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Technical Note—The Expected Remaining Service Time in a Single Server Queue

Author

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  • Demetrios Fakinos

    (University of Essex, Essex, England)

Abstract

For the G / G /1 queueing system, let ( p n ), n = 0, 1, 2, …, and ( r n ), n = 0, 1, 2, … be the limiting probability distributions of the number of customers in the system, when the system is considered “at any time” and when it is considered at arrival epochs respectively. Also let b n ( n = 1, 2, …) be the mean remaining duration of the service in progress at the epoch of an arrival which finds n customers in the system. In this note, a relation between the sequences ( p n ), ( r n ) and ( b n ) is given and it is used to provide alternative derivations for two well-known results in the theory of queues.

Suggested Citation

  • Demetrios Fakinos, 1982. "Technical Note—The Expected Remaining Service Time in a Single Server Queue," Operations Research, INFORMS, vol. 30(5), pages 1014-1018, October.
    • Handle: RePEc:inm:oropre:v:30:y:1982:i:5:p:1014-1018
    DOI: 10.1287/opre.30.5.1014
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    Cited by:

    1. Oz, Binyamin & Adan, Ivo & Haviv, Moshe, 2019. "The Mn/Gn/1 queue with vacations and exhaustive service," European Journal of Operational Research, Elsevier, vol. 277(3), pages 945-952.
    2. Antonis Economou & Athanasia Manou, 2022. "A probabilistic approach for the analysis of the $$M_n/G/1$$ M n / G / 1 queue," Annals of Operations Research, Springer, vol. 317(1), pages 19-27, October.

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