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Single-Server Queues with Service Time Dependent on Waiting Time

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  • M. Posner

    (University of Toronto, Toronto, Ontario, Canada)

Abstract

This paper discusses a class of queuing models in which the service time of a customer at a single-server facility is dependent on the amount of time that customer has spent queuing for service. A complete investigation is carried out in the particular case of exponential service times with the parameter having a step-function dependency on the waiting time. The stationary waiting-time distribution is investigated for the queue discipline by which customers are served in order of arrival. This class of model is particularly suited for applications wherein customer or item deterioration occurs during waiting or where the server wishes to provide a more appropriate level of service to counter the negative effects of customer impatience and loss of good will.

Suggested Citation

  • M. Posner, 1973. "Single-Server Queues with Service Time Dependent on Waiting Time," Operations Research, INFORMS, vol. 21(2), pages 610-616, April.
    • Handle: RePEc:inm:oropre:v:21:y:1973:i:2:p:610-616
    DOI: 10.1287/opre.21.2.610
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    Cited by:

    1. Caulkins, Jonathan P., 2010. "Might randomization in queue discipline be useful when waiting cost is a concave function of waiting time?," Socio-Economic Planning Sciences, Elsevier, vol. 44(1), pages 19-24, March.
    2. Yoshiaki Inoue & Onno Boxma & David Perry & Shelley Zacks, 2018. "Analysis of $$\hbox {M}^{\mathrm {x}}/\hbox {G}/1$$ M x / G / 1 queues with impatient customers," Queueing Systems: Theory and Applications, Springer, vol. 89(3), pages 303-350, August.
    3. O. J. Boxma & M. R. H. Mandjes, 2022. "Queueing and risk models with dependencies," Queueing Systems: Theory and Applications, Springer, vol. 102(1), pages 69-86, October.
    4. D’Auria, Bernardo & Adan, Ivo J.B.F. & Bekker, René & Kulkarni, Vidyadhar, 2022. "An M/M/c queue with queueing-time dependent service rates," European Journal of Operational Research, Elsevier, vol. 299(2), pages 566-579.
    5. G. M. Koole & B. F. Nielsen & T. B. Nielsen, 2012. "First in Line Waiting Times as a Tool for Analysing Queueing Systems," Operations Research, INFORMS, vol. 60(5), pages 1258-1266, October.

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