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On a Generalized M / G /1 Queuing Process in Which the First Customer of Each Busy Period Receives Exceptional Service

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  • Peter D. Welch

    (IBM Watson Research Center, Yorktown Heights, New York)

Abstract

The following generalization of the M / G /1 queue is considered. If a customer arrives when the server is busy, his service time has a distribution function, G b ( x ); while if he arrives when the server is idle, his service time has a different distribution function, G e ( x ). Results are obtained that characterize the transient and asymptotic distributions of the queue size, waiting time, and waiting-plus-service time. These results are then applied to the special case of a queue with a single service time distribution function, but with additional independent delay times that have one distribution function for the customers arriving when the server is idle and another for the customers arriving when the server is busy.

Suggested Citation

  • Peter D. Welch, 1964. "On a Generalized M / G /1 Queuing Process in Which the First Customer of Each Busy Period Receives Exceptional Service," Operations Research, INFORMS, vol. 12(5), pages 736-752, October.
    • Handle: RePEc:inm:oropre:v:12:y:1964:i:5:p:736-752
    DOI: 10.1287/opre.12.5.736
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    Cited by:

    1. Delasay, Mohammad & Ingolfsson, Armann & Kolfal, Bora & Schultz, Kenneth, 2019. "Load effect on service times," European Journal of Operational Research, Elsevier, vol. 279(3), pages 673-686.
    2. Meier, Christian & Li, Lingfei & Zhang, Gongqiu, 2023. "Simulation of multidimensional diffusions with sticky boundaries via Markov chain approximation," European Journal of Operational Research, Elsevier, vol. 305(3), pages 1292-1308.
    3. uit het Broek, Michiel A.J. & Van der Heide, Gerlach & Van Foreest, Nicky D., 2020. "Energy-saving policies for temperature-controlled production systems with state-dependent setup times and costs," European Journal of Operational Research, Elsevier, vol. 287(3), pages 916-928.
    4. Lillo, Rosa E., 2005. "Ergodicity and analysis of the process describing the system state in polling systems with two queues," European Journal of Operational Research, Elsevier, vol. 167(1), pages 144-162, November.
    5. Balcıõglu, Barış & Varol, Yãgız, 2022. "Fair and profitable: How pricing and lead-time quotation policies can help," European Journal of Operational Research, Elsevier, vol. 299(3), pages 977-986.
    6. Bozer, Yavuz A. & Hsieh, Ying-Jiun, 2004. "Expected waiting times at loading stations in discrete-space closed-loop conveyors," European Journal of Operational Research, Elsevier, vol. 155(2), pages 516-532, June.

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