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On Positive Recurrence of the M n / GI /1/ ∞ Model

Author

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  • Alexander Veretennikov

    (Kharkevich Institute for Information Transmission Problems, Moscow 127051, Russia)

Abstract

Positive recurrence for a single-server queueing system is established under generalized service intensity conditions, without the assumption of the existence of a service density distribution function, but with a certain integral type lower bound as a sufficient condition. Positive recurrence implies the existence of the invariant distribution and a guaranteed slow convergence to it in the total variation metric.

Suggested Citation

  • Alexander Veretennikov, 2023. "On Positive Recurrence of the M n / GI /1/ ∞ Model," Mathematics, MDPI, vol. 11(21), pages 1-18, November.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:21:p:4514-:d:1272571
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    References listed on IDEAS

    as
    1. Thorisson, Hermann, 1985. "The queue GI/G/1: Finite moments of the cycle variables and uniform rates of convergence," Stochastic Processes and their Applications, Elsevier, vol. 19(1), pages 85-99, February.
    2. Alexander Veretennikov, 2022. "An open problem about the rate of convergence in Erlang-Sevastyanov’s model," Queueing Systems: Theory and Applications, Springer, vol. 100(3), pages 357-359, April.
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