How to find the optimal paths in stochastic time-dependent transportation networks?

Abstract

This paper conducted a theoretical study on finding optimal paths in stochastic time-dependent (STD) transportation networks. A stochastic consistent network with STD link travel times was built. The methodology of robust optimization was applied to evaluate the paths for a priori optimization without requiring the probability distribution of travel times. The paths with greatest robustness, namely minimum upper bounds of travel times were defined as the optimal path. Under the stochastic consistent condition, the STD robust optimal path model can be converted into solving a time-dependent shortest path problem in a FIFO network. Then extended Dijkstra's algorithm can be applied to solve the simplified STD problem with computation complexity O(n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ). In the field experiment, several tests were conducted on finding robust optimal paths in a sampled STD transportation network of Shanghai, China. The numerical results confirmed the validity of the proposed approach and verified that the natural extension of conventional Dijkstra's algorithm can solve the STD robust optimal path problem as efficiently as a static network problem.