Stochastic quasi-gradient algorithm for the off-line stochastic dynamic traffic assignment problem

Abstract

This paper proposes a stochastic quasi-gradient (SQG) based algorithm to solve the off-line stochastic dynamic traffic assignment (DTA) problem that explicitly incorporates randomness in O–D demand, as part of a hybrid DTA deployment framework for real-time operations. The problem is formulated as a stochastic programming DTA model with multiple user classes. Due to the complexities introduced by real-time traffic dynamics and system characteristics, well-behaved properties cannot be guaranteed for the resulting formulation and analytical functional forms that adequately capture traffic realism typically do not exist for the associated objective functions. Hence, a simulation-based SQG method that is applicable for a generalized differentiable (locally Lipschitz) non-convex objective function and non-convex constraint set is proposed to solve the problem. Simulation is used to estimate quasi-gradients that are stochastic to incorporate demand randomness. The solution approach is a generalization of the deterministic DTA solution methodology; under it, deterministic DTA models are special cases. Of practical significance, it provides a robust solution for the field deployment of DTA, or an initial solution for hybrid real-time strategies. The solution algorithm searches a larger feasible domain of the solution space, leading to a potentially more robust and computationally more efficient solution than its deterministic counterparts. These advantages are highlighted through simulation experiments.