On the Conservation Law and the Performance Space of Single Server Systems

Leonidas Georgiadis and Ioannis Viniotis
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Leonidas Georgiadis: IBM T. J. Watson Research Center, Yorktown Heights, New York
Ioannis Viniotis: North Carolina State University, Raleigh, North Carolina

Operations Research, 1994, vol. 42, issue 2, 372-379

Abstract: We consider a multiclass GI / G /1 queueing system, operating under an arbitrary work-conserving scheduling policy π. We derive an invariance relation for the Cesaro sums of waiting times under π, which does not require the existence of limits of the Cesaro sums. This allows us to include important classes in the set of admissible policies such as time-dependent and adaptive policies. For these classes of policies, ergodicity is not known a priori and may not even exist. Therefore, the classical invariance relations that involve statistical averages do not hold. For an M / G /1 system, we derive inequalities involving the Cesaro sums of waiting times that further characterize the achievable performance region of the system.

Keywords: probability; statistic model applications: nonergodic rules; queues; limit theorems: nonergodic priority rules in steady state; queues; priority: derivation of conservation laws (search for similar items in EconPapers)
Date: 1994
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Persistent link: https://EconPapers.repec.org/RePEc:inm:oropre:v:42:y:1994:i:2:p:372-379

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