Optimal Adaptive Signal Control for Diamond Interchanges Using Dynamic Programming

1. Optimal Adaptive Signal Control for Diamond Interchanges Using Dynamic Programming FALL 2005 UMASS AmherstOperations 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 D = 400 – 800 ft or less Freeway Surface Street Freeway

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

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

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

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 MethodDynamic Programming (DP) • To optimize a sequence of inter-related decisions • Global optimal solution Optimal signal switch sequence Time Decision Tree

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

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

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

15. DP FormulationForward Recurrence Relation Minimal PMI from stage 0 to stage n-1 Minimal PMI from stage 0 to stage n 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 DP Horizon Implement Optimal Signal Plan 0 2.5 5 7.5 10 20 Stop-line Time, sec Queue Detection Period DP Calculation Detector Time, sec -16 -15 -12 -2 0 -8.5 -2 5.5 Detection Overlap

17. Detectors PlacementLayout

18. Signal ImplementationMajority 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 timefollowed 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 the DP algorithm by the calibrated simulation model Sensitivity Analysis Simulate three signal plans by the calibrated simulation model Comparisons DP Algorithm PASSER III TRANSYT-7F

20. Diamond InterchangeField Data

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

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

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. ComparisonsDynamic 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. ComparisonsDP, 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. Conclusionsfor 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?