This paper deals with stochastic transportation networks in which links’ travel times are random variables. Transitions among states of the network (each state differs from any other state by at least one link with different travel time) are assumed Markovian. The problem is to find an optimal location-relocation decision for p mobile servers in such a network. The criterion is to minimize the long-term expected average cost in units of time per period taking into account both response times and relocation costs. The paper generalizes its predecessor [see O. Berman and A. R. Odoni, Networks 12, 73-86 (1982; Zbl 0478.90016)], by permitting the chosen set of locations in a given state of the network to depend on the former state of the network. Markovian decision theory is employed with the problem’s special structure used to reduce the complexity of the resulting algorithm.