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Approximations of the Mean Waiting Time in an M / G / s Queueing System

Author

Listed:
  • O. J. Boxma

    (Rijksunwersiteit Utrecht, Utrecht, The Netherlands)

  • J. W. Cohen

    (Rijksunwersiteit Utrecht, Utrecht, The Netherlands)

  • N. Huffels

    (Rijksunwersiteit Utrecht, Utrecht, The Netherlands)

Abstract

This paper considers the problem of obtaining approximate expressions for the first moment W Gs of the stationary waiting time distribution in an M / G / s queueing system. Special attention is paid to the case G ≡ D , i.e., constant service times. Most known approximations are in fact heavy traffic approximations which have rather large relative errors in the light traffic case. In the present study both the light traffic and heavy traffic behavior of W Gs ( W Ds ) are taken into account. In order to obtain mean waiting time approximations it appears to be useful to introduce a quantity (the “normed cooperation coefficient”) which is inversely proportional to W Gs and which is in some sense a measure for the “cooperation” between the servers of the service facility. A part of the paper is devoted to the analysis of this normed cooperation coefficient.

Suggested Citation

  • O. J. Boxma & J. W. Cohen & N. Huffels, 1979. "Approximations of the Mean Waiting Time in an M / G / s Queueing System," Operations Research, INFORMS, vol. 27(6), pages 1115-1127, December.
    • Handle: RePEc:inm:oropre:v:27:y:1979:i:6:p:1115-1127
    DOI: 10.1287/opre.27.6.1115
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    Cited by:

    1. Venkateshan, Prahalad & Mathur, Kamlesh & Ballou, Ronald H., 2010. "Locating and staffing service centers under service level constraints," European Journal of Operational Research, Elsevier, vol. 201(1), pages 55-70, February.
    2. Wei Xiong & Tayfur Altiok, 2009. "An approximation for multi-server queues with deterministic reneging times," Annals of Operations Research, Springer, vol. 172(1), pages 143-151, November.
    3. Tijms, H.C., 1988. "Numerical methods for queueing models," Serie Research Memoranda 0043, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    4. John Lees-Miller, 2016. "Minimising average passenger waiting time in personal rapid transit systems," Annals of Operations Research, Springer, vol. 236(2), pages 405-424, January.
    5. Tianhu Deng & Ying‐Ju Chen & Zuo‐Jun Max Shen, 2015. "Optimal pricing and scheduling control of product shipping," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(3), pages 215-227, April.
    6. Anatoly Nazarov & Alexander Moiseev & Svetlana Moiseeva, 2021. "Mathematical Model of Call Center in the Form of Multi-Server Queueing System," Mathematics, MDPI, vol. 9(22), pages 1-13, November.
    7. John D. Lees-Miller, 2016. "Minimising average passenger waiting time in personal rapid transit systems," Annals of Operations Research, Springer, vol. 236(2), pages 405-424, January.

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