Bicriterion shortest paths in stochastic time-dependent networks

In recent years there has been a growing interest in using stochastic time-dependent (STD) networks as a modelling tool for a number of applications within such areas as transportation and telecommunications. It is known that an optimal routing policy does not necessarily correspond to a path, but rather to a time-adaptive strategy. In some applications, however, it makes good sense to require that the routing policy should correspond to a loopless path in the network, that is, the time-adaptive aspect disappears and a priori route choice is considered. In this paper we consider bicriterion a priori route choice in STD networks, i.e. the problem of finding the set of efficient paths. Both expectation and min-max criteria are considered and a solution method based on the two-phase method is devised. Experimental results reveal that the full set of efficient solutions can be determined on rather large test instances, which is in contrast to the time-adaptive case.