Asymptotic analysis for closed multiclass queueing networks in critical usage

Jie Wang, Keith W. Ross

    Research output: Contribution to journalArticlepeer-review


    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
    Issue number1-2
    StatePublished - Mar 1994


    • Queueing networks
    • asymptotic analysis
    • critical usage

    ASJC Scopus subject areas

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


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