A Computational Model for the Probit-Based Dynamic Stochastic User Optimal Traffic Assignment Problem

This article presents a computational model for the probit-based dynamic stochastic user optimal (P-DSUO) traffic assignment problem. Dynamic traffic assignment (DTA) models consist of three sub-models: travel choice, traffic performance, and network loadings. The authors first examine a general fixed-point formulation for the P-DSUO traffic assignment problem, and then propose a computational model that can find an approximated solution of the interest problem. The computational model includes four components: a strategy to determine a set of the prevailing routes between each origin–destination pair, a method to estimate the covariance of perceived travel time for any two prevailing routes, a cell transmission model-based traffic performance model to calculate the actual route travel time used by the probit-based dynamic stochastic network loading procedure, and an iterative solution algorithm solving the customized fixed-point model. The authors propose the Ishikawa algorithm to solve the computational model. They conduct a comparison study to investigate the efficiency and accuracy of the proposed algorithm with the method of successive averages. Two numerical examples are presented (the Nguyen & Dupius network and the Sioux Falls network). The authors conclude that the Ishikawa algorithm has better accuracy for a smaller network despite requiring longer computational time.

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