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A general workload conservation law with applications to queueing systems

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  • Muhammad El-Taha

    (University of Southern Maine)

Abstract

In the spirit of Little’s law $$L=\lambda W$$ L = λ W and its extension $$H=\lambda G$$ H = λ G we use sample-path analysis to give a general conservation law. For queueing models the law relates the asymptotic average workload in the system to the conditional asymptotic average sojourn time and service times distribution function. This law generalizes previously obtained conservation laws for both single- and multi-server systems, and anticipating and non-anticipating scheduling disciplines. Applications to single- and multi-class queueing and other systems that illustrate the versatility of this law are given. In particular, we show that, for anticipative and non-anticipative scheduling rules, the unconditional delay in a queue is related to the covariance of service times and queueing delays.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:queues:v:85:y:2017:i:3:d:10.1007_s11134-017-9515-4
    DOI: 10.1007/s11134-017-9515-4
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    References listed on IDEAS

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    1. Daniel P. Heyman & Shaler Stidham, 1980. "The Relation between Customer and Time Averages in Queues," Operations Research, INFORMS, vol. 28(4), pages 983-994, August.
    2. 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.
    3. Muhammad El-Taha, 2016. "Invariance of workload in queueing systems," Queueing Systems: Theory and Applications, Springer, vol. 83(1), pages 181-192, June.
    4. 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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