Ranking paths in stochastic time-dependent networks

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.