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

Erik A. van Doorn, Alexander I. Zeifman

    Research output: Book/ReportReportProfessional

    18 Citations (Scopus)
    58 Downloads (Pure)

    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
    Place of PublicationEnschede
    PublisherUniversity of Twente, Department of Applied Mathematics
    Number of pages16
    Publication statusPublished - Jul 2009

    Publication series

    NameMemorandum / Department of Applied Mathematics
    PublisherUniversity of Twente, Department of Applied Mathematics
    No.1901
    ISSN (Print)1874-4850
    ISSN (Electronic)1874-4850

    Keywords

    • MSC-60K25
    • MSC-90B22
    • METIS-263919
    • IR-67521
    • Charlier polynomials
    • Rate of convergence
    • Total variation distance
    • EWI-15695

    Cite this

    van Doorn, E. A., & Zeifman, A. I. (2009). On the speed of convergence to stationarity of the Erlang loss system. (Memorandum / Department of Applied Mathematics; No. 1901). Enschede: University of Twente, Department of Applied Mathematics.