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 ) …

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

Feasible Space 00 Z0Z0 Step 0-B: Simulate, update tt, calculate new extreme pt SD2

Feasible Space 00 Z0Z0 11 Step 1-A: Calculate combination of  0, Z 0 that min Gap Func SD3

Feasible Space 00 Z0Z0 11 Z1Z1 Step 1-B: Simulate, update tt, calculate new extreme pt SD4

Feasible Space 00 Z0Z0 11 Step 2: Converged?  < 0.02 ? 1- Z1Z1 SD5

Feasible Space 00 Z0Z0 11 Z1Z1 22 Step 1-A: Calculate combination of  1, Z 1 that min Gap Func SD6

00 Z0Z0 11 Z1Z1 22 Z2Z2 Step 1-B: Simulate, update tt, calculate new extreme pt SD7

00 Z0Z0 11 Z1Z1 22 Z2Z2 Step 2: Converged?  < 0.02 ? SD8

00 Z0Z0 11 Z1Z1 22 Z2Z2 33 Step 1-A: Calculate combination of  2, Z 2 that min Gap Func SD9

00 Z0Z0 11 Z1Z1 22 Z2Z2 33 Z4Z4 Step 1-B: Simulate, update tt, calculate new extreme pt SD10

00 Z0Z0 11 Z1Z1 22 Z2Z2 33 Z4Z4 Step 2: Converged?  < 0.02 ? SD11

00 Z0Z0 11 Z1Z1 22 Z2Z2 33 Z4Z4 44 Step 1-A: Calculate combination of  3, Z 3 that min Gap Func SD12

00 Z0Z0 11 Z1Z1 22 Z2Z2 33 Z4Z4 44 And so on until convergence... SD13

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

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

i j k Link Costs SP2

i j k Transfer Costs SP3

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

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

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

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

i j k Check Cost Label D ? SP8

i j k Update Cost Labels D SP9

i j k Update Travel Time Labels D SP10

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