Stability of parallel queueing systems with coupled service rates

S.C. Borst, M. Jonckheere, L. Leskelä

Research output: Contribution to journalArticleAcademicpeer-review

52 Citations (Scopus)
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Abstract

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.
Original languageEnglish
Pages (from-to)447-472
JournalDiscrete Event Dynamic Systems
Volume18
Issue number4
DOIs
Publication statusPublished - 2008

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