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 asymptotic behaviour of this type of networks is fundamentally different from classical queueing networks, where the service rate at each node is usually assumed to be independent of the state of the other nodes. We study the per-node rate stability and output rates for a class networks with a general capacity allocation function. More specifically, we derive necessary conditions of per-node 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 nodes, we further prove the convergence of the output rates for most parameters and give a sharp characterization of the per-node rate stability. The results provide new intuition and fundamental insight in the stability and throughput behaviour of queueing networks with shared resources.