Rate stability and output rates in queueing networks with shared resources

Motivated by a variety of applications in information and communication systems, we consider queueing networks in which the service rate at each of the individual nodes depends on the state of the entire system. The behavior of these types of networks is fundamentally different from classical queueing networks, where the service rate at each queue is usually assumed to be independent of the state of the other nodes. We study the per-queue rate stability and output rates for a class of networks with a general capacity allocation function. More specifically, we derive necessary conditions for per-queue rate stability, and give bounds for the per-node output rate and asymptotic growth rates, under mild assumptions on the allocation function. For a set of parallel queues, we further prove the convergence of the output rates (for almost all input parameters) to easily computable values and we give a sharp characterization of the per-queue rate stability. The results provide new intuition and fundamental insight into the stability and throughput behavior of queueing networks with shared resources.