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Approximations for the M / G / m Queue

Author

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  • Per Hokstad

    (University of Trondheim, Trondheim, Norway)

Abstract

We study the M / G / m queue and obtain difference-differential equations for the equilibrium joint distribution of the number of customers present and of the remaining holding times for services in progress. A study of these equations leads to the proposal of a simple approximation for the queue length distribution. Approximate waiting time and busy period distributions easily follow. Simple expressions for the means of the variables in question are obtained. Some numerical results on the mean waiting time indicate that the proposed approximation is rather accurate. The technique presented in this paper can also be applied to variants of the M / G / m queue. In particular, a short treatment of the queue with finite waiting room is included.

Suggested Citation

  • Per Hokstad, 1978. "Approximations for the M / G / m Queue," Operations Research, INFORMS, vol. 26(3), pages 510-523, June.
    • Handle: RePEc:inm:oropre:v:26:y:1978:i:3:p:510-523
    DOI: 10.1287/opre.26.3.510
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    Cited by:

    1. Benjaafar, Saifallah, 1995. "Performance bounds for the effectiveness of pooling in multi-processing systems," European Journal of Operational Research, Elsevier, vol. 87(2), pages 375-388, December.
    2. Ward Whitt, 2004. "A Diffusion Approximation for the G/GI/n/m Queue," Operations Research, INFORMS, vol. 52(6), pages 922-941, December.
    3. Zhang, Xuelu & Wang, Jinting & Do, Tien Van, 2015. "Threshold properties of the M/M/1 queue under T-policy with applications," Applied Mathematics and Computation, Elsevier, vol. 261(C), pages 284-301.
    4. David L. Jagerman & Benjamin Melamed, 2003. "Models and Approximations for Call Center Design," Methodology and Computing in Applied Probability, Springer, vol. 5(2), pages 159-181, June.
    5. Di Lin & Jonathan Patrick & Fabrice Labeau, 2014. "Estimating the waiting time of multi-priority emergency patients with downstream blocking," Health Care Management Science, Springer, vol. 17(1), pages 88-99, March.

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