Asymptotic analysis for closed multiclass queueing networks in critical usage

Jie Wang, Keith Ross

    Research output: Contribution to journalArticle

    Abstract

    We consider a class of closed multiclass queueing networks containing First-Come-First-Serve (FCFS) and Infinite Server (IS) stations. These networks have a productform solution for their equilibrium probabilities. We study these networks in an asymptotic regime for which the number of customers and the service rates at the FCFS stations go to infinity with the same order. We assume that the regime is in critical usage, whereby the utilizations of the FCFS servers slowly approach one. The asymptotic distribution of the normalized queue lengths is shown to be in many cases a truncated multivariate normal distribution. Traffic conditions for which the normalized queue lengths are almost asymptotically independent are determined. Asymptotic expansions of utilizations and expected queue lengths are presented. We show through an example how to obtain asymptotic expansions of performance measures when the networks are in mixed usage and how to apply the results to networks with finite data.

    Original languageEnglish (US)
    Pages (from-to)167-191
    Number of pages25
    JournalQueueing Systems
    Volume16
    Issue number1-2
    DOIs
    StatePublished - Mar 1994

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    Queueing networks
    Asymptotic analysis
    Servers
    Normal distribution
    Queue
    Asymptotic expansion

    Keywords

    • asymptotic analysis
    • critical usage
    • Queueing networks

    ASJC Scopus subject areas

    • Management Science and Operations Research
    • Computer Science Applications
    • Computational Theory and Mathematics

    Cite this

    Asymptotic analysis for closed multiclass queueing networks in critical usage. / Wang, Jie; Ross, Keith.

    In: Queueing Systems, Vol. 16, No. 1-2, 03.1994, p. 167-191.

    Research output: Contribution to journalArticle

    Wang, Jie ; Ross, Keith. / Asymptotic analysis for closed multiclass queueing networks in critical usage. In: Queueing Systems. 1994 ; Vol. 16, No. 1-2. pp. 167-191.
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