Robust path choice in networks with failures

The problem of adaptive routing 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 continuous-time Markov chain. The objective was to develop a routing strategy that minimizes the total expected travel time. Dynamic programming models and flow-oriented models were 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 models the rerouting problem after the state transition in the network. The models are illustrated on an example of the Sioux Falls transportation network. The computational results reveal striking properties of different routing policies and show that substantial improvements in both duration and size of jams can be achieved by employing robust strategies.