Abstract
In this paper we address optimal routing problems in networks where travel times are both stochastic and time-dependent. In these networks, the best route choice is not necessarily a path, but rather a time-adaptive strategy that assigns successors to nodes as a function of time. Nevertheless, in some particular cases an origin–destination path must be chosen a priori, since time-adaptive choices are not allowed. Unfortunately, finding the a priori shortest path is an NP-hard problem.In this paper, we propose a solution method for the a priori shortest path problem, and we show that it can be easily extended to the ranking of the first K shortest paths. Our method exploits the solution of the time-adaptive routing problem as a relaxation of the a priori problem. Computational results are presented showing that, under realistic distributions of travel times and costs, our solution methods are effective and robust.
Highlights
Classical optimization models for routing commodities, vehicles, passengers etc. in a transportation network assume that link travel times are deterministically known and do not evolve over time
In this paper we consider stochastic timedependent networks (STD networks) where link travel times are represented by random variables with probability distributions varying as a function of departure times
Optimal routing in STD networks was first addressed by Hall [8], who considered the minimization of expected travel time for a given origin/destination pair and starting time
Summary
Classical optimization models for routing commodities, vehicles, passengers etc. in a transportation network assume that link travel times are deterministically known and do not evolve over time. For discrete STD networks, Miller-Hooks and Mahmassani [12] proposed a labeling algorithm that finds a priori optimal paths, to a given destination, from all the other nodes and for all possible leaving time. They allow the paths to be looping, which is a major depart from Hall’s original model. Labeling methods for the discrete case are conceived for a much more general version of the problem; on the other hand, solution methods based on the continuous model are inherently approximate, even if they may offer a better trade-off between computational cost and solution quality Based on these premises, it seems apparent that a direct computational comparison to previous algorithmic proposals would be questionable, if not arbitrary. Appendix A provides an example illustrating several concepts introduced throughout the paper
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