Waiting times in polling systems with Markovian server routing

O.J. Boxma, J.A. Weststrate

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


    This study is devoted to a queueing analysis of polling systems with a probabilistic server routing mechanism. A single server serves a number of queues, switching between the queues according to a discrete time parameter Markov chain. The switchover times between queues are nonneghgible. It is observed that the total amount of work in this Markovian polling system can be decomposed into two independent parts, viz., (i) the total amount of work in the corresponding system without switchover times and (ii) the amount of work in the system at some epoch covered by a switching interval. This work decomposition leads to a pseudoconservation law for mean waiting times, i.e., an exact expression for a weighted sum of the mean waiting times at all queues. The results generalize known results for polling systems with strictly cyclic service.
    Original languageEnglish
    Title of host publicationMessung, Modellierung und Bewertung von Rechensystemen und Netzen
    Subtitle of host publication5. GI/ITG-Fachtagung Braunschweig, 26.–28. September 1989, Proceedings
    EditorsG. Stiege, J.S. Lie
    Place of PublicationBerlin
    ISBN (Electronic)978-3-642-75079-3
    ISBN (Print)3-540-51713-8, 978-3-540-51713-9
    Publication statusPublished - 1989

    Publication series

    ISSN (Print)0343-3005


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