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A linear programming approach to stability, optimisationand performance analysis for Markovian multiclassqueueing networks

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  • K.D. Glazebrook
  • J. Niño‐Mora

Abstract

Our object of study is a multiclass queueing network (MQNET) which consists of acollection of (connected) single‐server stations. Exogenous arrivals into the system formindependent Poisson streams, service times are exponential and we have Markovian routingof customers between stations. Recent results concerning linear programming (LP) basedapproaches enable us to establish a simple and intuitive stability condition. This is of interestin its own right, but also enables us to progress with a study of optimal scheduling andperformance analysis. Our methodology here is also based on LP. A primal‐dual approachexploits the fact that the system satisfies (approximate) conservation laws to yield perform-anceguarantees for a natural index‐based scheduling heuristic. We are also able to analysethe performance of an arbitrary priority policy. Copyright Kluwer Academic Publishers 1999

Suggested Citation

  • K.D. Glazebrook & J. Niño‐Mora, 1999. "A linear programming approach to stability, optimisationand performance analysis for Markovian multiclassqueueing networks," Annals of Operations Research, Springer, vol. 92(0), pages 1-18, January.
    • Handle: RePEc:spr:annopr:v:92:y:1999:i:0:p:1-18:10.1023/a:1018922412074
    DOI: 10.1023/A:1018922412074
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    Cited by:

    1. Kevin D. Glazebrook & José Niño-Mora, 2001. "Parallel Scheduling of Multiclass M/M/m Queues: Approximate and Heavy-Traffic Optimization of Achievable Performance," Operations Research, INFORMS, vol. 49(4), pages 609-623, August.
    2. Kevin D. Glazebrook & José Niño-Mora, 1997. "Assessing an intuitive condition for stability under a range of traffic conditions via a generalised Lu-Kumar network," Economics Working Papers 429, Department of Economics and Business, Universitat Pompeu Fabra, revised Jan 2000.

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