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April 22, 2003 Athanasios Ziliaskopoulos Elaine Chang

Regional Traffic Simulation/Assignment Model for Evaluation of Transit Performance and Asset Utilization. April 22, 2003 Athanasios Ziliaskopoulos Elaine Chang. Agenda. Project Overview Background Automobile Assignment-based Model Person Assignment-based Model

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April 22, 2003 Athanasios Ziliaskopoulos Elaine Chang

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  1. Regional Traffic Simulation/Assignment Model for Evaluation of Transit Performance and Asset Utilization April 22, 2003 Athanasios Ziliaskopoulos Elaine Chang

  2. Agenda • Project Overview • Background • Automobile Assignment-based Model • Person Assignment-based Model • Analytical Intermodal Formulation

  3. Project Overview • In parallel with RTA-funded transit signal priority (TSP) study • Evaluation of impacts of TSP on transit • Uses auto assignment-based multi-modal model • MRUTC-funded focus • Development of person assignment-based inter-modal model

  4. Background: Transit Impacts • Transit travel time • Transit travel time variability • Schedule adherence • Operational efficiency and cost • Ridership and revenue

  5. Background: DTA • Iteration between • Simulation • Shortest path calculation • Path assignment • VISTA software

  6. VISTA-1

  7. VISTA-2

  8. VISTA-3

  9. VISTA-4

  10. Auto Assignment-based Multi-modal Model • Uses basic DTA approach • p.5 • Enhancements • Simulation: buses incorporated • Path assignment: simplicial decomposition approach (replaces MSA) • p.15 • VI formulation • exact, not heuristic

  11. VI formulation

  12. Gap Function

  13. Simplicial Decomposition Approach • See page 17 • Step 0: based on ff tt, compute first extreme point (all-or-nothing assmt0) • …

  14. SD1 Feasible Space 0 Step 0-A: Initial solution based on free flow tt

  15. SD2 Feasible Space 0 Z0 Step 0-B: Simulate, update tt, calculate new extreme pt

  16. SD3 Feasible Space 0 1 Z0 Step 1-A: Calculate combination of 0, Z0 that min Gap Func

  17. SD4 Z1 Feasible Space 0 1 Z0 Step 1-B: Simulate, update tt, calculate new extreme pt

  18. SD5 Z1 Feasible Space 0  1 1- Z0 Step 2: Converged?  < 0.02 ?

  19. SD6 Z1 Feasible Space 0 2 1 Z0 Step 1-A: Calculate combination of 1, Z1 that min Gap Func

  20. SD7 Z2 Z1 0 2 1 Z0 Step 1-B: Simulate, update tt, calculate new extreme pt

  21. SD8 Z2 Z1 -1 0 2  1 Z0 Step 2: Converged?  < 0.02 ?

  22. SD9 Z2 Z1 3 0 2 1 Z0 Step 1-A: Calculate combination of 2, Z2 that min Gap Func

  23. SD10 Z2 Z1 Z4 3 0 2 1 Z0 Step 1-B: Simulate, update tt, calculate new extreme pt

  24. SD11 Z2 Z1 -1 Z4 3  0 2 1 Z0 Step 2: Converged?  < 0.02 ?

  25. SD12 Z2 Z1 Z4 3 4 0 2 1 Z0 Step 1-A: Calculate combination of 3, Z3 that min Gap Func

  26. SD13 Z2 Z1 Z4 3 4 0 2 1 Z0 And so on until convergence ...

  27. Auto Assignment-based Multi-modal Model • Captures • Automobile path choice (correct equilibrium solution found) • Transit travel time, tt variability • Transit schedule adherence • operational efficiency

  28. Auto Assignment-based Multi-modal Model • Does not directly capture • Ridership, mode choice (transit performance measures can be used in separate mode choice model)

  29. Auto Assignment-based Multi-modal Model • Strengths • Demand input is vehicle trip matrix - typically available • Travel cost is assumed to include only travel time, so not calibration of cost parameters is required • Weaknesses • Mode split is assumed fixed

  30. Person Assignment-based Inter-modal Model • DTA approach • p.22 • simulate traffic movements • calculate intermodal shortest paths • assign person-trips to equilibrium paths • simulate automobile portion of travel paths

  31. Person Assignment-based Inter-modal Model • Enhancements • Simulation: buses incorporated • Shortest path calculation: Time dependent intermodal least cost path algorithm (proof of correctness shown) • Path assignment: simplicial decomposition approach (replaces MSA)

  32. Shortest path algorithm • maintain both cost and time labels • find least cost path • account for transfer costs

  33. SP1 Inter-modal Network some route to D k D j i mode 1 mode 2 transfer

  34. SP2 Link Costs k j i

  35. SP3 Transfer Costs k j i

  36. SP4 Travel Time Labels k D j travel time of least cost path from k to D, when departing k at time t from j on m2 i

  37. SP5 Travel Time Labels k D j travel time of least cost path from j to D, when departing j at time t from i on m1 i

  38. SP6 Travel Time Labels k D j travel cost of least cost path from k to D, when departing k at time t from j on m2 i

  39. SP7 Travel Cost Labels k D j travel cost of least cost path from k to D, when arriving at k from j on mode m2 i

  40. SP8 Check Cost Label k D j i ?

  41. SP9 Update Cost Labels k D j i

  42. SP10 Update Travel Time Labels k D j i

  43. Person Assignment-based Inter-modal Model • Strengths • No assumption of fixed mode split • Ridership impacts can be directly observed • Weaknesses • Demand input is person trip matrix - not typically available • Calibration of generalized cost function extremely difficult

  44. Analytical Intermodal Formulation • formulation on p.38 • cell transmission-based propagation of cars and buses • solves for system optimal least cost assignment of intermodal person trips

  45. Analytical Intermodal Formulation • Summary of computational results: • buses may be held or may skip stops, depending on cost parameters • people may delay entering the transfer cell, and instead remain in the automobile subnetwork if cost of driving is less than cost of waiting at bus stop • FIFO behavior not maintained (depends on number of passengers on bus, cost parameters, etc.)

  46. Analytical Intermodal Formulation • Analytical Intermodal Formulation results are unsatisfactory because model adjusts traffic and person movements to equilibrate path costs. • Simulation-based approaches use simulation to determine the traffic movements, and equilibrate costs by shifting path choices.

  47. Conclusions • Auto Assignment-based Multi-modal Model captures bus movements and interactions between cars and buses, but does not directly capture mode split, ridership impacts. • Person Assignment-based Inter-modal Model directly captures mode split, ridership impacts, but person-trip data may not be available and calibration of cost parameters would be difficult.

  48. Conclusions • Analytical Intermodal Formulation results are unsatisfactory because model adjusts traffic and person movements to equilibrate path costs. • Enhancements to VISTA, DTA • Bus movements incorporated in simulator • Intermodal least cost path algorithm presented and correctness proven • Simplicial decomposition algorithm for calculation of equilibrium assignment developed

  49. Future Research • Evaluation of TSP will be completed using the Auto Assignment-based Multi-modal Model • Person Assignment-based Multi-modal Model will be implemented in VISTA • Intermodal least cost path algorithm to be coded • computational results on test network will be obtained • No further development is planned for the Analytical Intermodal Formulation

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