On the stationary dynamics of parallel queues with random server connectivities

We investigate the stationary dynamics of a system comprised of K parallel queues and a single server. The connectivities of the server to the various queues are randomly modulated by a stochastic process, taking values 1 (connected) or 0 (severed). At any given time, only the currently connected queues can be served. Such models capture the essential features of several practical situations of unreliable service, appearing in wireless communication networks with extraneous interference, flexible manufacturing systems with failing components etc. We focus on the problem of allocating the server to the connected queues in order to maximize the capacity (throughput) of the system. We analyze two simple dynamic server allocation policies which are shown to stabilize the system under the highest possible loading. Several applications are discussed. The system is studied under stationary ergodic input job flows and modulation processes