The M/G/1 processor sharing queue as the almost sure limit of feedback queues

J.A.C. Resing, G. Hooghiemstra, M.S. Keane

    Research output: Contribution to journalArticleAcademicpeer-review

    Abstract

    In the paper a probabilistic coupling between the M/G/1 processor sharing queue and the M/M/1 feedback queue, with general feedback probabilities, is established. This coupling is then used to prove the almost sure convergence of sojourn times in the feedback model to sojourn times in the M/G/1 processor sharing queue. Using the theory of regenerative processes it follows that for stable queues the stationary distribution of the sojourn time in the feedback model converges in law to the corresponding distribution in the processor sharing model. The results do not depend on Poisson arrival times, but are also valid for general arrival processes.
    Original languageEnglish
    Pages (from-to)913-918
    Number of pages6
    JournalJournal of Applied Probability
    Volume27
    Issue number4
    DOIs
    Publication statusPublished - 1990

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