The posterior probability distribution of traffic flow: a new scheme for the assignment of stochastic traffic flow

Abstract

This study proposes a new scheme for assigning traffic flows that aims to capture the stochastic nature of route traffic flows. We consider the route traffic flows to be random variables. The distribution of these random variables is formulated as a conditional probability distribution for a given assumption: the traffic network is in stochastic user equilibrium. From a Bayesian perspective, we treat the conditional distribution as a posterior distribution of route traffic flows, which is obtained using Bayes’ theorem. We develop a basic Metropolis–Hastings (M–H) sampling scheme, as well as a M–H within Gibbs sampling scheme, to draw samples from the posterior distribution. We estimate characteristics such as the means and variances of route traffic flows from simulated samples. The proposed model can directly output the route traffic flows, and has a highly flexible computation process.

Keywords:

• stochastic traffic assignment
• Bayes’ theorem
• posterior distribution
• Markov chain Monte Carlo
• contemporaneous model

Acknowledgements

We would like to thank Professor Seungjae Lee for his discussions on this manuscript. The comments and suggestions of the anonymous referees are gratefully acknowledged.