Routing in networks with random topologies

We examine the problems of routing and server assignement in networks with random connectivities. In such a network the basic topology is fixed, but during each time slot and for each of its input queues, each server (node) is either connected to or disconnected from each of its input queues with some probability. During each time slot a server must decide which of its connected input queues to serve and into which of its output queues the completed job should be placed. For single-input single-output acyclic queueing networks with random connectivities, we show that the joint routing/service policy that routes customers along the least populated path to the destination and serves any non-empty queue maximumizes throughput. We briefly discuss some implementation aspects of the proposed policy, including its robustness in stabilizing the system with respect to delayed state information.