Robust Path Choice and Vehicle Guidance in Networks With Failures

The problem of vehicle guidance in a network with failures is considered. The network may be in one of finitely many states characterized by different travel times along the arcs, and transitions between the states occur according to a continuos-time Markov chain. The objective is to guide the vehicles in a manner minimizing the total expected travel time. Dynamic programming models and flow-oriented models are developed and analyzed in the uncapacitated and the capacitated case. It is shown that the robust plan can be found from a special two-stage stochastic programming problem in which the second stage problem describes the re-routing of vehicles that experienced state transition during their travel. The models are illustrated on an example of the Sioux Falls transportation network. The computational results reveal striking properties of different guidance policies and show that substantial improvements in both duration and size of traffic jams can be achieved by employing robust gu..