Analysis of the asymmetric shortest queue problem with threshold jockeying

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    In this paper we study a system consisting of two parallel servers with possibly different service rates. Jobs arrive according to a Poisson stream and generate an exponentially distributed workload. On arrival a job joins the shortest queue and in case both queues have equal lengths, he joins the first queue with probability 1 - a and the second one with probability a, where a is an arbitrary number between 0 and 1. If the difference between the lengths of both queues exceeds some threshold value T, then one job switches from the longest to the shortest queue. It is shown that the equilibrium probabilities of the queue lengths satisfy a product form for states where the longer queue exceeds the threshold value T. Furthermore, it is shown that for a sensible partitioning of the state space the matrix-geometrie approach essentially leads to the same results.
    Original languageEnglish
    Pages (from-to)615-627
    Number of pages7
    JournalCommunications in Statistics. Part C, Stochastic Models
    Issue number4
    Publication statusPublished - 1991

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