The M/G/1 queue with processor sharing and its relation to a feedback queue

J.L. Berg, van den, O.J. Boxma

    Research output: Contribution to journalArticleAcademicpeer-review

    48 Citations (Scopus)


    The central model of this paper is anM/M/1 queue with a general probabilistic feedback mechanism. When a customer completes his ith service, he departs from the system with probability 1–p(i) and he cycles back with probabilityp(i). The mean service time of each customer is the same for each cycle. We determine the joint distribution of the successive sojourn times of a tagged customer at his loops through the system. Subsequently we let the mean service time at each loop shrink to zero and the feedback probabilities approach one in such a way that the mean total required service time remains constant. The behaviour of the feedback queue then approaches that of anM/G/1 processor sharing queue, different choices of the feedback probabilities leading to different service time distributions in the processor sharing model. This is exploited to analyse the sojourn time distribution in theM/G/1 queue with processor sharing. Some variants are also considered, viz., anM/M/1 feedback queue with additional customers who are always present, and anM/G/1 processor sharing queue with feedback.
    Original languageEnglish
    Pages (from-to)365-401
    Number of pages37
    JournalQueueing Systems: Theory and Applications
    Issue number4
    Publication statusPublished - 1991


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