Stability of parallel queueing systems with coupled service rates

Details Stability of parallel queueing systems with coupled service rates Stability of parallel queueing systems with coupled service rates

2010-01-10

arxiv.org/abs/1001.1560v1

Discrete Event Dyn Syst (2008) 18:447-472

Mathematics

Probability

This is a corrected version of the article published in Discrete Event Dyn Syst (2008) 18:447-472

Scientific paper

10.1007/s10626-007-0021-4

This paper considers a parallel system of queues fed by independent arrival streams, where the service rate of each queue depends on the number of customers in all of the queues. Necessary and sufficient conditions for the stability of the system are derived, based on stochastic monotonicity and marginal drift properties of multiclass birth and death processes. These conditions yield a sharp characterization of stability for systems, where the service rate of each queue is decreasing in the number of customers in other queues, and has uniform limits as the queue lengths tend to infinity. The results are illustrated with applications where the stability region may be nonconvex.

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