Stochastic Demand Dynamic Traffic Models Using Generalized Beta-Gaussian Bayesian Networks

Abstract

A stochastic demand dynamic traffic model is presented to predict some traffic variables, such as link travel times, link flows, or link densities, and their time evolution in real networks. The model considers that the variables are generalized beta variables such that when they are marginally transformed to standard normal, they become multivariate normal. This gives sufficient degrees of freedom to reproduce (approximate) the considered variables at a discrete set of time-location pairs. Two options to learn the parameters of the model are provided-one based on previous observations of the same variables and one based on simulated data using existing dynamic models. The model is able to provide a point estimate, a confidence interval, or the density of the variable being predicted. To this end, a closed formula for the conditional future variable values (link travel times or flows), given the available past variable information, is provided. Since only local information is relevant to short-term link flow predictions, the model is applicable to very large networks. The following three examples of application are given: (1) the Nguyen-Dupuis network; (2) the Ciudad Real network; and (3) the Vermont state network. The resulting traffic predictions seem to be promising for real traffic networks and can be done in real time.