Solving the stochastic multi-class traffic assignment problem with asymmetric interactions, route overlapping, and vehicle restrictions

In this paper, we develop a customized path-based algorithm for solving the stochastic multi-class traffic assignment problem with asymmetric interactions, route overlapping, and vehicle restrictions. The algorithm consists of an iterative balancing scheme to find the search direction, a self-regulated averaging line search scheme to determine a suitable stepsize, and a column generation scheme to generate a universal path set for multiple vehicle classes. These three schemes work together in the customized path-based algorithm to solve the stochastic multi-class traffic assignment problem. The solution algorithm simultaneously considers the asymmetric interactions among different vehicle types through the link travel time functions, various vehicle restrictions in a transportation network, and route overlapping using the path-size logit model for accounting random perceptions of network conditions in a stochastic user equilibrium framework. A real network in the city of Winnipeg, Canada, is used to examine the computational performance of the customized path-based algorithm. In addition, sensitivity analyses are conducted to test the algorithmic effectiveness with respect to several model parameters and percentages of trucks in the transportation network. Numerical results reveal that the path-based algorithm with the self-regulated averaging line search scheme is computationally effective in solving the stochastic multi-class traffic assignment problem with different modeling considerations. The algorithm is also computationally robust against various model parameters in the sensitivity analyses.