Direct formulation and algorithms for the probit-based stochastic user equilibrium traffic assignment problem

This paper proposes simple and direct formulation and algorithms for the probit-based stochastic user equilibrium traffic assignment problem. It is only necessary to account for random variables independent of link flows by performing a simple transformation of the perceived link travel time with a normal distribution. At every iteration of a Monte-Carlo simulation procedure, the values of the random variables are sampled based on their probability distributions, and then a regular deterministic user equilibrium assignment is carried out to produce link flows. The link flows produced at each iteration of the Monte-Carlo simulation are averaged to yield the final flow pattern. Two test networks demonstrate that the proposed algorithms and the traditional algorithm (the Method of Successive Averages) produce similar results and that the proposed algorithms can be extended to the computation of the case in which the random error term depends on measured travel time.