On the Optimal-Loop Control Policy for Deterministic and Exponential Polling Systems

D.A. van der Laan, B. Gaujal, A. Hordijk

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    Abstract

    In this article, we consider deterministic (both fluid and discrete) polling systems with N queues with infinite buffers and we show how to compute the best polling sequence (minimizing the average total workload). With two queues, we show that the best polling sequence is always periodic when the system is stable and forms a regular sequence. The fraction of time spent by the server in the first queue is highly noncontinuous in the parameters of the system (arrival rate and service rate) and shows a fractal behavior. Moreover, convexity properties are shown and are used in a generalization of the computation of the optimal control policy (in open loop) for the stochastic exponential case. © 2007 Cambridge University Press.
    Original languageEnglish
    Pages (from-to)157-187
    JournalProbability in the Engineering and Informational Sciences
    Volume21
    Issue number2
    DOIs
    Publication statusPublished - 2007

    Bibliographical note

    ISSN 0269-9648

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