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On the longest service time in a busy period of the M[+45 degree rule]G[+45 degree rule]1 queue

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  • Boxma, O. J.

Abstract

This paper considers the supremum m of the service times of the customers served in a busy period of the M[+45 degree rule]G[+45 degree rule]1 queueing system. An implicit expression for the distribution m(w) of m is derived. This expression leads to some bounds for m(w), while it can also be used to obtain numerical results. The tail behaviour of m(w) is investigated, too. The results are particularly useful in the analysis of a class of tandem queueing systems.

Suggested Citation

  • Boxma, O. J., 1978. "On the longest service time in a busy period of the M[+45 degree rule]G[+45 degree rule]1 queue," Stochastic Processes and their Applications, Elsevier, vol. 8(1), pages 93-100, November.
    • Handle: RePEc:eee:spapps:v:8:y:1978:i:1:p:93-100
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    Cited by:

    1. Kamphorst, Bart & Zwart, Bert, 2019. "Uniform asymptotics for compound Poisson processes with regularly varying jumps and vanishing drift," Stochastic Processes and their Applications, Elsevier, vol. 129(2), pages 572-603.
    2. Gromoll, H. Christian & Terwilliger, Bryce & Zwart, Bert, 2020. "Heavy traffic limit for the workload plateau process in a tandem queue with identical service times," Stochastic Processes and their Applications, Elsevier, vol. 130(3), pages 1435-1460.

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