Robust path choice and vehicle guidance in networks with failuresMichael

The problem of vehicle guidance in a network with failures is considered. The network may be in one of nitely many states characterized by diierent 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 ow-oriented models are developed and analyzed in the uncapacitated and the ca-pacitated 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 rerouting 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 diierent guidance policies and show that substantial improvements in both duration and size of traac jams can be achieved by employing robust guidance strategies.