Endogenous route sets for spatially diverse traffic assignment

Abstract

This paper develops a new stochastic traffic assignment model that overcomes two basic assumptions (namely, independence and positivity) rooted in the logit-based model. These two assumptions are jointly violated on transportation networks, where travelers’ perceptions of spatial similarity (reflecting dependence) between routes may lead to route rejection (violating positivity). The developed model, termed hierarchical truncated traffic equilibrium (H-TTE), assigns zero flow to and therefore eliminates routes that are too costly and/or excessively similar to routes used by travelers. Through a hierarchical structure, the H-TTE model captures spatial similarity without explicit comparisons of all possible routes, rendering it feasible to perform network-wide assignment without complete route enumeration. The presented hierarchical structure is rather flexible, subsuming several existing relevant structures in route choice. While the hierarchical nature of the H-TTE condition yields a challenging two-level optimization problem, we provide an equivalent convex programming formulation that guarantees a unique solution. We further devise a column generation algorithm that ensures convergence across the entire network. Numerical results demonstrate the model's features and the algorithm's applicability to real-world networks.