A Bayesian approach to traffic estimation in stochastic user equilibrium networks

Abstract

This study proposes a statistical model to estimate route traffic flows in congested networks. In the study, it is assumed that route traffic flows conform to the stochastic user equilibrium (SUE) principle while being treated as random variables in order to exploit the stochastic nature of traffic. The proposed model formulates the distribution of these random variables as the conditional distribution of route flows given the observed link flows and the SUE principle. Here, the SUE principle is accounted for through the likelihood of user behaviours rather than by using a bi-level formulation. In this study, the Bayesian theorem is applied to derive the probability density function (PDF) of the conditional distribution. Based on the PDF, characteristics such as the means and variances of route/link traffic flows are estimated using a blocked Metropolis–Hastings (M–H) algorithm. To facilitate the use of prior knowledge, a hierarchical form is designed to provide a straightforward way to integrate prior knowledge into the traffic estimation model. The performance of the proposed method is tested on the Sioux–Falls network through a series of numerical examples.