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Analysis of the GI/PH/∞ system with high-rate arrivals

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Abstract

The work presents an analysis of infinite-server queueing systems with renewal arrival process and phase-type services. Analysis was carried out using the N-dimensional Markov processes. The study was implemented in the asymptotic condition of high intensity of arrivals. It has been shown that, under these conditions, the stationary distribution of the number of customers in the system is Gaussian, and the parameters of this distribution were received. A prelimit analytical expression has also been derived for the dispersion of the number of customers in the system, and a numerical comparison has been carried out with asymptotic values that allow one to determine the domain of applicability of asymptotic results.

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Authors and Affiliations

  1. Tomsk State National Research University, pr. Lenina 36, Tomsk, 634050, Russia

    A. A. Nazarov & A. N. Moiseev

Authors
  1. A. A. Nazarov
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  2. A. N. Moiseev
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Correspondence to A. A. Nazarov.

Additional information

Original Russian Text © A.A. Nazarov, A.N. Moiseev, 2015, published in Avtomatika i Vychislitel’naya Tekhnika, 2015, No. 6, pp. 14–27.

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Nazarov, A.A., Moiseev, A.N. Analysis of the GI/PH/∞ system with high-rate arrivals. Aut. Control Comp. Sci. 49, 328–339 (2015). https://doi.org/10.3103/S0146411615060085

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  • DOI: https://doi.org/10.3103/S0146411615060085

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