Regional Traffic Simulation/Assignment Model for Evaluation of Transit Performance and Asset Utilization

April 22, 2003

Athanasios ZiliaskopoulosElaine 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

kp = the number of vehicles choosing to

follow path pk -- in vector notation

kp = the travel time on path pk -- () in vector notation

VI(,D) formulation:(*)(-*)T 0 Dwhere * = equilibrium assignment

Feasible space:

(,,)

k

k

p trs

pPrst

d

closed, bounded, convex space DR

0 pk

closed, bounded, convex space DR

r,s,t

12

Gap Function

An is the set of extreme points

13

Simplicial Decomposition Approach See page 17

Step 0: based on ff tt, compute first extreme point (all-or-nothing assmt0)

…

Feasible Space

( , , )

k

k

p trs

p P r s t

d

0

Step 0-A: Initial solution based on free flow tt

SD1

Feasible Space

( , , )

k

k

p trs

p P r s t

d

0

Z0

Step 0-B: Simulate, update tt, calculate new extreme pt

SD2

Feasible Space

( , , )

k

k

p trs

p P r s t

d

0

Z0

1

Step 1-A: Calculate combination of 0, Z0 that min Gap Func

SD3

Feasible Space

( , , )

k

k

p trs

p P r s t

d

0

Z0

1

Z1

Step 1-B: Simulate, update tt, calculate new extreme pt

SD4

Feasible Space

( , , )

k

k

p trs

p P r s t

d

0

Z0

1

Step 2: Converged? < 0.02 ?

1-

Z1SD5

Feasible Space

( , , )

k

k

p trs

p P r s t

d

0

Z0

1

Z1

2

Step 1-A: Calculate combination of 1, Z1 that min Gap Func

SD6

0

Z0

1

Z1

2

Z2

Step 1-B: Simulate, update tt, calculate new extreme pt

SD7

0

Z0

1

Z1

2

Z2

Step 2: Converged? < 0.02 ?

-1

SD8

0

Z0

1

Z1

2

Z2

3

Step 1-A: Calculate combination of 2, Z2 that min Gap Func

SD9

0

Z0

1

Z1

2

Z2

3

Z4

Step 1-B: Simulate, update tt, calculate new extreme pt

SD10

0

Z0

1

Z1

2

Z2

3

Z4

Step 2: Converged? < 0.02 ?

-1

SD11

0

Z0

1

Z1

2

Z2

3

Z4

4

Step 1-A: Calculate combination of 3, Z3 that min Gap Func

SD12

0

Z0

1

Z1

2

Z2

3

Z4

4

And so on until convergence ...

SD13

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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)

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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

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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

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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)

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Shortest path algorithm maintain both cost and time

labels find least cost path account for transfer costs

i

j

k

mode 1mode 2transfer

Inter-modal Network

D

some route to D

SP1

i

j

kil

m1(t)=il

m1(t)+ m1(t)il

m1(t)

jk

m2(t)=jk

m2(t)+ m2(t)jk

m2(t)

Link Costs

- total link cost - link fixed cost - travel time cost parameter - link travel time

SP2

i

j

k

Transfer Costs

- total transfer cost - fixed transfer cost - travel time cost parameter - transfer time

ijk

m1m2(t)=ijk

m1m2(t)+ m1m2(t)ijk

m1m2(t)

SP3

i

j

k

Travel Time Labels

D

travel time of least cost pathfrom k to D, when departing k at time t from j on m2

jk

m2(t) SP4

i

j

k

Travel Time Labels

D

travel time of least cost pathfrom j to D, when departing j at time t from i on m1

jk

m2(t)

ij

m1(t)

SP5

i

j

k

Travel Time Labels

D

travel cost of least cost pathfrom k to D, when departing k at time t from j on m2

jk

m2(t) SP6

i

j

k

Travel Cost Labels

D

travel cost of least cost pathfrom k to D, when arriving at k from j on mode m2

jk

m2(t)

ij

m1(t)

SP7

i

j

k

Check Cost Label

D

jk

m2(t)

ij

m1(t)

ij

m1(t)>{ ijkm1m2(t)

+jkm2(t+ijk

m1m2(t)) +jk

m2(t+ijkm1m2(t) +jk

m2(t+ijkm1m2(t)))} ?

SP8

i

j

k

Update Cost Labels

D

jk

m2(t)

ij

m1(t)

ij

m1(t)={ ijkm1m2(t)

+jkm2(t+ijk

m1m2(t)) +jk

m2(t+ijkm1m2(t) +jk

m2(t+ijkm1m2(t)))}

SP9

i

j

k

Update Travel Time Labels

D

ij

m1(t)={ ijkm1m2(t)

+jkm2(t+ijk

m1m2(t)) +jk

m2(t+ijkm1m2(t) +jk

m2(t+ijkm1m2(t)))}

jk

m2(t)

ij

m1(t)

SP10

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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

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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

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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.)

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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.

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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.

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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

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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