 11.1 23.5 11.4
23.7 16.4 19.7 11.9 23.4 11.1
27.1 15.4 19.0 14.5 22.7 10.3
21.0 13.7 17.8 10.6 21.9 10.5
17.1 12.4 16.5 9.7 20.4 9.5
18.1 12.0 16.9 8.8 18.6 10.0
17.4 11.3 14.9 9.2 19.9 9.3
15.3 11.1 13.2 9.2 18.4 8.8
16.6 10.4 13.7 8.7 17.6 8.7
15.6 12.6 14.3 8.8 19.7 8.1
17.0 13.8 12.9 8.5 17.0 8.4
15.3 10.8 13.0 8.1 16.0 8.5
15.0 13.2 15.2 9.1 20.1 10.6
14.9 10.7 13.1 8.1 18.1 9.8
16.6 12.3 13.6 7.7 19.2 9.0
16.0 12.8 13.4 7.2 21.1 7.9
17.7 12.6 13.5 7.8 19.9 8.8
16.9 11.4 12.0 8.9 18.9 8.0
16.2 11.9 13.5 8.1 17.5 7.5
15.0 11.2 13.3 7.4 16.5 7.7
14.9 9.5 11.6 7.1 17.3 7.7
2
8
15.6
17.0
17.8
16.3
16.7
19.8
20.5
18.0
17.9
15.5
17.0
16.2
16.1
17.9
17.3
18.6
16.4
18.1
18.3
18.6
18.8
19.4
20.1
19.1
20.4
19.5
19.5
20.2
18.7
20.1
18.9
19.7
20.8
19.6
20.3
19.7
21.4
21.1
21.8
20.6
20.9
22.2
21.7
24.2
25.7
24.4
21.7
19.2
19.7
17.9
16.5
15.8
20.2
21.3
15.5
16.5
16.3
17.2
21.3
20.4
18.9
18.7
17.6
15.8
66
Variance of Green Durations (sec )
1
2
3
4
5
6
7
8
36.6 27.3 5.6 36.1 0.4 76.5 2.6 49.6
35.1 49.6 10.4 35.7 3.3 87.0 3.8 47.2
0.6 92.1 25.4 48.9 6.5 60.8 5.4 45.6
11.1 113.8 23.4 48.4 12.3 70.0 12.8 52.4
4.0 106.9 19.7 55.5 5.7 74.9 14.0 28.1
11.0 94.7 31.3 77.2 10.0 80.3 23.2 28.4
5.8 76.5 26.1 45.6 14.3 63.1 19.1 22.0
7.6 76.3 22.8 37.6 9.9 61.1 16.5 28.5
6.7 104.5 19.1 45.8 8.3 63.5 14.6 44.7
3.1 118.0 19.8 39.1 7.7 65.9 13.9 30.6
10.0 76.6 15.8 38.0 9.0 67.3 14.0 35.6
2.9 114.4 18.1 48.2 11.5 63.3 11.8 25.6
1.6 92.7 18.6 35.8 13.5 71.0 7.9 27.5
4.4 90.8 26.6 39.8 15.7 59.8 7.1 45.2
5.5 90.5 13.6 33.9 3.4 65.3 12.0 36.2
2.9 95.6 24.4 47.3 16.3 52.1 7.1 31.3
3.5 72.2 17.6 55.4 8.3 76.0 10.5 31.0
10.8 92.1 19.3 46.0 10.8 44.2 12.2 42.1
7.7 55.1 19.5 44.7 17.6 52.4 13.9 23.0
5.7 51.5 19.4 42.8 10.4 50.9 10.4 35.0
6.0 67.5 23.6 40.0 7.5 52.0 7.7 28.5
13.0 60.6 20.6 22.3 16.0 60.0 8.0 20.5
6.8 68.6 20.8 23.4 12.0 52.6 11.7 42.7
4.9 79.0 21.0 25.9 14.3 48.9 11.9 26.8
8.7 78.9 26.1 41.8 17.8 48.3 19.5 21.0
8.5 59.3 20.2 24.5 11.1 55.1 11.1 27.7
13.2 47.9 23.2 25.8 13.0 50.7 17.9 30.1
11.8 80.7 21.6 44.2 9.8 47.1 10.8 32.5
5.3 86.1 21.9 32.1 11.4 47.8 10.7 36.0
8.3 68.8 22.5 55.0 12.1 50.3 8.1 27.8
5.6 77.1 14.3 44.1 11.1 47.9 16.4 28.3
6.7 66.0 24.8 44.7 14.1 37.8 7.7 31.0
8.3 41.7 25.8 36.7 7.0 51.7 14.3 49.8
8.7 85.4 16.7 33.5 11.9 40.9 10.3 38.2
7.4 49.5 18.5 35.1 10.7 42.1 7.7 32.9
7.6 87.7 21.7 50.3 13.5 44.0 11.7 39.4
12.5 46.3 26.8 39.1 9.1 55.5 8.7 43.2
12.6 62.8 26.9 20.6 10.5 50.6 11.9 28.2
10.4 86.3 13.5 18.8 19.0 34.4 11.5 35.1
10.1 88.7 25.6 23.6 12.9 41.3 7.6 34.3
8.7 52.9 22.1 22.7 13.1 35.9 6.6 30.3
13.2 65.9 18.5 19.6 14.3 42.2 7.5 24.6
11.0 56.3 13.4 26.2 14.4 33.4 10.9 25.8
8.5 53.6 19.3 17.7 12.7 24.7 14.4 24.7
11.8 58.3 33.1 20.6 16.0 25.6 8.4 47.7
12.6 108.6 14.2 17.8 17.3 30.6 6.5 20.4
13.6 67.1 20.0 29.3 13.5 38.9 10.4 36.3
6.6 55.0 16.1 15.2 13.2 55.4 9.9 35.0
7.7 40.4 19.3 20.6 4.6 34.9 9.4 30.8
6.8 60.2 12.5 32.9 5.6 49.0 10.0 33.5
14.1 63.0 18.8 25.6 4.7 54.3 4.6 40.3
11.5 60.4 18.3 23.7 6.7 46.8 3.5 36.4
5.7 62.3 39.5 31.8 5.5 62.4 2.9 91.3
6.6 68.1 50.5 13.2 3.3 46.8 4.2 75.7
8.3 59.0 25.3 30.3 3.1 64.8 13.4 71.5
26.2 72.9 42.6 43.0 12.3 99.2 33.5 52.4
9.7 55.3 21.3 46.5 3.1 73.0 31.3 60.5
6.3 92.1 29.9 23.9 1.5 75.2 15.7 47.4
3.5 74.4 29.1 30.0 0.2 50.9 2.8 71.9
4.9 124.5 26.4 41.0 1.5 74.3 13.2 98.7
12.7 84.2 28.4 22.4 8.2 87.2 3.7 59.9
11.1 73.8 32.2 41.4 3.5 82.3 1.6 83.9
7.7 77.9 28.1 36.7 0.7 72.6 2.5 120.8
7.0 137.8 14.7 28.2 0.3 134.2 3.0 63.5
Table 16. Bryan―Mean and Variance of Change in Green Durations (Mondays).
Monday
Interval
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
1
3.9
‐0.8
‐2.9
1.1
0.1
0.6
‐1.0
0.2
‐0.1
‐0.3
0.9
‐1.0
0.0
0.5
0.2
‐0.2
0.7
‐0.2
0.2
‐0.2
0.7
0.7
‐0.8
‐0.4
0.8
0.2
0.2
‐0.7
‐0.1
‐0.2
0.2
‐0.2
0.5
0.1
‐0.6
0.4
0.3
0.5
0.0
‐0.7
0.1
1.1
‐0.9
0.7
1.0
‐1.3
1.0
‐1.4
‐0.8
‐0.1
0.0
0.1
‐0.3
‐0.2
0.0
1.6
‐1.7
0.5
‐0.9
0.4
0.9
‐1.0
0.0
‐0.3
Average Change (sec)
2 3 4 5 6 7
‐0.1 0.7 2.7 0.0 4.2 0.4
2.9 0.7 2.9 0.6 3.1 0.2
4.6 2.1 0.9 0.6 ‐1.8 1.0
1.3 0.8 ‐1.0 0.6 1.7 1.0
1.5 ‐0.3 1.6 ‐0.1 2.0 1.0
2.1 2.4 3.9 1.0 ‐0.1 3.6
1.8 ‐0.1 0.2 0.6 1.1 0.6
‐3.7 ‐2.4 ‐3.2 ‐0.8 ‐1.4 ‐3.1
‐1.7 ‐0.6 ‐0.5 ‐0.7 0.2 ‐0.6
2.0 0.0 ‐0.7 0.3 0.2 ‐0.9
‐1.5 ‐0.1 0.8 0.0 ‐0.1 0.2
0.1 ‐0.2 ‐1.1 ‐0.4 0.0 0.2
‐0.1 ‐0.4 0.1 1.2 0.1 ‐1.1
1.3 0.9 ‐0.7 ‐0.1 2.4 0.0
‐0.6 ‐0.8 0.3 ‐1.7 ‐2.5 0.4
0.0 1.1 1.4 2.6 0.6 ‐0.4
0.9 ‐0.2 ‐0.8 ‐1.5 ‐0.3 0.2
‐1.9 ‐0.5 ‐0.4 0.8 ‐1.8 0.4
‐1.0 0.4 0.4 0.6 0.7 0.1
0.0 0.3 0.1 ‐1.4 0.7 ‐0.8
0.2 0.8 ‐0.4 0.1 ‐0.5 0.7
2.0 ‐0.9 ‐0.9 1.7 0.2 ‐0.8
1.2 ‐0.1 2.0 ‐0.7 0.2 1.2
‐0.3 1.2 0.2 0.8 0.0 1.4
‐0.2 0.3 1.0 0.2 0.4 ‐0.3
‐1.7 ‐1.4 ‐0.1 ‐0.9 1.1 ‐0.7
0.7 0.2 ‐0.1 0.0 0.6 0.3
1.2 1.1 ‐1.4 ‐0.2 0.0 ‐0.7
‐2.9 ‐1.7 ‐0.1 ‐0.3 ‐1.0 ‐0.7
3.1 1.2 1.0 0.2 ‐1.8 ‐0.4
‐1.8 ‐1.8 1.0 0.4 2.0 1.0
1.4 1.6 ‐1.7 ‐0.2 ‐0.5 ‐0.8
‐4.6 0.0 0.7 ‐0.6 0.3 0.7
3.5 0.2 ‐1.4 0.3 0.5 ‐0.6
‐0.9 ‐0.6 1.5 ‐0.3 ‐1.4 0.4
1.5 0.2 ‐1.9 0.1 1.3 ‐0.3
‐1.6 ‐0.2 1.0 0.1 ‐1.6 ‐0.9
0.6 1.3 0.1 ‐0.2 2.3 1.7
3.5 0.3 ‐0.5 2.1 0.4 ‐0.6
‐1.5 0.5 ‐0.6 ‐0.6 ‐1.0 ‐0.6
‐0.4 ‐0.8 ‐0.4 ‐0.4 0.3 ‐0.3
‐0.2 1.0 0.8 0.3 0.8 0.4
3.2 ‐0.1 0.6 0.6 0.4 0.7
‐1.3 2.0 0.8 ‐0.8 1.6 0.5
0.8 0.7 ‐0.2 0.8 0.0 ‐0.3
3.5 ‐1.2 ‐0.6 2.6 ‐0.6 ‐0.8
‐6.2 ‐1.8 ‐1.2 ‐3.8 ‐0.7 0.2
‐4.0 ‐1.3 ‐1.4 ‐1.0 ‐1.6 ‐1.1
1.1 ‐0.3 0.5 ‐0.9 ‐1.7 0.5
‐0.6 ‐0.8 ‐2.1 0.4 1.2 ‐0.6
‐2.0 ‐0.2 ‐1.6 0.0 ‐1.3 ‐0.6
1.4 ‐0.6 0.4 ‐0.5 ‐0.8 ‐0.2
‐0.8 2.3 0.5 0.0 2.1 ‐0.5
1.3 1.5 ‐1.3 ‐0.3 ‐2.6 0.2
‐1.6 ‐3.4 0.1 ‐0.3 ‐0.7 0.3
‐0.4 2.8 2.5 0.9 3.8 2.2
‐0.2 ‐2.9 ‐2.2 ‐0.9 ‐2.1 ‐1.2
1.5 1.6 0.3 ‐0.4 1.1 ‐0.6
‐0.1 0.7 0.0 ‐0.5 2.2 ‐1.2
2.4 ‐0.2 0.2 0.5 ‐0.7 1.1
‐1.5 ‐0.9 ‐1.7 1.4 ‐0.9 ‐0.9
‐0.9 ‐0.1 1.6 ‐0.8 ‐1.6 ‐0.5
‐1.2 ‐0.3 0.0 ‐1.0 ‐1.2 0.2
0.8 ‐2.0 ‐1.9 ‐0.2 1.4 0.0
2
8
2.3
1.4
1.4
‐1.3
0.1
2.8
0.5
‐2.5
0.0
‐2.6
1.5
‐0.6
‐0.3
1.9
‐0.5
1.3
‐1.9
1.3
0.3
0.3
0.2
0.6
0.8
‐1.2
1.3
‐0.8
0.0
0.7
‐1.4
1.3
‐1.2
0.8
1.2
‐1.4
0.8
‐0.6
1.7
‐0.3
0.7
‐1.0
0.2
1.3
‐0.6
2.5
1.9
‐1.5
‐2.7
‐2.8
0.7
‐1.9
‐1.4
‐0.7
4.4
1.2
‐5.9
0.8
‐0.2
1.1
4.1
‐0.1
‐1.8
‐0.4
‐0.3
‐2.5
67
Variance of Change in Green (sec )
1
2
3
4 5 6
7
8
29.3 0.6 1.2 2.3 0.1 22.2 0.1 1.1
40.3 42.2 0.7 5.3 0.6 82.2 0.7 9.3
16.8 11.0 3.5 6.9 1.7 48.4 0.8 26.7
4.1 10.3 3.4 9.8 0.9 20.7 0.8 3.1
2.1 18.0 2.1 11.9 4.8 3.8 0.5 6.3
8.1 9.0 6.9 18.9 6.2 5.5 7.6 2.5
5.3 17.5 7.3 10.9 5.5 2.3 4.9 1.6
2.5 28.9 10.6 2.9 2.0 2.2 1.5 1.5
0.5 7.9 10.3 3.4 3.1 6.5 5.6 4.0
3.9 5.9 5.9 0.5 0.5 2.3 1.5 9.1
2.0 14.5 5.1 7.8 1.1 8.9 1.0 5.2
0.9 8.7 3.3 10.8 1.9 3.8 0.4 1.1
0.4 7.2 3.9 4.5 2.2 9.4 0.5 7.4
1.1 3.3 2.6 5.8 2.2 9.5 1.0 2.6
2.8 13.0 2.6 1.2 2.6 5.7 1.7 6.6
2.1 38.4 0.1 1.8 4.3 3.4 2.3 4.8
0.6 41.7 5.1 5.4 3.9 9.3 1.5 16.1
1.5 21.6 10.7 7.5 2.2 12.7 0.6 30.7
1.8 13.4 2.9 2.5 3.1 1.6 2.4 6.4
1.3 5.4 7.3 12.2 3.2 0.6 1.2 7.5
1.4 3.7 3.7 16.5 2.0 3.6 1.7 1.1
1.4 20.2 10.6 2.0 4.2 2.6 0.6 1.1
2.6 35.4 1.5 4.2 4.3 8.2 1.9 3.9
0.8 24.6 3.0 5.1 4.6 0.5 3.4 1.7
0.7 12.5 4.8 9.5 0.2 5.5 6.1 5.4
0.8 7.2 3.6 6.5 0.8 8.1 2.8 5.7
0.5 3.4 0.5 2.3 6.4 9.4 1.9 2.9
0.9 16.3 2.4 4.4 8.4 6.4 2.3 5.3
2.0 7.6 1.1 3.2 2.6 3.7 2.0 10.7
0.5 7.2 6.1 1.6 2.3 3.3 0.9 10.8
0.3 13.8 3.2 1.3 5.6 4.2 1.6 7.0
1.5 18.1 3.2 6.5 5.6 9.2 4.1 3.8
1.2 6.5 9.4 3.5 2.1 3.2 2.5 1.8
2.4 5.4 4.8 7.2 0.4 0.7 1.7 4.6
3.4 2.5 0.3 8.4 1.4 1.5 1.7 6.8
1.0 7.1 2.3 5.0 3.4 7.0 1.6 1.9
5.0 15.6 3.7 4.9 1.6 12.2 1.3 1.2
3.1 8.1 2.2 3.5 4.3 6.2 0.9 0.6
3.7 8.7 4.1 2.3 2.2 2.4 2.2 5.0
3.6 8.6 6.5 3.9 2.2 1.5 0.5 8.2
1.3 3.4 3.2 1.4 3.4 3.9 1.0 4.0
3.5 16.6 2.4 1.0 9.2 3.4 1.6 8.7
1.7 11.6 4.7 4.8 4.3 9.7 1.4 1.0
0.2 9.3 3.4 3.7 3.0 3.7 2.9 3.7
0.9 1.9 14.9 11.3 0.7 3.6 4.7 14.8
3.4 9.6 15.4 3.6 1.8 5.5 0.7 6.3
7.0 11.3 2.9 1.5 3.4 1.6 2.0 1.0
1.7 5.9 2.0 1.7 1.4 3.3 1.7 1.4
1.2 5.7 1.3 2.4 2.2 3.4 0.7 4.5
0.6 3.0 3.0 4.9 0.4 9.5 2.6 8.3
3.9 3.6 6.8 4.8 2.8 16.2 2.8 4.5
3.2 2.9 1.9 8.4 2.6 4.2 0.7 1.9
1.1 4.1 5.6 2.1 2.7 4.1 0.5 12.3
1.7 10.7 12.4 2.8 0.3 1.8 0.1 17.8
1.4 4.7 17.8 0.6 2.8 8.7 3.3 10.5
9.0 5.4 18.4 5.5 4.1 26.9 24.0 16.5
10.7 12.5 25.7 14.4 6.9 18.5 55.1 5.6
2.1 17.8 9.0 3.7 0.6 2.6 6.9 14.4
0.9 10.7 1.1 5.1 0.2 13.6 1.6 18.6
1.3 7.7 7.1 0.9 0.3 8.4 2.1 22.9
6.0 9.9 1.6 2.9 3.1 2.9 3.3 7.1
2.3 4.7 4.7 2.2 1.1 5.4 0.3 1.5
1.3 1.0 3.7 5.9 2.3 10.3 0.1 24.3
1.1 7.6 7.5 5.3 0.3 12.8 0.8 52.1
Table 17 through Table 20 summarize the performance evaluation results by phase and
by intersection (all phases).
Table 17. Naïve Prediction versus Ground Truth by Phase (Bryan, 50% Failure).
Phase
Number of Compared Intervals
RMSE (sec)
MAE (sec)
MAPE
Mean Error (Bias)
SD of Error
1
2
3
4
5
6
7
8
1819 1853 1832 1854 1709 1853 1837 1853
1.1
5.4
1.7
1.7
1.0
5.7
1.2
2.1
0.7
3.6
1.1
1.2
0.7
3.8
0.8
1.5
7.3% 18.0% 10.4% 8.9% 7.2% 17.9% 8.6% 9.9%
0.0 ‐0.6 0.0 ‐0.1 0.0 ‐0.7 ‐0.1 ‐0.1
1.1
5.4
1.7
1.7
1.0
5.7
1.2
2.1
Table 18. Advanced Algorithm versus Ground Truth by Phase (Bryan, 50%
Failure).
Phase
Number of Compared Intervals
RMSE
MAE
MAPE
Mean Error (Bias)
SD of Error
1
2
3
4
5
6
7
8
1819 1853 1832 1854 1709 1853 1837 1853
1.1
4.4
1.7
1.9
1.1
4.5
1.3
2.2
0.7
2.9
1.2
1.4
0.7
2.9
0.9
1.7
7.7% 15.0% 11.5% 10.4% 8.0% 14.1% 9.4% 11.2%
0.0
0.0
0.0
0.0
0.0
0.0 ‐0.1 ‐0.1
1.1
4.4
1.7
1.9
1.1
4.5
1.3
2.2
Table 19. Comparison of Algorithm Performance by Phase (Bryan, 50% Failure).
Comparison by Phase
1
2
3
4
RMSE Improvement
‐2.7% 17.5% ‐4.5% ‐11.2%
MAE Improvement
‐5.3% 18.8% ‐9.5% ‐16.9%
MAPE Improvement
‐0.4% 3.0% ‐1.1% ‐1.6%
Bias Improvement
487.9% 93.6% 76.2% 78.9%
Error Variance Improvement
‐2.7% 17.0% ‐4.5% ‐11.3%
* Base: Naïve prediction using historical means.
** Advanced: Proposed algorithm using means and variances.
*** Difference = Advanced ‐ Base
68
5
‐8.9%
‐12.3%
‐0.8%
23.1%
‐8.9%
6
20.8%
24.8%
3.8%
94.8%
20.2%
7
‐7.4%
‐10.3%
‐0.8%
‐30.6%
‐7.3%
8
‐5.0%
‐11.9%
‐1.3%
43.8%
‐5.2%
Table 20. Comparison of Algorithm Performance for All Phases (Bryan, 50%
Failure).
All Phases
Base Advanced Difference
RMSE Improvement
3.1
2.7
14.0%
MAE Improvement
1.7
1.6
7.1%
Bias Improvement
‐0.2
0.0
82.6%
Error Variance Improvement
9.5
7.1
25.3%
* Base: Naïve prediction using historical means.
** Advanced: Proposed algorithm using means and variances.
Figure 38 through Figure 40 display the comparison of the prediction algorithms on
phases 2, 4, and 5 on selected time of day and day of week. All the graphs shown were the
evaluation results from the 50 percent detector failure scenario.
Phase 2
41.0
36.0
31.0
26.0
21.0
16.0
11.0
1
5
9
13
17
21
25
29
33
37
41
45
49
53
57
61
65
69
73
77
81
85
89
93
97
101
105
109
113
117
121
125
129
133
137
141
145
149
153
157
161
165
169
173
177
181
185
189
6.0
Actual
Base Prediction
Proposed Algorithm
Figure 38. Example Comparison of Algorithms (Bryan, Phase 2, 50% Failure).
Phase 4
24.0
22.0
20.0
18.0
16.0
14.0
12.0
10.0
8.0
1
5
9
13
17
21
25
29
33
37
41
45
49
53
57
61
65
69
73
77
81
85
89
93
97
101
105
109
113
117
121
125
129
133
137
141
145
149
153
157
161
165
169
173
177
181
185
189
6.0
Actual
Base Prediction
Proposed Algorithm
Figure 39. Example Comparison of Algorithms (Bryan, Phase 4, 50% Failure).
69
Phase 5
14.0
13.0
12.0
11.0
10.0
9.0
8.0
7.0
1
5
9
13
17
21
25
29
33
37
41
45
49
53
57
61
65
69
73
77
81
85
89
93
97
101
105
109
113
117
121
125
129
133
137
141
145
149
153
157
161
165
169
173
177
181
185
189
6.0
Actual
Base Prediction
Proposed Algorithm
Figure 40. Example Comparison of Algorithms (Bryan, Phase 5, 50% Failure).
Overall Performance Comparison
Table 21 compares the evaluation results using all phases combined for each study site
with varying rates of detector failure. The one-interval prediction refers to the scenario at which
the detector only fails one interval at a time and thus the immediate past data are always
available as an input into the prediction equation using the proposed algorithm. With varying
rates of the detector failure, the likelihood of the availability of immediate past data decreases
with the increasing rates of detector failure. In cases where the immediate past data are not
available, the proposed algorithm will utilize the predicted values from the previous intervals as
the immediate past data and continue this pattern recursively until the detector resumes normal
behavior. With 100 percent detector failure rate, the advanced algorithm will rely entirely upon
the predicted values as model inputs rather than the immediate past data (as the data are not
available). As a result, the advantage of utilizing the immediate past data for the proposed
algorithm diminishes with the increasing rates of detector failure.
Researchers can convert the rates of detector failure into the average length of time the
algorithm will go into recursive prediction mode, i.e., utilizing the predicted values from the
previous interval rather than the actual immediate past data. Table 22 summarizes the
relationship between the detector failure rate and average length of time.
Figure 41 shows the performance of the algorithms at different detector failure rates. The
Bryan site sees the largest improvement among those evaluated because the site is the
intersection of two moderate-volume roadways with consistent demand for all phases, unlike the
other two sites where the volumes are heavy on the main street and very intermittent on the side
street.
70
Table 21. Overall Performance Comparison at Varying Rates of Detector Failure.
Percent Failure
90% 75% 50% 25%
0.7% 0.4% 1.5% 4.5%
‐3.3% ‐4.4% ‐7.2% ‐5.9%
12.1% 25.8% 40.8% 48.4%
1.2% 0.3% 2.4% 7.9%
10%
2.6%
‐8.8%
22.5%
4.8%
Continuous Prediction
1‐Interval
3.8%
‐5.5%
43.7%
6.7%
Percent Failure
Bryan
Overall Comparison
100% 90% 75% 50% 25%
RMSE Improvement
0.6% 11.9% 14.7% 14.0% 17.5%
MAE Improvement
0.0% 6.1% 8.1% 7.1% 7.9%
Bias Improvement
‐0.6% 51.2% 81.3% 82.6% 94.2%
Error Variance Improvement 1.1% 22.0% 26.6% 25.3% 31.5%
10%
17.5%
7.3%
0.3%
32.2%
Continuous Prediction
1‐Interval
17.6%
9.1%
87.6%
31.5%
10%
3.5%
‐1.3%
32.0%
4.7%
‐1.3%
Continuous Prediction
1‐Interval
2.4%
‐3.2%
33.8%
2.3%
‐1.6%
Conroe
Overall Comparison
RMSE Improvement
MAE Improvement
Bias Improvement
Error Variance Improvement
Waco
Overall Comparison
RMSE Improvement
MAE Improvement
Bias Improvement
Error Variance Improvement
MAPE Improvement
100%
0.2%
‐1.5%
1.0%
0.4%
100%
0.1%
‐1.6%
3.3%
‐0.2%
‐0.5%
Percent Failure
90% 75% 50% 25%
0.2% 0.8% 1.5% 1.7%
‐1.8% ‐2.4% ‐3.0% ‐3.6%
8.8% 15.8% 26.3% 26.9%
‐0.3% 0.2% 1.1% 1.9%
‐0.6% ‐1.0% ‐1.3% ‐1.2%
Table 22. Detector Failure Rate and Average Length of Failure Time.
% Failure Average Length of Failure Time (min)
90%
150
75%
60
50%
30
25%
20
10%
17
71
Proposed Algorithm versus Historical Means (RMSE Improvement)
20.0%
18.0%
16.0%
14.0%
12.0%
10.0%
8.0%
6.0%
4.0%
2.0%
0.0%
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Percent of Detector Failure
Conroe
Bryan
Waco
Figure 41. Comparison of Algorithm Performance by Site (RMSE).
CONCLUSIONS
TTI researchers developed and evaluated the adaptive variable initial module (Module 1)
and the detector failure module (Module 2) in this project. Researchers compared Module 1
performance with actual queue clearance times and found good correlation between the predicted
initial green and the queue clearance times after considering the minimum green factor. The
performance was accurate for both of the approach phases as well as weekdays and weekends.
Module 1 can be used at intersections where stop-bar detectors are not installed to improve the
intersection operations. It can also be used at intersections that have both stop-bar and upstream
detectors if the stop-bar detectors malfunction.
The detector failure module (Module 2) predicted the phase duration at the onset of the
phase using two methodologies. One was a rolling average of the phase utilization from a
database of four weeks of data. The second was a model that used variances in phase utilization
both within the historical database as well as from the current day. These two models predicted
72
the phase utilizations for detector failures ranging from 10 percent to 100 percent. The rolling
average model was implemented in the field. TTI researchers then compared these two
predictions with the actual phase duration for each phase. This project discovered that the rolling
average model was very accurate for predicting the phase duration. These predictions were more
accurate during time periods having consistent activity on the phases (peak periods). During the
extremely low volume periods, the predictions were not very accurate due to the randomness of
vehicle arrival patterns. The advance module predicted the phase duration as accurately as the
rolling average module in the Waco and Conroe sites. However, the advance module was more
accurate than the rolling average in Bryan. The sites in Waco and Conroe had very low volumes
on the cross streets for most of the day. Random arrival patterns on the minor streets during low
volume periods impacted the accuracy of the major movements by both the prediction models.
However, the Bryan site experienced equally high volumes on the minor streets as compared to
the major movements. These volume patterns caused the advance phase prediction model to be
more accurate than the rolling average model. Data requirements for the two models are easily
available within the traffic signal controller.
73
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