1. Optimal Adaptive Signal Control for Diamond Interchanges Using Dynamic Programming Optimal Adaptive Signal Control for Diamond Interchanges Using Dynamic Programming FALL 2005 UMASS Amherst Operations Research / Management Science Seminar Series Fang (Clara) Fang, Ph.D. Assistant Professor The University of Hartford FALL 2005 UMASS Amherst Operations Research / Management Science Seminar Series Fang (Clara) Fang, Ph.D. Assistant Professor The University of Hartford

2. Outline of Presentation Background Methodology Dynamic Programming Formulation Vehicle Arrival-Discharge Projection Model Algorithm Implementation Using Simulation for Evaluation Sensitivity Analysis and Comparisons Conclusions and Recommendations

3. Diamond Interchanges Freeway D = 400 – 800 ft or less Surface Street Freeway

4. Geometric Layout of a Diamond Interchange Arterial Freeway Off-Ramp Freeway On-Ramp Freeway Off-Ramp Freeway On-Ramp

5. Arterial Freeway On-Ramp Freeway On-Ramp Freeway Off-Ramp Freeway Off-Ramp Common Signalization Schemes Three-phase Plan Four-phase Plan

6. Common Signalization Schemes Phase - part of cycle (sum of green, yellow and red times) allocated to any combination of traffic movements receiving the right-of-way simultaneously.

7. Arterial Freeway On-Ramp Freeway On-Ramp Freeway Off-Ramp Freeway Off-Ramp Common Signalization Schemes Three-phase Plan Four-phase Plan 2 6 5 2 6 4 1 8 2 6 1 5

8. Background PASSER III (Signal Optimization Tool for Diamond Interchanges) Off-line and pre-timed Search: three-phase or four-phase plan

9. Background Adaptive Control Generates and implements the signal plan dynamically based on real time traffic conditions that are measured through a traffic detection system

10. Objectives To develop a methodology for real- time signal optimization of diamond interchanges To evaluate the developed optimal signal control using micro-simulation

11. Optimization Method Dynamic Programming (DP) Decision Tree To optimize a sequence of inter-related decisions Global optimal solution Time Optimal signal switch sequence

12. DP Formulation - Decision Network Three-Phase Ring Structure Optimization Horizon (10 seconds) Input: Initial Phase & Queue Length Arrivals from t0 – t4 Output: Optimal Decision Path Stage 1Stage 2 Stage 3 Stage 4 State

13. Optimization Objective Performance Measure Index (PMI) Weights Queue Length, Storage Ratio, Delay, etc.

14. Fixed Weights vs.Dynamic Weights Fixed Values Dynamic Values:

15. DP Formulation Forward Recurrence Relation Minimal PMI from stage 0 to stage n Minimal PMI from stage 0 to stage n-1 Immediate Return over stage n, due to decision k, state (n-1,j) changing to state (n,i), given initial queue lengths at stage n-1 Minimal PMI over all decisions

16. Vehicle Projection Model Distance, ft Stop-line Detector Time, sec 0 2.5 5 7.5 10 20 -16 -15 -12 -2 0 DP Horizon Queue -8.5 -2 5.5 Detection Overlap DP Calculation Implement Optimal Signal Plan Detection Period

17. Detectors Placement Layout

18. Signal Implementation Majority Rolling Concept For each horizon of 10s, a majority signal phase is implemented for Either 7.5s green if this majority phase is the same as the previous one, Or otherwise 2.5s yellow-and-all-red clearance time followed by 5s green

19. Using Simulation to Evaluate the DP Algorithm Select one diamond interchange, Collect field data Select a simulation model from AIMSUN, CORSIM & VISSIM Calibrate the model Simulate three signal plans by the calibrated simulation model Comparisons PASSER IIITRANSYT-7FDP Algorithm Simulate the DP algorithm by the calibrated simulation model Sensitivity Analysis

20. Diamond Interchange Field Data

21. AIMSUN and the DP Algorithm Signal Timing DP Algorithm Coded in C++ Generate *.DLL GETRAM Extension Module Detection Information AIMSUN Simulation

22. Code Flow Structure and Time Logic Detection Overlapping If time >=284 If isimustep<27 GetExtLoad GetExtInit Detecting over every 0.5 seconds for all lane groups. 1. Discharging headway 2. Arrival vehicles traveling speed 3. Arrival vehicle number If time =298 Estimating the initial queue at t=300+idprollong*10, based on the queue and signal at t=298, and the averaged number of arrival vehicles every 0.5 second If 298<time <300 Arrival Projection and discharge dynamics calculation DP value forward iteration DP optimal signal backward declaration If time = 300 Disable the current fixed control plan If time=300+idp*2.5 Implement the DP optimal signal, rolling 2.5 sec forward, for a total of 4 DP intervals If time=7200, Switch to fixed control Time = time + 0.5 Step-wise simulation is finished GetExtFinish GetExtUnLoad GetExtManage idprolling=0 isimustep=-1 idp=0 isimustep=isimustep+1 If isimustep=27, isumstep=0 Layer 0 to 4 i=0~3 idp=idp+1 If idp=4, then idp=0 Idprolling=0 No Yes Block 1 Block 2 & Block 3 Block 4

24. Sensitivity Analysis Delay vs. PMI Sum of Average Queue Length Per Lane for All Approaches Sum of Average Delay Per Lane for All Approaches Sum of Total Delays for All Approaches Sum of Storage Ratio Per Lane for All Approaches Delay vs. Weights Ramp Weights Arterial Weights Internal Link Left Turning Weights Weights

25. Comparisons Dynamic Weights & Fixed Weights System Delays (sec/veh) Saving 36% - 49%

26. Summary Fixed Weights and Dynamic Weights When the demand varies unpredictably every 15 minutes and is unbalanced, using dynamic weights can reduce the system delay up to 49%, compared to using fixed weights. With dynamic weights, operations remain under- saturated for higher demands than with fixed weights. With dynamic weights, users do not need to manually adjusting the weights. The performance of dynamic weights also depends on how their values are defined.

27. Comparisons DP, PASSER III & TRANSYT-7F System Delays (sec/veh)

28. Conclusions Developed a methodology and the corresponding algorithm for optimal and adaptive signal control of diamond interchanges Various performance measures Dynamic weights Built a vehicle arrival-discharge projection model at the microscopic level Simulated the algorithm using AIMSUN Studied the algorithm performance

29. Conclusions for the Algorithm Performance Optimize both phase sequence and phase duration The real-time DP signal algorithm is superior to PASSER III and TRANSYT-7F in handling demand fluctuations The dynamic weighted algorithm is appropriate to be applied in special events or incidents when high demands are unexpected and varying

30. Future Research Expand the decision network of signal control When it is not possible or practical to place detectors far enough Results compared to other adaptive signal systems and/or actuated control systems Apply the method for urban arterials and small networks

31. Questions and Comments?