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Approximation of the Mean Queue Length of an M/G/c Queueing System

Author

Listed:
  • Bobby N. W. Ma

    (Ryerson Polytechnical Institute, Toronto, Ontario, Canada)

  • Jon W. Mark

    (University of Waterloo, Waterloo, Ontario, Canada)

Abstract

A relatively robust method for the approximate analysis of the mean queue length of an M/G/c queueing system is proposed. The approximation method is developed based on the following assumptions: the residual service time of one busy server is independent of those of the other busy servers, and the system in which all the servers are busy is treated in the same way as a single-server system with c times the service rate of one of the servers. The application of these two assumptions is coupled through the introduction of a parameter n p . If the number of customers in the system is larger than n p , assumption 2 is used; otherwise assumption 1 is used. We found that certain properties of n p allow an estimation of the mean queue length of a large M/G/c queueing system through the approximate analysis of the mean queue length of a much smaller M/G/c queueing system. Numerical results show that the approximation is accurate even when the coefficient of variation of the service time and the number of channels of the system are as large as 20 and 200, respectively.

Suggested Citation

  • Bobby N. W. Ma & Jon W. Mark, 1995. "Approximation of the Mean Queue Length of an M/G/c Queueing System," Operations Research, INFORMS, vol. 43(1), pages 158-165, February.
    • Handle: RePEc:inm:oropre:v:43:y:1995:i:1:p:158-165
    DOI: 10.1287/opre.43.1.158
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    Cited by:

    1. Kleijnen, J.P.C. & Bettonvil, B.W.M. & van Groenendaal, W.J.H., 1996. "Validation of Simulation Models : Regression Analysis Revisited," Discussion Paper 1996-07, Tilburg University, Center for Economic Research.
    2. Guo, Pengfei & Sun, Wei & Wang, Yulan, 2011. "Equilibrium and optimal strategies to join a queue with partial information on service times," European Journal of Operational Research, Elsevier, vol. 214(2), pages 284-297, October.
    3. Yu, Guodong & Liu, Aijun & Zhang, Jianghua & Sun, Huiping, 2021. "Optimal operations planning of electric autonomous vehicles via asynchronous learning in ride-hailing systems," Omega, Elsevier, vol. 103(C).
    4. Evsey Morozov & Michele Pagano & Irina Peshkova & Alexander Rumyantsev, 2020. "Sensitivity Analysis and Simulation of a Multiserver Queueing System with Mixed Service Time Distribution," Mathematics, MDPI, vol. 8(8), pages 1-16, August.
    5. Muhammad El-Taha & Bacel Maddah, 2006. "Allocation of Service Time in a Multiserver System," Management Science, INFORMS, vol. 52(4), pages 623-637, April.

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