Generalized Traffic Equilibrium with Probabilistic Travel Times and Perceptions

TLDR

Traditional traffic equilibrium models assume deterministic travel times and accurate perceptions, whereas GTESP extends this by incorporating both probabilistic travel times and potentially inaccurate perceptions, making it a general framework that subsumes existing models but is challenging to solve for nonlinear disutilities. The study aims to predict traffic equilibrium in networks under probabilistic travel times and uncertain perceptions. GTESP models each route’s travel time as a random variable and allows travelers to perceive possibly inaccurate probability distributions, then selects routes by minimizing expected disutility, and admits tractable solutions for independent arc times with linear, exponential, or quadratic disutilities. Illustrative examples show that GTESP captures travelers’ risk‑taking behavior more realistically than existing traffic equilibrium models.

Abstract

The paper studies the problem of predicting traffic equilibrium (TE) in a transportation network within the framework of decision making among discrete choices in a probabilistic and uncertain environment. Conventional approaches to predict TE typically assume that travel times are deterministic and perceived accurately by the travelers; and some new TE models have considered probabilistic travel times or inaccurate perceptions but not both. In our generalized model, which we refer to as GTESP, the travel time on each route is random and each traveler perceives, possibly inaccurately, a travel time probability distribution for each route which may vary from traveler to traveler. Each traveler uses a disutility function of travel time to evaluate each route and chooses that route which minimizes his expected disutility. GTESP is difficult to solve for general nonlinear disutility functions. However, special cases—in particular when arc travel times are statistically independent and the disutility functions to evaluate route travel times are linear, exponential, or quadratic—are solvable, at least approximately. GTESP is general in the sense that most existing TE models can be shown to be special or limiting cases of GTESP. Furthermore, this paper demonstrates, with illustrative examples, that GTESP appears to capture travelers' risk-taking behavior more realistically than existing TE models.