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Invariance of workload in queueing systems

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  • Muhammad El-Taha

    (University of Southern Maine)

Abstract

In multi-server systems, invariance of workload is a key step in establishing conservation and strong conservation laws. Although several articles have dealt with the issue, invariance of workload has been either assumed, asserted without proof, or the proof given is unsatisfactory, except when service times are exponential. In this article we consider a multi-server queueing system with a work-conserving, non-preemptive, and non-anticipative scheduling rule and give a proof for the invariance of the workload in queue and in system for all such rules. We also show that invariance of workload holds for a subclass of strict priority rules.

Suggested Citation

  • Muhammad El-Taha, 2016. "Invariance of workload in queueing systems," Queueing Systems: Theory and Applications, Springer, vol. 83(1), pages 181-192, June.
    • Handle: RePEc:spr:queues:v:83:y:2016:i:1:d:10.1007_s11134-016-9474-1
    DOI: 10.1007/s11134-016-9474-1
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    References listed on IDEAS

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    1. A. Federgruen & H. Groenevelt, 1988. "M/G/c Queueing Systems with Multiple Customer Classes: Characterization and Control of Achievable Performance Under Nonpreemptive Priority Rules," Management Science, INFORMS, vol. 34(9), pages 1121-1138, September.
    2. A. Federgruen & H. Groenevelt, 1988. "Characterization and Optimization of Achievable Performance in General Queueing Systems," Operations Research, INFORMS, vol. 36(5), pages 733-741, October.
    3. M. Dacre & K. Glazebrook & J. Niño‐Mora, 1999. "The achievable region approach to the optimal control of stochastic systems," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(4), pages 747-791.
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    Cited by:

    1. Muhammad El-Taha, 2017. "A general workload conservation law with applications to queueing systems," Queueing Systems: Theory and Applications, Springer, vol. 85(3), pages 361-381, April.

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