Traffic Assignment Convergence and its Effects on Selecting Network Improvements

1. Traffic Assignment Convergence and its Effects on Selecting Network Improvements By Chris Blaschuk, City of Calgary and JD Hunt, University of Calgary October 20, 2004 18th Annual International EMME/2 User’s Conference Mexico City, Mexico

2. Outline • About the Calgary Regional Transportation Model • Multiclass Assignment Process and Algorithms • Project Evaluation Process and Issues • Project Evaluation Measures • Mobility Benefits • Vehicle Hours Traveled (VHT) • Empirical Testing • Candidate Projects • Observations • Results of Testing • Conclusions

3. City of Calgary • Population just over 1 million people

4. Calgary RTM • Both city and surrounding region modeled • Consists of 1447 zones and over 14000 links • 24-Hour model broken into five time periods • System of logit choice models • 25 trip purposes • 5 person types 75km

6. Calgary RTM • Steep VDF Curves used • Links not overloaded • Forces changes in generation, distribution and mode split

7. Multiclass Assignment in RTM • Generalized cost multiclass assignment is used in the Calgary RTM. • Five classes assigned simultaneously. • Truck penalty on non-truck routes for medium and heavy trucks. • Stored as extra attribute of fixed link costs for these classes. • Originally was 1000 min / 250 meters for skimming -- now is 5 min / 100 meters.

8. Using RTM in Project Evaluation • 34 separate projects to be tested for network benefits • These included • Road Widenings • Interchanges • Lane Reversal Systems • New Roadways • Some Bundles of the above • Goal was to determine the benefit each improvement on the network in order to decide where money should be invested. • Wanted to use ‘Mobility Benefits’

9. Generalized Cost of Travel Demand Curve for Network Links C1 Consumer Surplus C2 0 V1 V2 LinkVolumes Mobility Benefits • Change in daily composite utility by model segment • Equal to change in traveler consumer surplus • Indicates benefits of changes to person types and trip types • Useful for analyzing transit and other mode improvements as well as network changes.

10. Problem with Results • Got confusing results • Lots of unexpected negative benefits • Results were not intuitive • Unacceptable - clearly something wrong • Needed to investigate • decided on assignment convergence • Approach: isolate problem • fixed trip table • considered just VHT • examine assignment process • experiment with convergence criteria

11. Reasons for Approach • Simplify to auto network • Eliminated ‘induced demand’ • Simple to understand • Results more certain, more predictable • Smaller, so quick to produce and process • Observe assignment convergence effects

12. Empirical Testing • Two projects were tested at various levels of convergence • Effects observed included • Fluctuation of volumes on links • Time taken to conduct assignment • VHT of network at said level of convergence

13. Empirical Testing • Project 1: John Laurie Boulevard widening from Sarcee Trail to 53 ST NW (4 to 6 Lanes): • Simple widening, impact generally limited to peak periods only. • Network effects are more local than far-reaching.

14. Empirical Testing • Project 2: Glenmore Trail widening from Crowchild Trail to 14 ST SW (7 to 10 Lanes): • Major East-West corridor, important link in network. • Network effects are far-reaching with no close alternative routes.

15. Empirical Testing Observations • Volume Fluctuation on Links would occur in areas where travel times were very close. • “Flip-Flopping” would occur -- case when two scenarios are compared, an amount of volume takes path A in one scenario and path B in another. • More of a concern in the offpeak period than peak periods.

16. Empirical Testing Observations • Fixed Link Costs affect assignment convergence and time. • Used in Commercial Vehicle Model to represent non-truck routes (penalty applied to links) • Increased fixed link costs cause the multiclass assignment to think it has converged quickly when it has not.

17. Results John Laurie Boulevard Widening Project

18. Results John Laurie Boulevard Widening Project

19. Results Glenmore Trail Widening Project

20. Results Glenmore Trail Widening Project

21. Results • Computer time increases drastically as relative gap is decreased (more iterations required). • Link fluctuations decreased with increased convergence. • Large VHT differences from 0% RG value at 0.1% RG. • VHT stabilizes as relative gap is decreased.

22. Results Savings in VHT from Network Improvements

23. Results • Effect of convergence on savings unclear in AM Crown scenario • Increased convergence lead to increased savings in AM Shoulder scenario • Important to obtain stable values, particularly in projects that may not have much benefit in some time periods. • Most stable VHT results again near 0% RG

24. Results Stability of Network • At 0.1 % RG, Volume differences from link instability begin to outshadow that of the improvement. • Volumes more refined with increased convergence.

25. Results

26. Results

27. Results • Links approach 0% RG value with increased assignment. • Anderson Road link has most dramatic change - this is a link where flip-flopping occurs. • Remaining links are more or less stable around 0.05 % RG (differences are 10 or less) • With Anderson Road included, differences are about 30 or less vehicles at 0.05 % RG

28. Results • Assignments below 0.01% RG may stop for a variety of reasons: • RG or Normalized Gap may go negative and stop assignment. • Unsure if assignments are then equally converged (same distance from the optimum objective function) • Differences in assignment should be small, but practitioners should be aware • EMME/2 will only allow assignment of up to two decimals for RG -- Must use iterations to get between 0.01 % or 0 % RG.

29. Conclusions • Small differences in large numbers • Tighter convergence needed to see benefits • Important tradeoffs to be made • More converged assignment vs. increased computing time • End criteria depends on use of data and needs

30. Conclusions • For comparing VHT values between scenarios, RG of 0.01 % recommended • RG of 0.01 % also recommended for link volumes • If volumes are to be rounded, and practitioners are aware of areas with link fluctuations, an RG of 0.05 % can be used to save time. • Knowledge of the importance of convergence will be used in refining mobility benefits process.