Shortest Paths in Stochastic Time-Dependent Networks with Link Travel Time Correlation

Abstract

This paper develops a simple, robust framework for the problem of finding the route with the least expected travel time from any node to any given destination in a stochastic and time-dependent network. Spatial and temporal link travel time correlations are both considered in the proposed solution, which is based on a dynamic programming approach. In particular, the spatial correlation is represented by a Markovian property of the link states, in which each link is assumed to experience congested or uncongested conditions. The temporal correlation is manifested through the time-dependent expected link travel time given the condition of the link traversed. The framework enables the use of a route guidance system, in which at any decision node within a network, a decision can be made on the basis of current traffic information about which node to take next to achieve the shortest expected travel time to the destination. Numerical examples are presented to illustrate the computational steps involved in the framework to make route choices and to demonstrate the effectiveness of the proposed solution.

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