Path Finding in Stochastic Time Varying Networks with Spatial and Temporal Correlations for Heterogeneous Travelers

Abstract

This paper studies the path finding problem in stochastic networks with known travel time distributions on each link of the network, in the presence of spatial and temporal travel time correlations. As a result of traffic dynamics and the decisions of network users, distributions with different characteristics can be observed for the link travel time at different time intervals. Considering correlations in a dynamic stochastic network and applying simulation-based realistic travel time distributions and correlations in the path finding problem in stochastic networks are the main contributions of this study. Two reliability-based optimal path finding problems were considered: the shortest path problem with on-time arrival probability and the minimum travel time budget path problem. For each problem, user heterogeneity can be considered in the developed approach, as users are allowed to have different preferences for travel time reliability. Solution algorithms for both problems were implemented and tested on a large-scale network in Chicago, Illinois, with networkwide link travel time distributions and correlations obtained from a traffic simulator. Numerical results demonstrate the impacts of correlations in a dynamic stochastic network on the optimal path travel time distribution. The developed approach can be used in the reliability-based user equilibrium problem to solve the main subproblem, the path finding problem, in dynamic stochastic networks.