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Bounds for Some Generalizations of the GI / G /1 Queue

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  • K. T. Marshall

    (Bell Telephone Laboratories, Incorporated, Holmdel, New Jersey)

Abstract

Expressions are derived for the expected number and expected wait in queue for the following generalizations of the GI / G /1 queue: (1) arrivals in batches of random size, (2) service in batches of fixed size, (3) queues with added delay for the first customer in a busy period. These expressions contain the mean and variance of the idle time distribution. Results on the idle period moments, which were derived by the author in a previous paper, are used to obtain bounds for the expected wait and expected number in queue under two different assumptions on A ( t ), the interarrival time distribution. As an example of (3) we mention the queue where the server, once he becomes idle, does not restart until m customers have arrived (called the GI m / G /1 queue). Such a queue arises when one considers a class of optimization problems in single server queues.

Suggested Citation

  • K. T. Marshall, 1968. "Bounds for Some Generalizations of the GI / G /1 Queue," Operations Research, INFORMS, vol. 16(4), pages 841-848, August.
    • Handle: RePEc:inm:oropre:v:16:y:1968:i:4:p:841-848
    DOI: 10.1287/opre.16.4.841
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    Cited by:

    1. Tielemans, Peter F. J. & Kuik, Roelof, 1996. "An exploration of models that minimize leadtime through batching of arrived orders," European Journal of Operational Research, Elsevier, vol. 95(2), pages 374-389, December.

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