Operation of Traffic Signal Systems in Oversaturated Conditions, Volume 2 – Final Report (2014)

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Contents List of Figures ............................................................................................................................... vii List of Tables .................................................................................................................................xii List of Equations .......................................................................................................................... xiv Author Acknowledgments ........................................................................................................... xvi Abstract ....................................................................................................................................... xvii Executive Summary ........................................................................................................................ 1 Summary of Task 1: Literature Review .................................................................................... 2 Summary of Task 2: Definitions and Diagnosis ....................................................................... 2 Summary of Task 3: Development of Objectives and Strategies ........................................... 3 Summary of Expert Practitioner Interviews ............................................................................. 5 Summary of Practitioner Guidance ........................................................................................... 7 Summary of Test Applications ................................................................................................. 9 Test Cases for the Multi-Objective Pareto Analysis ............................................................ 11 Test Cases for Direct Application of TOSI and SOSI to Re-allocate Green Time .............. 12 Test Cases for the Application of the Practitioner Guidance and Online Evaluation of Mitigations ........................................................................................................................... 12 Conclusions and Directions for Further Research .................................................................. 13 Directions for Future Research ............................................................................................... 14 Chapter 1: Background and Motivation ........................................................................................ 16 Consolidated Results of Interviews with Expert Practitioners ............................................... 17 Expert Practitioners Thoughts on Definitions............................................................................... 18 Expert Practitioners Thoughts on Diagnosis................................................................................. 18 Expert Practitioners Thoughts on Strategies ................................................................................. 19 Automated Performance Measures and Central System Diagnostics ........................................... 22 Detection Systems and Needs ....................................................................................................... 22 Summary of Expert Practitioner Interviews ................................................................................. 23 Summary of Motivation and Background..................................................................................... 23 Chapter 2: Research Approach ................................................................................................... 25 Definitions..................................................................................................................................... 25 Operation of traffic signal systems in oversaturated conditions Page i

Extension of the Definition for Spatial Extent .............................................................................. 28 Detrimental Effects ....................................................................................................................... 29 Blocking and Non-Blocking Conditions ....................................................................................... 30 Oversaturation on a Route ............................................................................................................ 31 Oversaturation on a Network ........................................................................................................ 32 Special Cases of Network Oversaturation .................................................................................... 33 Large-Scale Problems and Gridlock ............................................................................................. 35 Duration of Oversaturation ........................................................................................................... 36 Causal Factors ............................................................................................................................... 37 Occurrence Frequency .................................................................................................................. 38 Specific Symptoms on Routes and at Intersections ...................................................................... 39 Summary of Characteristics that Define an Oversaturated Scenario ............................................ 42 Oversaturation Problem Characterization and System Dynamics ................................................ 43 Summary ....................................................................................................................................... 45 Measuring Length of Queue and Overflow Queuing Effects ....................................................... 46 Quantitative Characterization of the Severity of Oversaturation .................................................. 46 Motivation for the Measurement of Queue Length and Oversaturation Severity ........................ 47 A Quantifiable Measure of Oversaturation ................................................................................... 48 Algorithms for Identification of Oversaturation ........................................................................... 50 Example: Field-test Results .......................................................................................................... 59 Estimation Results of Overflow Queue Length ............................................................................ 61 Summary of Diagnostics for Severity of Oversaturation .............................................................. 67 A Multi-Objective Methodology for Designing and Evaluating Signal Timing Plans Under Oversaturated Conditions........................................................................................................... 69 Overview of the Methodology ...................................................................................................... 70 Framework for Determination of the Traffic Flows on Critical Routes ....................................... 71 Cycle Length Determination ......................................................................................................... 73 Determination of Splits ................................................................................................................. 76 Design of Offsets .......................................................................................................................... 77 Offsets to Avoid Spillback ............................................................................................................ 77 Offsets to Avoid Starvation .......................................................................................................... 78 Operation of traffic signal systems in oversaturated conditions Page ii

Combining the Design of Splits and Offsets................................................................................. 80 Optimization Problem Formulation .............................................................................................. 82 Construction of the Pareto Front ................................................................................................... 84 Control Objectives ........................................................................................................................ 86 Delay Minimization ...................................................................................................................... 87 Throughput Maximization ............................................................................................................ 88 Queue Management ...................................................................................................................... 89 Formulation for Delay Minimization Objective ........................................................................... 90 Throughput Maximization ............................................................................................................ 91 Queue Management Control ......................................................................................................... 93 Development and Analysis of Timing Plans for Managing Oversaturated Conditions ................ 94 Using Volume Profiles on Critical Routes in the Design of Signal Timing Plans ....................... 95 Explicit Consideration of Volume Spillover................................................................................. 96 Optimization Procedure ................................................................................................................ 97 Performance Measure Evaluation for the Generated Optimal Timing Plans ............................... 97 Switching Between Control Strategies ......................................................................................... 99 Summary ..................................................................................................................................... 101 Online Implementation of Mitigation Strategies ........................................................................ 103 Determining Detector Locations ........................................................................................ 104 Placement of Detectors for Online Recognition of a Scenario .......................................... 105 Detector Data Aggregation Intervals and Persistence Time .............................................. 106 Logic Configuration Example............................................................................................ 106 Online Performance Evaluation Framework ..................................................................... 110 Summary ..................................................................................................................................... 115 Chapter 3: Test Applications ...................................................................................................... 117 Arterial Test Case: Application of the multi-Objective Timing Plan Development and Evaluation Framework ............................................................................................................. 119 Traffic Patterns on Reston Parkway ........................................................................................... 120 Illustration Using of Critical Routes to Determine Mitigation Strategies .................................. 124 Cycle Length Calculations .......................................................................................................... 128 Design of Splits and Offsets ....................................................................................................... 130 Operation of traffic signal systems in oversaturated conditions Page iii

Simulation Experiment ............................................................................................................... 133 Simulation Results and Evaluation ............................................................................................. 134 Pareto Front Analysis .................................................................................................................. 137 Scenario 5 Results: Pareto Front ................................................................................................. 138 Scenario 1 Results ....................................................................................................................... 143 Scenario 2 Results ....................................................................................................................... 145 Scenario 3 Results ....................................................................................................................... 147 Scenario 4 Results ....................................................................................................................... 149 Scenario 6 Results ....................................................................................................................... 152 Lessons Learned and Guidance from the Reston Parkway Case Study ...................................... 154 Summary and Conclusions ......................................................................................................... 155 Network Test Case: Application of the Multi-Objective Evaluation Process with Explicit Consideration of Operational Regimes .................................................................................... 156 Background ................................................................................................................................. 156 Development of Critical Route Scenarios................................................................................... 158 Scenario 1: Routes Passing Through the Area to Other Destinations ...................................... 159 Development of Arrival Demand Profiles on Critical Routes .................................................... 163 Scenario 2: Critical Routes Generated from Traffic Inside the Network ................................. 165 Development of Control Strategies for Scenarios 1 and 2 .......................................................... 167 Problematic Symptoms of Oversaturation in the Network ......................................................... 167 Scenario 1: Timing Plan Development ....................................................................................... 171 Scenario 1: Simulation Experiment ............................................................................................ 173 Scenario 1: Results for Critical Routes Passing Through the Network ...................................... 174 Scenario 2: Critical Route Flows from Origins Inside the Network ........................................ 180 Scenario 2: Development of Timing Plans ................................................................................. 181 Conclusions from the Post Oak Test Case .................................................................................. 188 Using TOSI and SOSI Measures to Directly Calculate Green Time Adjustments ..................... 190 Forward-Backward Procedure .................................................................................................... 190 Control Variables ........................................................................................................................ 191 Forrward-Backward Procedure (FBP) ........................................................................................ 195 FBP for an Oversaturated Network............................................................................................. 198 Operation of traffic signal systems in oversaturated conditions Page iv

A Simple Illustrative Example .................................................................................................... 200 Real-World Examples ................................................................................................................. 202 An Oversaturated Intersection .................................................................................................... 202 An Oversaturated Arterial ........................................................................................................... 206 Summary ..................................................................................................................................... 211 Online Application Test Case: Response to Incident at a Single Common Destination ............ 213 Scenario Modeling ...................................................................................................................... 217 Intersection Strategies ................................................................................................................. 219 Route/Arterial Strategies ............................................................................................................. 229 Performance Analysis ................................................................................................................. 230 Throughput Analysis ................................................................................................................... 245 Summary ..................................................................................................................................... 248 Test Case: Arterial with Special Event Traffic ......................................................................... 249 Simulation Test Configuration .................................................................................................... 253 Mitigation Strategy Development ............................................................................................... 255 Average Delay Analysis ............................................................................................................. 257 Throughput Analysis ................................................................................................................... 271 Travel Time Analysis .................................................................................................................. 275 Summary ..................................................................................................................................... 276 Chapter 4: Conclusions and Future Directions ........................................................................... 277 Definitions and Diagnosis ........................................................................................................... 277 Development of Management Objectives and Characterizing Oversaturated Conditions Scenarios .................................................................................................................................. 278 Mitigation Strategies ................................................................................................................... 280 Practitioner Guidance.................................................................................................................. 281 Test Applications ........................................................................................................................ 282 Project Summary and Directions for Further Research .............................................................. 287 Directions for Future Research ................................................................................................... 289 References ................................................................................................................................... 292 Appendix A: Literature Review .................................................................................................. A-1 Summary of the Literature Review ............................................................................................. A-1 Operation of traffic signal systems in oversaturated conditions Page v

Literature Review on Diagnosis of Oversaturated Conditions ................................................... A-2 Definitions of Congestion and Level of Service ................................................................ A-3 Definitions Based on Queue Length .................................................................................. A-4 Measures of Oversaturation Based on Delay/Stops/Speed/Travel Time ........................... A-6 Flow-Occupancy Diagram/Fundamental Diagram ............................................................ A-8 Utilization of Green Time .................................................................................................. A-9 The State of the Practice in Diagnosis of Oversaturated Conditions ............................... A-11 NCHRP 3-79 .................................................................................................................... A-19 Section 2: Control Strategies for Oversaturated Conditions ................................................... A-23 Strategy Taxonomies for Managing Urban Congestion .................................................. A-23 Strategies for Coordinated Intersections .......................................................................... A-26 Models for Queue Interactions between Closely-Spaced Intersections ........................... A-28 Real-Time Adaptive Control Algorithms ........................................................................ A-30 Traffic Metering/Gating ................................................................................................... A-34 Recovery from Severe Congestion .................................................................................. A-35 Dynamic Optimization Algorithms.................................................................................. A-36 Reduced Cycle Times ...................................................................................................... A-37 Multi-Objective Analysis ................................................................................................. A-38 Summary of Literature Review ................................................................................................. A-39 Research Directions from the Literature Review...................................................................... A-41 Operation of traffic signal systems in oversaturated conditions Page vi

List of Figures Figure 1. Research methodology for development and evaluation of mitigation strategies ........... 5 Figure 2. Process of identifying and addressing oversaturated conditions ..................................... 8 Figure 3. An oversaturated traffic movement ............................................................................... 27 Figure 4. An oversaturated approach for both through and left-turn movements ........................ 28 Figure 5. Illustration of oversaturated approach due to starvation ............................................... 30 Figure 6. Oversaturation at an intersection caused by blocking ................................................... 31 Figure 7. Oversaturated condition on a route ................................................................................ 32 Figure 8. Illustration of an oversaturated network ........................................................................ 33 Figure 9. Illustration of oversaturated condition on a two-way arterial ....................................... 35 Figure 10. A challenging regional network scenario .................................................................... 36 Figure 11. Approach spillback (de facto red) ............................................................................... 40 Figure 12. Approach starvation due to signal timing .................................................................... 40 Figure 13. Storage bay spillback ................................................................................................... 41 Figure 14. Storage bay blocking ................................................................................................... 41 Figure 15. Cross-blocking effects ................................................................................................. 42 Figure 16. Loading, oversaturation, and recovery regimes of operation ...................................... 44 Figure 17. Shockwave profile within a cycle ................................................................................ 52 Figure 18. a) detector occupancy profile in a cycle; b) time gap between consecutive vehicles in a cycle. ........................................................................................................................ 53 Figure 19. Break points identification (Point C cannot be identified) .......................................... 55 Figure 20. Calculation of overflow queue length when Point C cannot be found ........................ 56 Figure 21. Queue-over-detector phenomena ................................................................................. 58 Figure 22. Updated breakpoints A’, B’, and C’ ............................................................................ 59 Figure 23. a) TH55 data collection site; b) detector layout .......................................................... 60 Figure 24. Sample data collected at the test site ........................................................................... 61 Figure 25. Estimation results of overflow queue for eastbound approach at Glenwood .............. 62 Figure 26. Estimated overflow queue length for eastbound approach at Boone Avenue ............. 62 Figure 27. Identification of QOD caused by downstream spillover ............................................. 63 Figure 28. Vehicle trajectories in the case of spillover from Winnetka to Rhode Island ............. 64 Figure 29. Queue length profile at the intersection of Winnetka when Rhode Island intersection is oversaturated .......................................................................................................... 65 Figure 30. Framework for determination of control strategies used in this research ................... 71 Figure 31. Framework for volume estimation on critical routes .................................................. 72 Figure 32. Timing framework for oversaturated conditions ......................................................... 73 Figure 33. Shockwave at signalized intersection .......................................................................... 74 Figure 34. Upper-bound of cycle length that prevents spillback .................................................. 75 Figure 35. Upper-bound of cycle length as a function of saturation flow rate ............................. 76 Figure 36. Spillback avoidance offset ........................................................................................... 78 Figure 37. Starvation avoidance offset ......................................................................................... 79 Operation of traffic signal systems in oversaturated conditions Page vii

Figure 38. Offset values feasible region ....................................................................................... 79 Figure 39. Split-offset calculation procedure................................................................................ 81 Figure 40. Split-offset optimization framework ........................................................................... 84 Figure 41. Conceptual illustration of Pareto front in assessing multiple objectives ..................... 85 Figure 42. Information provided by the shape of the Pareto Front (a) Pareto front of unrestricted solution range (b) Pareto front of restricted solution range .......................................................... 86 Figure 43. Two conflicting movement volume profiles ............................................................... 96 Figure 44. Concept of volume profiles that generate unserved demand....................................... 97 Figure 45. Delay surface representing the performance of each timing plan for each time period ................................................................................................................................... 98 Figure 46. Throughput surface representing the performance of each timing plan for each time period .................................................................................................................................... 99 Figure 47. Example of optimal timing plans and scheduling based on the minimum delay objective ............................................................................................................................ 101 Figure 48. Example of optimal timing plans and scheduling based on the throughput – maximization objective ............................................................................................................... 101 Figure 49. Recommended placement of oversaturation detection zones .................................... 105 Figure 50. Example placement of oversaturation detection points ............................................. 106 Figure 51. Set up for inputs, logic, and actions .......................................................................... 107 Figure 52. Logic engine example................................................................................................ 109 Figure 53. Online oversaturation management research software integration ........................... 111 Figure 54. Research software integration – Step 2 ..................................................................... 112 Figure 55. Research software integration – Step 3 ..................................................................... 113 Figure 56. Research software integration – Step 4 ..................................................................... 114 Figure 57. Research software integration – Step 5 ..................................................................... 115 Figure 58. Reston Parkway network ........................................................................................... 120 Figure 59. Changes in traffic patterns in Reston Parkway at 3:30 P.M. ..................................... 121 Figure 60. Changes in traffic patterns in Reston Parkway at 5:00 P.M. ..................................... 121 Figure 61. Changes in traffic patterns in Reston Parkway at 7:30 P.M. ..................................... 122 Figure 62. Critical route scenarios on the Reston Parkway network .......................................... 123 Figure 63. Adjusted demand profile for Route AH to account for demand unrepresented in the system detector counts .......................................................................................................... 124 Figure 64. Problematic Scenario 5: critical movements and diagnosis ...................................... 125 Figure 65. Key attributes of Scenario 5 ...................................................................................... 126 Figure 66. Comparison of phase reservice and metering strategies ............................................ 126 Figure 67. Storage capacity of the link used for metering in the Reston Parkway network ....... 128 Figure 68. Split-offset calculation procedure.............................................................................. 131 Figure 69. Oversaturation offsets for the southbound critical route ........................................... 131 Figure 70. Oversaturation offsets for both southbound and northbound critical routes ............. 132 Operation of traffic signal systems in oversaturated conditions Page viii

Figure 71. Scenario 5 offset design values (min and max), for northbound and southbound progression .................................................................................................................................. 132 Figure 72. Illustration example of the Pareto front for Scenario 5: metering strategy ............... 136 Figure 73. Scenario 5 with phase reservice ................................................................................ 138 Figure 74. Scenario 5 with metering ........................................................................................... 139 Figure 75. Scenario 5: optimal control strategies for each 15-minute period ............................. 141 Figure 76. Scenario 5: Example performance profiles of a mitigation strategy versus the baseline timing plan .................................................................................................................... 142 Figure 77. Scenario 1: non-dominated strategies ........................................................................ 143 Figure 78. Scenario 1: optimal control strategies by time .......................................................... 144 Figure 79. Scenario 1: example Strategy 5 improvement percentage over the baseline ............ 144 Figure 80. Scenario 2: Pareto fronts ........................................................................................... 145 Figure 81. Scenario 2: optimal control strategies by time .......................................................... 146 Figure 82. Scenario 2: strategy 7 improvement % by time......................................................... 146 Figure 83. Scenario 3: Pareto fronts ........................................................................................... 147 Figure 84. Scenario 3: optimal control strategies by time .......................................................... 148 Figure 85. Scenario 3: Strategy 4 improvement % by time for performance measures (delay, stop, and throughput) .................................................................................................................. 148 Figure 86. Scenario 4: Pareto fronts ........................................................................................... 149 Figure 87. Scenario 4: optimal control strategies by time for performance measures (delay, stop, and throughput) .................................................................................................................. 150 Figure 88. Scenario 4: Strategy 8 improvement % by time for performance measures (delay, stop, and throughput) .................................................................................................................. 151 Figure 89. Scenario 6: network performance measures of the optimal control strategies during peak period .................................................................................................................................. 152 Figure 90. Scenario 6: optimal control strategies by time .......................................................... 153 Figure 91. Scenario 6: Strategy 7 improvement % by time ........................................................ 154 Figure 92. Post Oak area of Houston, TX ................................................................................... 156 Figure 93. I-610 loop and US 59 interchange, Houston, TX ...................................................... 157 Figure 94. Skyline view of Uptown Houston ............................................................................. 158 Figure 95. Parking lot facilities in Post Oak Network ................................................................ 159 Figure 96. Network exits and routes to the highways interchange ramps .................................. 160 Figure 97. Post Oak Ave./W Alabama Ave.; exit to I-610 southbound and US 59 ramps ......... 161 Figure 98. Richmond Ave. and Post Oak Blvd.; exits to I-610 northbound and US-59 ramps .. 161 Figure 99. Critical routes for Scenario 1 ..................................................................................... 163 Figure 100. Volume profiles for critical routes in Scenario 1 .................................................... 164 Figure 101. Critical routes 2, 3, 5 and the corresponding critical movements ........................... 164 Figure 102. Critical routes for Scenario 2 ................................................................................... 166 Figure 103. Volume profiles for critical routes in Scenario 2 .................................................... 166 Figure 104. Symptoms of oversaturation in the Post Oak network ............................................ 168 Operation of traffic signal systems in oversaturated conditions Page ix

Figure 105. Simulation snapshot showing queue spillback along a critical route ...................... 168 Figure 106. Control strategies applied in Scenario 1 .................................................................. 171 Figure 107. Min Delay-Queue Management-Max Throughput Strategy (Strategy 1) ............... 172 Figure 108. Max Throughput-Queue Management- Max Throughput Strategy (Strategy 2) .... 172 Figure 109. Post Oak network modeled in Vissim ..................................................................... 174 Figure 110. Network summary performance measures for Scenario 1 ...................................... 175 Figure 111. Intersection throughput improvement for Strategy 1 .............................................. 176 Figure 112. Intersection throughput improvement for Strategy 2 .............................................. 177 Figure 113. Comparison of intersection throughput between the two strategies ........................ 178 Figure 114. Number of vehicles in the system for each strategy for Scenario 1 ........................ 179 Figure 115. Spatial illustration of control strategies for Scenario 2 ........................................... 181 Figure 116. Min Delay-Queue Management-Max Throughput timing plan schedule ............... 182 Figure 117. Max Throughput-Queue Management-Max Throughput timing plan schedule ..... 182 Figure 118. Comparison of performance improvements of the two strategies with the baseline for Scenario 2 ................................................................................................................ 184 Figure 119. Intersection throughput improvements for Strategy 1 on Scenario 2 ...................... 185 Figure 120. Intersection throughput improvements for Strategy 2 on Scenario 2 ...................... 186 Figure 121. Comparison of throughput improvements between the two strategies ................... 187 Figure 122. Number of vehicles in the system for each strategy for Scenario 2 ........................ 188 Figure 123. Red time changes and green time changes .............................................................. 191 Figure 124. Signal timing changes ( , 0n ir∆ < , , 0n ig∆ > ) ............................................................ 192 Figure 125. Green extension for Scenario 1 ............................................................................... 193 Figure 126. Red extension for Scenario 2 ................................................................................... 194 Figure 127. Red reduction at downstream intersection for Scenario 3 ....................................... 195 Figure 128. FBP for an oversaturated route ................................................................................ 195 Figure 129: Oversaturated route and critical intersection ........................................................... 199 Figure 130. Test arterial on TH55, Minneapolis, MN ................................................................ 203 Figure 131. Signal timing plan (A.M. peak) for Winnetka and Rhode Island ............................ 203 Figure 132. SOSI and TOSI values of Rhode Island westbound ................................................ 204 Figure 133. SOSI values of Rhode Island westbound before and after the FBP ........................ 204 Figure 134. TOSI values of Rhode Island westbound before and after the FBP ........................ 205 Figure 135. Estimated queue lengths at Winnetka westbound before and after the FBP ........... 205 Figure 136. Queue lengths on the side street (southbound) at Winnetka intersection before and after the FBP ........................................................................................................................ 205 Figure 137.Vissim simulation network ....................................................................................... 206 Figure 138.: Comparison of spillover time and overflow queue discharge time ........................ 209 Figure 139. Comparison of throughput by route ........................................................................ 210 Figure 140. Comparison of side streets’ maximum queue length in each cycle ...................... 211 Figure 141. City of Windsor, ON arterial and freeway network ................................................ 214 Figure 142. Intersections near the Detroit-Windsor Tunnel border crossing ............................. 215 Operation of traffic signal systems in oversaturated conditions Page x

Figure 143. Detail of detector deployment and operational strategies at Tunnel entrance ......... 215 Figure 144. Baseline oversaturated scenario .............................................................................. 218 Figure 145. Detection points in the Windsor, ON traffic network ............................................. 220 Figure 146. Logic engines for (a) Plan 2 [omit eastbound left turn] (b) Plan 3 [increase northbound through] (c) Plan 4 [increase westbound through] .................................................. 221 Figure 147. Logic engines for expanded mitigation logic .......................................................... 224 Figure 148. Performance summary 8:00 – 8:15.......................................................................... 233 Figure 149. Performance summary 8:15 – 8:30.......................................................................... 235 Figure 150. Performance summary 8:30 – 8:45.......................................................................... 237 Figure 151. Performance summary 8:45 – 9:00.......................................................................... 239 Figure 152. Performance summary 9:00 – 9:15.......................................................................... 241 Figure 153. Performance summary 9:15 – 9:30.......................................................................... 243 Figure 154. Performance summary total (3 hours) ..................................................................... 245 Figure 155. Average input rates under different mitigations ...................................................... 246 Figure 156. Average output rates under different mitigations .................................................... 247 Figure 157. Average vehicles in the system ............................................................................... 247 Figure 158. Location of test case in the Phoenix, AZ metropolitan area.................................... 249 Figure 159. Illustration of relative flows along the arterial during P.M. peak ........................... 249 Figure 160. Progression patterns during the P.M. peak .............................................................. 250 Figure 161. Critical routes during game overlaid with P.M. peak flows .................................... 251 Figure 162. Queue growth at the beginning of the arriving event traffic ................................... 252 Figure 163. Queue dissipation as the event traffic flows subside ............................................... 253 Figure 164. Traffic arrival volumes and turning percentage profile during game traffic ........... 254 Figure 165. Number of vehicles in system and I/O rates of baseline scenario ........................... 254 Figure 166. Illustration of dynamic lane allocation for two-lane left turn movement ................ 257 Figure 167. Performance summary 4:30 – 5:00.......................................................................... 259 Figure 168. Performance summary 5:00 – 5:30.......................................................................... 261 Figure 169. Performance Summary 5:30 – 6:00 ......................................................................... 263 Figure 170. Performance summary 6:00 – 6:30.......................................................................... 265 Figure 171. Performance summary 6:30 – 7:00.......................................................................... 267 Figure 172. Performance summary (3 hour total) ....................................................................... 269 Figure 173. Performance summary comparison to extended left-turn split at Bullard (3 hour total) ............................................................................................................................... 271 Figure 174. Average input rates under different mitigations ...................................................... 272 Figure 175. Average output rates under different mitigations .................................................... 273 Figure 176. Average vehicles in the system ............................................................................... 274 Figure 177. Average travel time under different mitigation strategies ....................................... 275 Figure 178. Travel time comparison to Bullard from eastbound and westbound directions ...... 276 Figure 179 Comparison of output processing rates during recovery period ...................................289 Operation of traffic signal systems in oversaturated conditions Page xi

List of Tables Table 1: Summary of attributes of test cases ................................................................................ 10 Table 2. Special cases of network oversaturation ......................................................................... 34 Table 3. Duration of oversaturation .............................................................................................. 37 Table 4. Causal factors .................................................................................................................. 38 Table 5. Frequency of oversaturation ........................................................................................... 39 Table 6. Summary of characteristics of oversaturated scenario ................................................... 42 Table 7. Oversaturation Severity Indices (OSI) for Winnetka Avenue Intersection .................... 66 Table 8. OSI for Rhode Island intersection .................................................................................. 66 Table 9. Example logic conditions and actions .......................................................................... 108 Table 10. Cross reference of link names in Table 9 with Detectors in Figure 50. ..................... 108 Table 11. Summary of test case attributes .................................................................................. 118 Table 12. Maximum cycle length before spillback occurs on critical network links ................. 129 Table 13. Critical network links and left-turn bay storage lengths ............................................. 129 Table 14. Shockwave Modeling Parameters ............................................................................... 130 Table 15. Combination of cycle time and offset values for each strategy .................................. 133 Table 16. Control strategy combinations with metering or phase reservice ............................... 134 Table 17. Scenario 5: total improvement over the baseline strategy .......................................... 140 Table 18. Scenario 1: total improvement over the baseline strategy .......................................... 144 Table 19. Scenario 2: total % improvement over the baseline plan ............................................ 146 Table 20. Scenario 3: total % improvement over baseline plan ................................................. 148 Table 21. Scenario 4: total improvement % over baseline plan ................................................. 150 Table 22. Scenario 6: total improvement % over baseline plan ................................................. 153 Table 23. Critical routes for Scenario 1 ...................................................................................... 162 Table 24. Critical routes for Scenario 2 (outbound routes) ........................................................ 165 Table 25. Control strategies applied in Scenario 1 ..................................................................... 170 Table 26. Description of strategies ............................................................................................. 173 Table 27. Cycle lengths used in each strategy ............................................................................ 173 Table 28. Performance evaluation of strategies on Scenario 1 ................................................... 175 Table 29. System-wide Summary performance measures .......................................................... 179 Table 30. Attributes of control strategies selected for testing on Scenario 2 ............................. 180 Table 31. Plan start times for each strategy ................................................................................ 183 Table 32. Cycle lengths used in each plan for Scenario 2 .......................................................... 183 Table 33. System-level comparison of performance of the two strategies for Scenario 2 ......... 184 Table 34. System-wide Performance Results for Scenario 2 ...................................................... 188 Table 35. Illustration of calculation procedure ........................................................................... 201 Table 36. Illustration of calculations for green time modifications ............................................ 202 Table 37. Southbound average SOSI and TOSI values under original signal timings ............... 207 Table 38. FBP calculation process .............................................................................................. 208 Table 39. Offset and green time of two plans ............................................................................. 208 Operation of traffic signal systems in oversaturated conditions Page xii

Table 40. Network performance comparison.............................................................................. 210 Table 41. Comparison of throughput by route ............................................................................ 211 Table 42. Proposed operational strategy at the Tunnel entrance ................................................ 216 Table 43. Schedule of volume changes during the scenario ....................................................... 217 Table 44. Summary of mitigation strategies ............................................................................... 219 Table 45. Windsor queue-responsive logic ................................................................................. 220 Table 46. Expanded Windsor logic ............................................................................................. 223 Table 47. Average delay per link 8:00 – 8:15 ............................................................................. 232 Table 48. Average delay per link 8:15 – 8:30 ............................................................................. 234 Table 49. Average delay per link 8:30 – 8:45 ............................................................................. 236 Table 50. Average delay per link 8:45 – 9:00 ............................................................................. 238 Table 51. Average delay per link 9:00 – 9:15 ............................................................................. 240 Table 52. Average delay per link 9:15 – 9:30 ............................................................................. 242 Table 53. Average delay per link total (3 hours) ........................................................................ 244 Table 54. Allocation of Bell Road game traffic case study on the oversaturated scenario taxonomy..................................................................................................................................... 251 Table 55. Mitigation strategies evaluated in this test case .......................................................... 256 Table 56. Average delay per link 4:30 – 5:00 ............................................................................. 258 Table 57. Average delay per link 5:00 – 5:30 ............................................................................. 260 Table 58. Average delay per link 5:30 – 6:00 ............................................................................. 262 Table 59. Average delay per link 6:00 – 6:30 ............................................................................. 264 Table 60. Average delay per link 6:30 – 7:00 ............................................................................. 266 Table 61. Average delay per link (3 hour total) .......................................................................... 268 Table 62. Average delay comparison with extended left turn at Bullard (3 hour total) ............. 270 Operation of traffic signal systems in oversaturated conditions Page xiii

List of Equations Equation (Eq.) 1 ............................................................................................................................ 47 Eq. 2 .............................................................................................................................................. 47 Eq. 3 .............................................................................................................................................. 53 Eq. 4 .............................................................................................................................................. 54 Eq. 5 .............................................................................................................................................. 54 Eq. 6 .............................................................................................................................................. 54 Eq. 7 .............................................................................................................................................. 55 Eq. 8 .............................................................................................................................................. 56 Eq. 9 .............................................................................................................................................. 56 Eq. 10 ............................................................................................................................................ 58 Eq. 11 ............................................................................................................................................ 75 Eq. 12 ............................................................................................................................................ 78 Eq. 13 ............................................................................................................................................ 78 Eq. 14 ............................................................................................................................................ 81 Eq. 15 ............................................................................................................................................ 81 Eq. 16 ............................................................................................................................................ 82 Eq. 17 ............................................................................................................................................ 82 Eq. 18 ............................................................................................................................................ 82 Eq. 19 ............................................................................................................................................ 82 Eq. 20 ............................................................................................................................................ 82 Eq. 21 ............................................................................................................................................ 83 Eq. 22 ............................................................................................................................................ 83 Eq. 23 ............................................................................................................................................ 83 Eq. 24 ............................................................................................................................................ 83 Eq. 25 ............................................................................................................................................ 83 Eq. 26 ............................................................................................................................................ 83 Eq. 27 ............................................................................................................................................ 83 Eq. 28 ............................................................................................................................................ 83 Eq. 29 ............................................................................................................................................ 90 Eq. 30 ............................................................................................................................................ 90 Eq. 31 ............................................................................................................................................ 91 Eq. 32 ............................................................................................................................................ 91 Eq. 33 ............................................................................................................................................ 91 Eq. 34 ............................................................................................................................................ 91 Eq. 35 ............................................................................................................................................ 91 Eq. 36 ............................................................................................................................................ 91 Eq. 37 ............................................................................................................................................ 91 Eq. 38 ............................................................................................................................................ 91 Eq. 39 ............................................................................................................................................ 92 Operation of traffic signal systems in oversaturated conditions Page xiv

Eq. 40 ............................................................................................................................................ 92 Eq. 41 ............................................................................................................................................ 92 Eq. 42 ............................................................................................................................................ 92 Eq. 43 ............................................................................................................................................ 92 Eq. 44 ............................................................................................................................................ 92 Eq. 45 ............................................................................................................................................ 93 Eq. 46 ............................................................................................................................................ 93 Eq. 47 ............................................................................................................................................ 93 Eq. 48 ............................................................................................................................................ 93 Eq. 49 ............................................................................................................................................ 93 Eq. 50 ............................................................................................................................................ 94 Eq. 51 .......................................................................................................................................... 192 Eq. 52 .......................................................................................................................................... 192 Eq. 53 .......................................................................................................................................... 193 Eq. 54 .......................................................................................................................................... 194 Eq. 55 .......................................................................................................................................... 196 Eq. 56 .......................................................................................................................................... 196 Eq. 57 .......................................................................................................................................... 197 Eq. 58 .......................................................................................................................................... 197 Eq. 59 .......................................................................................................................................... 197 Eq. 60 .......................................................................................................................................... 198 Eq. 61 .......................................................................................................................................... 198 Eq. 62 .......................................................................................................................................... 198 Eq. 63 .......................................................................................................................................... 199 Eq. 64 .......................................................................................................................................... 199 Eq. 65 .......................................................................................................................................... 200 Eq. 66 .......................................................................................................................................... 200 Eq. 67 .......................................................................................................................................... 200 Eq. A-1 ........................................................................................................................................ A-2 Eq. A-2 ........................................................................................................................................ A-2 Eq. A-3 ........................................................................................................................................ A-3 Eq. A-4 ...................................................................................................................................... A-10 Eq. A-5 ...................................................................................................................................... A-10 Eq. A-6 ...................................................................................................................................... A-11 Eq. A-7 ...................................................................................................................................... A-12 Eq. A-8 ...................................................................................................................................... A-14 Eq. A-9 ...................................................................................................................................... A-17 Eq. A-10 .................................................................................................................................... A-17 Eq. A-11 .................................................................................................................................... A-18 Eq. A-12 .................................................................................................................................... A-19 Operation of traffic signal systems in oversaturated conditions Page xv