1. After Evans: Working on an Approximation of a Combined Equilibrium Model Based on Precision Assignment
May, 2011
TRB Planning Applications Conference, Reno, NV
Presented by:
Thomas Walker, Wolfgang Scherr, Chris Puchalsky
DVRPC, Office of Modeling and Analysis

2. Motivation Objectives We need combined equilibrium
Consistent agreement of model inputs and outputs:
Travel time input for trip distribution and mode choice
SHOULD EQUAL
Congested travel time output from highway assignment
Elimination of “model noise” in scenario comparison
We need combined equilibrium
Equilibrium in highway assignment alone is not enough
Equilibrium of the entire system is needed
How to achieve it with an iterative travel model:
Iteration of the 4-stage-model
Feedback
Averaging of travel impedance between iterations

3. DVRPC’s Regional Travel Model
TRANPLAN Model
Migrated from UTPS (1980)
Evans implementation (2000):
Fixed weights for first 2 feedback iterations
Calculation of optimal weights for 5 remaining iterations
TIM 1.0 – in use since 2010
Migrated from TRANPLAN to VISUM
Equilibrium method:
Precision hwy assignment (path-based)
Averaging of the impedance matrix between model iterations
Simplified by constant weights (50/50)

4. Search for Optimal Solutions
Feasible Solutions as Ordered by Weighting Routine 5 10 15 20 25 30 35 40 S 1
Objective Function Value

5. TIM 1.0 – Elimination of “Noise”
TRANPLAN
TIM 1.0
Network change

6. TIM 1.0: Model Convergence
Run Time
RAM
Processor Speed
Cores
4.5 hr
48 GB
2.67 GHz 16
5.5 hr
16 GB
2.4 GHz 8
Model termination if 3 criteria are met:
Highway assignment Relative gap <
Difference in highway trip matrx %RSME < 0.5
Difference in hwy impedance matrix %RSME < 0.1
Relative Gap

7. Conclusions and Summary
Evans
Mathematically great
Implemented only in TRANPLAN
Not supported in newer precision assignment software
Alternative: feedback with constant weights
Provides excellent convergence with reasonable computation time
Good experience in DVRPC’s TIM 1.0
Future perspective – research needed
Measuring combined equilibrium
New “Evans” within precision highway assignment
Convergence of microscopic activity-based models (ABM)