Traditional Traffic Assignment

1. Multi-modal Bi-criterion Highway Assignment for Toll RoadsJian Zhang Andres RabinowiczJonathan BrandonCaliper Corporation5-9-2007

2. Traditional Traffic Assignment Assuming uniformity among users’： • Access to network • Link cost function (VDF) • Value of time (VOT) • Out-of-pocket cost

3. Advantages of MMA(multi-modal assignment) Simulating user variety in： • Vehicle type (car，bus，light / heavy trucks, etc.) • Occupancy（HOV，LOV) • Driver characteristics (cost or time sensitive) • Class-specific VOT’s

4. Advantages of MMA Simulating vehicle-type-specific network accessibility： • Lane usage (HOV, HOT) • Height/Weight limits • Toll charge • Access to network status info.

5. MMA Model Analysis • Standardized volume vak — total PCE on link a for type k αk— PCE conversion factor for type k Cost function based on standardized volume: cak — cost for type k (e.g. toll payment) βk — VOT for type k

6. T2 Traffic Assignment Model Developed by Robert Dial, features include: • VOT as a random variable in calculating link cost: P — path,α— random VOT variable with known probability density • Bi-criterion multiple path building • Fast path calculation using “Efficient Frontier” • One user class (|K|=1)

7. New MMA-T2 Model Combining MMA and T2: • Multiple user classes • VOT of each user class as a random variable with its unique mean and distribution • Bi-criterion multiple path building for each user type

8. MMA-T2 Model Advantages • Representing various user income levels • Considering VOT variation within each user group • Allowing more realistic simulation of user response to different highway toll policies.

9. MMA-T2 Model Structure(variational inequality)

10. MMA-T2 Model Solution Model Solution Equilibrium Conditions: gpk — travel cost on path p for type k uwk — min. travel cost between w-th OD pair for type k fpk — type k volume on path p Note: Only min.-cost paths have flow, which satisfies multi-modal traffic assignment equilibrium condition

11. MMA-T2 Model Solution Algorithm Step 0: Initialization: do non-equilibrium T2 assignment for each user type Step 1: Renew link times Step 2: Conduct non-equilibrium T2 assignment for each user type based on new link times so as to get auxiliary link flows. Step 3: Compute step size and combine current and auxiliary link flows(MSA) Step 4: Check convergence. Stop if converged, otherwise go to Step 1

12. Example 1: Network Capacity and Free-flow Speed Free-flow Time and Cost

13. Example 1: Users VOT Probability Density O-D Demand

14. Example 1: Results Class 1 Flows Class 2 Flows Class 3 Flows Total Flows

15. Example 2: Network Mass. Highway Network (5627 links, 2025 nodes, 106 toll links)

16. Example 2: User Demands Classes : Car, Light Truck, Heavy Truck # of O-D pairs = 19,460 Total demand = 416,426 (70%, 23%, 7%)

17. Example 2: Toll Scenarios Original Toll Matrices Toll Scenarios : 1 – original 2 – original * 2 3 – original * 3 4 – original * 4

18. Example 2: User VOT DistributionScenarios SD = 5 SD = 10 SD = 15 Pearson Type III Distribution Means: Car = 20, Light Truck = 40, Heavy Truck = 60 ($/hr)

19. Example 2 Result: Toll Road Usages

20. Example 2 Results: Average Trip Time

21. Observations • When toll charge is high, MMA model tends to underestimate toll road usages than predicted by MMA-T2 model • When toll charge is high, MMA model tends to overestimate average trip times than forecast by MMA-T2 model • As user VOT distributions become wider, toll road usages increase and average trip times drop

22. Conclusion • MMA-T2 model has the advantages of both MMA and T2 (bi-criterion multi-path building, multi-user-class specifications, etc.) • The new model is able to capture heterogeneous users’ response to toll charges for a more accurate evaluation of different toll scenarios

23. Thanks!