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The queue GI/G/1: Finite moments of the cycle variables and uniform rates of convergence

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  • Thorisson, Hermann

Abstract

We study the classical single server queue and establish finite geometric moments and [phi] moments of the cycle variables. Here [phi](x) = xn[phi]0(x) where n is integer and [phi]0 is concave. More generally, we consider systems with different initial conditions and prove moment and stochastic domination results for the delay variables. This, together with the general results of [5], yields ergodic results for the time and customer dependent processes.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:19:y:1985:i:1:p:85-99
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    Cited by:

    1. Irina Peshkova & Evsey Morozov & Michele Pagano, 2024. "Regenerative Analysis and Approximation of Queueing Systems with Superposed Input Processes," Mathematics, MDPI, vol. 12(14), pages 1-22, July.
    2. L. Dai, 1999. "Effective Bandwidths and Performance Bounds in High-Speed Communication Systems," Journal of Optimization Theory and Applications, Springer, vol. 100(3), pages 549-574, March.
    3. Alexander Veretennikov, 2023. "On Positive Recurrence of the M n / GI /1/ ∞ Model," Mathematics, MDPI, vol. 11(21), pages 1-18, November.

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