Defending and attacking a network of two arcs subject to traffic congestion

To study the effects of intentional attacks on transportation systems, we consider drivers who choose the more time-efficient of two arcs (possibly of different lengths). Both arcs are subjected to traffic congestion, and also to interdiction or blockage (e.g., by a terrorist attack). The model has three types of strategic actors: the government; the terrorist; and potential drivers. The government protects travel, while the terrorist interdicts travel, along the two arcs. Drivers choose the arc that gives the shortest travel time, and cannot choose an interdicted arc. The drivers have reservation travel times, such that if the actual travel time will exceed an individual driver's reservation travel time, that driver would prefer not to travel; the reservation travel times are allowed to vary among drivers. The objective function of the master problem, which the government minimizes and the terrorist maximizes, is the sum of the total travel time plus the reservation travel times of the non-travelers. Each potential driver decides endogenously whether to travel, according to whether the actual travel time is greater or lesser than that driver's reservation travel time.