Sojourn times in feedback queues

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

    Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

    Abstract

    In many modern computer-communication systems, a job may be processed in several phases, or a job may generate new tasks. Such phenomena can be modeled by service systems with feedback. In the queueing literature, attention has been mainly devoted to single-service queues with so-called Bernoulli feedback: when a customer (task) completes his service, he departs from the system with probability l-p and is fed back with probability p. In the present study a more general feedback mechanism is allowed: when a customer completes his i-th service, he departs from the system with probability l-p(i) and is fed back with probability p(i). We mainly restrict ourselves to the case of a Poisson external arrival process and identically, negative exponentially, distributed service times at each service. The resulting queueing model has the property that the joint queue-length distribution of type-i customers, i=1,2,⋯, is of product-form type. This property is exploited to analyse the sojourn-time process.
    Original languageEnglish
    Title of host publicationDGOR/NSOR
    Subtitle of host publicationPapers of the 16th Annual Meeting of DGOR in Cooperation with NSOR/Vorträge der 16. Jahrestagung der DGOR zusammen mit der NSOR
    EditorsH. Schellhaas, P. van Beek, H. Isermann
    Place of PublicationBerlin
    PublisherSpringer
    Pages478-478
    ISBN (Electronic)978-3-642-73778-7
    ISBN (Print)978-3-540-19365-4
    DOIs
    Publication statusPublished - 1989
    Event16th Annual Meeting of DGOR - Veldhoven, Netherlands
    Duration: 23 Sep 198725 Sep 1987

    Publication series

    NameOperations Research Proceedings (ORP)
    Volume1987

    Conference

    Conference16th Annual Meeting of DGOR
    Country/TerritoryNetherlands
    CityVeldhoven
    Period23/09/8725/09/87

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