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Convergence Bounds for Limited Processor Sharing Queue with Impatience for Analyzing Non-Stationary File Transfer in Wireless Network

Author

Listed:
  • Irina Kochetkova

    (Applied Probability and Informatics Department, Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St., 117198 Moscow, Russia
    Institute of Informatics Problems, Federal Research Center “Computer Sciences and Control” of the Russian Academy of Sciences, 44-2 Vavilova St., 119333 Moscow, Russia)

  • Yacov Satin

    (Department of Applied Mathematics, Vologda State University, Lenina 15, 160000 Vologda, Russia)

  • Ivan Kovalev

    (Department of Applied Mathematics, Vologda State University, Lenina 15, 160000 Vologda, Russia)

  • Elena Makeeva

    (Applied Probability and Informatics Department, Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St., 117198 Moscow, Russia)

  • Alexander Chursin

    (Applied Probability and Informatics Department, Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St., 117198 Moscow, Russia)

  • Alexander Zeifman

    (Institute of Informatics Problems, Federal Research Center “Computer Sciences and Control” of the Russian Academy of Sciences, 44-2 Vavilova St., 119333 Moscow, Russia
    Department of Applied Mathematics, Vologda State University, Lenina 15, 160000 Vologda, Russia)

Abstract

The data transmission in wireless networks is usually analyzed under the assumption of non-stationary rates. Nevertheless, they strictly depend on the time of day, that is, the intensity of arrival and daily workload profiles confirm this fact. In this article, we consider the process of downloading a file within a single network segment and unsteady speeds—for arrivals, file sizes, and losses due to impatience. To simulate the scenario, a queuing system with elastic traffic with non-stationary intensity is used. Formulas are given for the main characteristics of the model: the probability of blocking a new user, the average number of users in service, and the queue. A method for calculating the boundaries of convergence of the model is proposed, which is based on the logarithmic norm of linear operators. The boundaries of the rate of convergence of the main limiting characteristics of the queue length process were also established. For clarity of the influence of the parameters, a numerical analysis was carried out and presented.

Suggested Citation

  • Irina Kochetkova & Yacov Satin & Ivan Kovalev & Elena Makeeva & Alexander Chursin & Alexander Zeifman, 2021. "Convergence Bounds for Limited Processor Sharing Queue with Impatience for Analyzing Non-Stationary File Transfer in Wireless Network," Mathematics, MDPI, vol. 10(1), pages 1-16, December.
    • Handle: RePEc:gam:jmathe:v:10:y:2021:i:1:p:30-:d:708613
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