Finding Reliable Shortest Paths in Dynamic Stochastic Networks

Abstract

A reliable a priori shortest path (RASP) offers the least time budget and ensures that a traveler can arrive at the destination on time with the desired probability. A RASP is equivalent to enumerating all nondominated paths under the first-order stochastic dominance rule. Compared with the problem in static networks, the RASP problem becomes more complex in dynamic networks because it is more difficult to compute path travel time distributions. Two modules of process are the keys to solving the RASP problem. One module is the convolution scheme (how to compute a path travel time distribution from its member links' travel time distributions), and the other module is the stochastic dominance scheme (how to determine nondominated paths). This study aims to find an efficient solution algorithm for this problem. An alternative convolution method is developed on the basis of the adaptive discretization approach, which was originally proposed to solve the RASP problem in static networks. In contrast, the higher-order stochastic dominance rule can be shown to reduce the number of nondominated paths; this rule promises to improve computational efficiency. Numerical experiments show that the second-order stochastic dominance rule offers good approximations, and the central processing unit time is reduced by at least 50%.