A probability model and sampling algorithm for the inter-day stochastic traffic assignment problem

In this study, we consider that inter-day traffic flow fluctuations in a network are caused by stochastic travel behavior. We treat route traffic flows at each time interval as random variables. Therefore, the solution of the stochastic assignment problem should be the conditional joint probability distribution of the route flows given that the network is in stochastic user equilibrium. We formulate the conditional joint distribution and develop a Gibbs sampler to draw samples from the conditional joint distribution. The characteristics of the route flows at each time interval during the time horizon can be estimated on the basis of the simulated samples.