Application of Accelerated User Equilibrium Traffic Assignments

1. Application of Accelerated User Equilibrium Traffic Assignments Howard Slavin Jonathan Brandon Andres Rabinowicz Srinivasan Sundaram Caliper Corporation May 2009

2. Traffic Assignment Convergence • Most traffic assignments not sufficiently converged and give semi-random results • At low convergence-Counter-intuitive or error-prone forecasts and noise all over the network for even minor local changes • More rapid convergence is now readily available and very helpful in modeling. • Congested speeds are key model inputs as well as a primary benefit measure.

3. Empirical Testing of Faster Algorithms & Convergence Impacts Examination of algorithmic sales claims from the transportation science literature Speed enhancements through distributed processing and multi-threading Benefits of tighter convergence Use of more realistic and appropriate test cases

4. Two approaches now proven for faster traffic assignment convergence • Multi-threaded (and/or distributed) FW • Dial’s Algorithm B (“OUE” in TransCAD) • B is a significant innovation • Both improvements provided in TransCAD 5

5. Test Case • Well-calibrated regional model for Washington DC that Caliper developed for MNCPPC-Prince George’s County • 2500 zones, 6 purposes, 3 time periods, 5 assignment classes • Feedback through distribution, mode choice, & assignment • Calibrated to Relative Gap of .001, Skim matrix root mean square error < .1%, Close match to ground counts. • 80 – 170 Assignment iterations and 4 feedback loops • HCM planning BPR coefficients that vary by road class • Subsequent more accurate traffic assignments performed • Primary test computer-3 year old 3GHz dual Xeons

6. Washington Regional Network

7. Cold Start Convergence Rates PM Assignment

8. Cold Start Convergence Times (Min) PM Assignment

9. Warm Start Convergence with Random Trip Table Perturbations RG=10-5

10. Cold Start and Warm Start Convergence Rate Comparison

11. Feedback loop run times with OUE assignment (0.001 RG)

12. Comparison of OUE and FW solutions at the same Relative Gap

13. Model run times with OUE assignment (0.0001 RG)

14. How much error is there in the link flows in an unconverged assignment? • Easy to quantify with these tools • Using the lens of OUE, we compare less converged solutions with more highly converged ones.

15. Average and Maximum Link Flow Differences between the OUE equilibrium solution and the solutions at lower relative gaps

16. Differences from the equilibrium solution (RG 10-15)

17. Flow Differences of OUE assignments at different relative gaps with the equilibrium OUE solution computed to a RG of 10-15

18. Convergence Levels & Project Impacts • Three Examples Examined • An Irrelevant network change-doubling the capacity of 2 links in rural VA • New MD-5 and Beltway Interchange-Addition of a flyover ramp in PG County • Woodrow Wilson Bridge Improvement-from 6 to 10 lanes.

19. Links with flow differences greater than 200 vehicles – Irrelevant Change Example

20. Links with flow changes greater than 200 vehicles – Interchange Project

21. Comparison of Base and Scenario – Interchange Project

23. Links with flow differences greater than 200 vehicles – Bridge Project

24. Comparison of Base and Scenario – Bridge Project

25. Other Findings • Benefits estimated from FW were similar • Our real problem was much tougher computationally than problems reported in the literature • In these examples, a relative gap of 10-4 seems sufficient for impact analysis. • Convergence levels should be tested for other assignment models

26. Conclusions • Orders of magnitude greater convergence can be achieved with low computing times • Greater convergence can reduce errors in models and estimated project impacts • There is little risk in taking advantage of these developments