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Note on the service time in an M/G/1 queue with bounded workload

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  • Brill, Percy H.

Abstract

We consider a workload-barrier M/G/1 queue where service times that overshoot the barrier are truncated. We derive the pdf and expected value of an arbitrary service, the expected number served in a busy period, and related quantities. Examples are given.

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  • Brill, Percy H., 2015. "Note on the service time in an M/G/1 queue with bounded workload," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 162-169.
    • Handle: RePEc:eee:stapro:v:96:y:2015:i:c:p:162-169
    DOI: 10.1016/j.spl.2014.09.019
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    References listed on IDEAS

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    1. Brill, Percy H. & Yu, Kaiqi, 2011. "Analysis of risk models using a level crossing technique," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 298-309.
    2. Percy H. Brill, 2008. "Level Crossing Methods in Stochastic Models," International Series in Operations Research and Management Science, Springer, number 978-0-387-09421-2, April.
    3. Ronald W. Wolff, 1982. "Poisson Arrivals See Time Averages," Operations Research, INFORMS, vol. 30(2), pages 223-231, April.
    4. Gerber, Hans U. & Shiu, Elias S. W., 1997. "The joint distribution of the time of ruin, the surplus immediately before ruin, and the deficit at ruin," Insurance: Mathematics and Economics, Elsevier, vol. 21(2), pages 129-137, November.
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    Cited by:

    1. Brill, P.H. & Huang, M.L. & Hlynka, M., 2020. "On the service time in a workload-barrier M/G/1 queue with accepted and blocked customers," European Journal of Operational Research, Elsevier, vol. 283(1), pages 235-243.

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