A Note on the GI/GI/∞ System with Identical Service and Interarrival-Time Distributions

E.A. van Doorn, A.A. Jagers

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    Abstract

    We study the stationary distribution of the number of busy servers in a GI/GI/∞ system in which the service-time distribution is identical to the interarrival-time distribution, and obtain several representations for the variance. As a result we can verify an expression for the variance, conjectured by Rajaratnam and Takawira (IEEE Trans. Vehicular Technol. 50 (2001) 954–970), when the common distribution of interarrival and service times is a gamma distribution.
    Original languageEnglish
    Place of PublicationEnschede
    PublisherUniversity of Twente, Department of Applied Mathematics
    Number of pages8
    Publication statusPublished - 2002

    Publication series

    NameMemorandum Faculty of Mathematical Sciences
    PublisherUniversity of Twente, Department of Applied Mathematics
    No.1664
    ISSN (Print)0169-2690

    Keywords

    • MSC-90B22
    • MSC-44A15
    • MSC-68M20
    • EWI-3484
    • MSC-60K25
    • METIS-209230
    • IR-65850

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