Robust Synchronization of Actuated Signals on Arterials

1. Robust Synchronization of Actuated Signals on Arterials Project #2008-003: Simulation-Based Robust Optimization for Actuated Signal Timing and Setting Lihui Zhang Yafeng Yin

2. Outline • Background Introduction Bandwidth Maximization • Robust Coordination Model • Numerical Example • Concluding Remarks

3. Background -- Coordination • Synchronize traffic signals to provide smooth progression for major traffic movements along arterials • Offset + Cycle length

4. Background • Actuated signals • Current practice performing coordination • Uncertainty of start and end of the green • Semi-Actuated signal coordination

5. Background • Two approaches: by maximizing green bandwidth (MAXBAND and PASSER-II ) by minimizing total delay (TRANSY-7F )

6. Coordination Distance Bandwidth Offset Cycle length Signal i Trajectory Signal h Speed Time Red Interval

7. Little’s Bandwidth Maximization Offset Cycle lengthRed interval s.t.

8. Bandwidth Maximization Geometry of the Green Bands

9. Background --Early Return to Green

10. Synchronization of Actuated System • Stochastic optimization to generate robust synchronization plan • Scenario based Scenario set K={k: Rk=(r1k, r2k……rnk)} Represent traffic uncertainty Loss function • Deal with 10% worst case scenarios

11. Model Formulation

12. Numerical Example • Network (Corsim: ActCtrl Example) • Plan Generation • Plan Evaluation Macro-simulation Micro-simulation Modeling System: GAMS Solver: CPLEX

14. Numerical Example --Plan Generation Robust Plan • 250 scenarios • Red times of the sync phases: independently normally distributed with specific mean and same variance. • Scenarios have equal probability to occur • Confidence level 0.90 Nominal Plan • Red times: use fixed mean red times

15. Numerical Example --Plan Evaluation Macro-Simulation • 2000 samples generated from independent normal distributions • 2000 samples generated from uniform distributions • Under Robust Plan and Nominal Plan • Performance measure: • Mean bandwidth • Worst case bandwidth • 90% CVaR • 90th percentile minimum bandwidth

16. Monte Carlo Simulation--Normal Distribution

17. Monte Carlo Simulation --Uniform Distribution

18. Micro-Simulation and Hypothesis Test

19. Conclusions & Remarks • Robust synchronization model: MILP • Perform better against high-consequence scenarios • Can be applied to design coordination plans as well as fine-tune plans Current research • Formulate and solve a deterministic integrated model for signal optimization, simultaneously optimizing cycle length, green splits, offsets, phase sequences • Formulate and solve a robust counterpart of the deterministic model considering day-to-day demand variations

20. Thank you ! Question?

21. Numerical Example --Plan Generation Computational time and plan difference

22. Robust synchronization--CVaR