Stochastic User Equilibrium Model with a Bounded Perceived Travel Time

TL;DR

This paper introduces an eUnit-SUE model that incorporates bounded perceived travel times into stochastic user equilibrium, providing a more realistic traffic assignment framework that accounts for perception limits.

Contribution

It develops a novel bounded perception model within SUE, derived from a bounded probability distribution, and proves its mathematical properties and impact on traffic assignment.

Findings

Larger bounds increase route choice diversity and dispersion.

Decreasing bounds lead to flow patterns similar to deterministic equilibrium.

Bound range significantly influences route usage and perception variance.

Abstract

Stochastic User Equilibrium (SUE) models depict the perception differences in traffic assignment problems. According to the assumption of an unbounded perceived travel time distribution, the conventional SUE problems result in a positive choice probability for all available routes, regardless of their unappealing travel time. This study provides an eUnit-SUE model to relax this assumption. The eUnit model is derived from a bounded probability distribution. This closed-form model aligns with an exponentiated random utility maximization (ERUM) paradigm with the exponentiated uniform distributed random error, where the lower and upper bounds endogeneously determine the route usage. Specifically, a Beckmann-type mathematical programming formulation is presented for the eUnit-SUE problem. The equivalency and uniqueness properties are rigorously proven. Numerical examples reveal that the eUnit bound range between the lower and upper bounds greatly affects the SUE assignment results. A larger bound range increases not only the number of routes in the choice set but also the degree of dispersion in the assignment results due to a larger route-specific perception variance. The misperception is contingent upon the disparity between the shortest and longest travel times and the bounds. As the bound range decreases, the shortest route receives significant flow allocation, and the assignment result approaches the deterministic user equilibrium (DUE) flow pattern.