On the speed of convergence to stationarity of the Erlang loss system

Erik A. van Doorn, Alexander I. Zeifman

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    Abstract

    We consider the Erlang loss system, characterized by $N$ servers, Poisson arrivals and exponential service times, and allow the arrival rate to be a function of $N.$ We discuss representations and bounds for the rate of convergence to stationarity of the number of customers in the system, and display some bounds for the total variation distance between the time-dependent and stationary distributions. We also pay attention to time-dependent rates.
    Original languageUndefined
    Article number10.1007/s11134-009-9134-9
    Pages (from-to)241-252
    Number of pages12
    JournalQueueing systems
    Volume63
    Issue number1-4
    DOIs
    Publication statusPublished - Jul 2009

    Keywords

    • EWI-17002
    • Rate of convergence
    • IR-68868
    • Charlier polynomials
    • METIS-264240
    • MSC-90B22
    • MSC-60K25
    • Total variation distance

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