Routing in stochastic networks

Abstract

This paper considers the problem of routing in a network where the travel times along the arcs are modeled as independent random variables. A standard approach to routing in such networks is to select a path with the least expected travel time. One of the problems with this approach is that it does not take into consideration, factors such as the travel time variance. Additionally, such an approach implicitly assumes each user in the network has the same routing objective. In this paper we develop an approach to routing in stochastic networks in which these problems are addressed. The fundamental concept in our approach is that, for a given user with a set of routing options at a given node, we approximate the distributions of travel time for these options. Using these approximate distributions, the options are compared according to a user-specified routing objective, and the best option is selected. The primary benefit of this approach is that one is not limited to a particular routing objective as the computed distributions of travel time allow us to efficiently determine an effective routing option for an arbitrary routing objective that depends on factors of random travel time other than the mean. The distribution of travel time adopted in this paper is the minimum travel time probability distribution, which is the distribution of travel time over all fastest paths. In a class of networks termed as series-parallel networks, the minimum travel time distribution can be calculated efficiently. For general, non-series-parallel networks, the approximation we adopt is the minimum travel time distribution obtained from a related series-parallel network. The performance and the benefits of this approach to routing are illustrated on an example network.