Analysis of the asymmetric shortest queue problem : part 2: numerical analysis

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    Abstract

    In this paper we study a system consisting of two parallel servers with 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 q and the second one with probability 1-q, where q is an arbitrary number between 0 and 1. In a previous paper we showed that the equilibrium distribution of the lengths of the two queues can be represented by an infinite sum of product form solutions by using an elementary compensation procedure. The main purpose of the present paper is to show that the product form representation leads to a numerically highly attractive algorithm. Essentially, the method exploits the convergence properties of the series of product forms. Because of the fast convergence an efficient method is obtained with upper and lower bounds for the exact solution. For states further away from the origin the convergence is faster. This aspect is also exploited in the paper.
    Original languageEnglish
    Place of PublicationEindhoven
    PublisherTechnische Universiteit Eindhoven
    Number of pages34
    Publication statusPublished - 1990

    Publication series

    NameMemorandum COSOR
    Volume9003
    ISSN (Print)0926-4493

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