Rate of convergence to stationarity of the system $M/M/N/N+R$

Erik A. van Doorn

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    Abstract

    We consider the $M/M/N/N+R$ service system, characterized by $N$ servers, $R$ waiting positions, Poisson arrivals and exponential service times. We discuss representations and bounds for the rate of convergence to stationarity of the number of customers in the system, and study its behaviour as a function of $R$, $N$ and the arrival rate $\lambda$, allowing $\lambda$ to be a function of $N.$
    Original languageUndefined
    Place of PublicationEnschede
    PublisherUniversity of Twente, Department of Applied Mathematics
    Number of pages18
    Publication statusPublished - Jul 2010

    Publication series

    NameMemorandum / Department of Applied Mathematics
    PublisherUniversity of Twente, Department of Applied Mathematics
    No.1923
    ISSN (Print)1874-4850
    ISSN (Electronic)1874-4850

    Keywords

    • EWI-18166
    • MSC-90B22
    • METIS-270921
    • MSC-60K25
    • IR-72428

    Cite this

    van Doorn, E. A. (2010). Rate of convergence to stationarity of the system $M/M/N/N+R$. (Memorandum / Department of Applied Mathematics; No. 1923). Enschede: University of Twente, Department of Applied Mathematics.