Two queues with alternating service and switching times

O.J. Boxma, W.P. Groenendijk

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    Abstract

    tlThis paper is concerned with a system of two queues, attended by a single server who alternately serves one customer of each queue (if not empty). The server experiences switching times in his transition from one queue to the other. It is shown that the joint stationary queue-Iength distribution, at the instants at which the server becomes available to a queue, can be determined via transformation to a Riemann boundary value problem. The latter problem can be completely solved for general service- and switching-time distributions. The stationary distributions of the waiting times at both queues, and of the cycle times of the server, are also derived. The results obtained, and in particular the extensive numerical data for moments of waiting times and cycle times, yield insight into the behavior of more general cyclic-service modeIs. Such modeIs are frequenUy used to analyse polling systems.
    Original languageEnglish
    Title of host publicationQueueing Theory and its Applications (Liber Amicorum for J.W. Cohen)
    EditorsO.J. Boxma, R. Syski
    Place of PublicationAmsterdam
    PublisherNorth-Holland Publishing Company
    Pages261-282
    ISBN (Print)0444-70497-3
    Publication statusPublished - 1988

    Publication series

    NameCWI Monographs
    Volume7

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