The Travelers Route Choice Problem Under Uncertainty: Dominance Relations Between Strategies

In this paper we describe the Traveler's Route Choice Problem (TRCP). This is the problem of a traveler in a railway system who plans to take the fastest route to a destination but is faced with a disruption of unknown length on this route. In that case, he can wait until the disruption is over or take a detour route as an alternative. Since the duration of the disruption is not known in advance, he is left with a decision problem under uncertainty. In this paper we model the problem and describe the strategies that may be used in such a situation. Instead of finding optimal strategies for a specialized quality measure, we consider dominance relations between strategies and show that dominated strategies are nonoptimal for the common quality measures. We then analyze which strategies for the TRCP are dominated. In general, the set of nondominated strategies is strongly reduced. We also show that, under certain assumptions, only a small set of strategies is nondominated and conclude that in this case the TRCP can be solved by enumeration for any of the quality measures.