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 publicationOperations Research Proceedings 1987 (Papers of the 16th Annual Meeting of DGOR, in cooperation with NSOR, Veldhoven, The Netherlands, September 23-25, 1987)
    EditorsH. Schellhaas, P. Beek, van, H. Isermann, R. Schmidt, M. Zijlstra
    Place of PublicationBerlin
    PublisherSpringer
    Pages478
    ISBN (Print)3-540-19365-0
    DOIs
    Publication statusPublished - 1988

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