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Two new heuristics for the GI/G/n/0 queueing loss system with examples based on the two-phase Coxian distribution

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  • J B Atkinson

    (London Metropolitan University)

Abstract

In this paper, we introduce a new heuristic approach for the numerical analysis of queueing systems. In particular, we study the general, multi-server queueing loss system, the GI/G/n/0 queue, with an emphasis on the calculation of steady-state loss probabilities. Two new heuristics are developed, called the GM Heuristic and the MG Heuristic, both of which make use of an exact analysis of the corresponding single-server GI/G/1/0 queue. The GM Heuristic also uses an exact analysis of the GI/M/n/0 queue, while the MG Heuristic uses an exact analysis of the M/G/n/0 queue. Experimental results are based on the use of two-phase Coxian distributions for both the inter-arrival time and the service time; these include an error analysis for each heuristic and the derivation of experimental probability bounds for the loss probability. For the class of problems studied, it is concluded that there are likely to be many situations where the accuracy of the GM Heuristic is adequate for practical purposes. Methods are also developed for combining the GM and MG Heuristics. In some cases, this leads to approximations that are significantly more accurate than those obtained by the individual heuristics.

Suggested Citation

  • J B Atkinson, 2009. "Two new heuristics for the GI/G/n/0 queueing loss system with examples based on the two-phase Coxian distribution," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(6), pages 818-830, June.
    • Handle: RePEc:pal:jorsoc:v:60:y:2009:i:6:d:10.1057_palgrave.jors.2602628
    DOI: 10.1057/palgrave.jors.2602628
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    References listed on IDEAS

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    1. Dae W. Choi & Nam K. Kim & Kyung C. Chae, 2005. "A Two-Moment Approximation for the GI / G / c Queue with Finite Capacity," INFORMS Journal on Computing, INFORMS, vol. 17(1), pages 75-81, February.
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    5. Yao, David D. W. & Buzacott, J. A., 1985. "Queueing models for a flexible machining station Part II: The method of Coxian phases," European Journal of Operational Research, Elsevier, vol. 19(2), pages 241-252, February.
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