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This paper considers a parallel system of queues fed by independent arrivalstreams, where the service rate of each queue depends on the number ofcustomers in all of the queues. Necessary and sufficient conditions for thestability of the system are derived, based on stochastic monotonicity andmarginal drift properties of multiclass birth and death processes. Theseconditions yield a sharp characterization of stability for systems, where theservice rate of each queue is decreasing in the number of customers in otherqueues, and has uniform limits as the queue lengths tend to infinity. Theresults are illustrated with applications where the stability region may benonconvex.

Stability of parallel queueing systems with coupled service rates