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On the Rate of Convergence and Limiting Characteristics for a Nonstationary Queueing Model

Author

Listed:
  • Yacov Satin

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

  • Alexander Zeifman

    (Department of Applied Mathematics, Vologda State University, 160000 Vologda, Russia
    Institute of Informatics Problems of the Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, 119333 Moscow, Russia
    Vologda Research Center of the Russian Academy of Sciences, 160014 Vologda, Russia)

  • Anastasia Kryukova

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

Abstract

Consideration is given to the nonstationary analogue of M / M / 1 queueing model in which the service happens only in batches of size 2, with the arrival rate λ ( t ) and the service rate μ ( t ) . One proposes a new and simple method for the study of the queue-length process. The main probability characteristics of the queue-length process are computed. A numerical example is provided.

Suggested Citation

  • Yacov Satin & Alexander Zeifman & Anastasia Kryukova, 2019. "On the Rate of Convergence and Limiting Characteristics for a Nonstationary Queueing Model," Mathematics, MDPI, vol. 7(8), pages 1-11, July.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:8:p:678-:d:252854
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    References listed on IDEAS

    as
    1. Zeifman, A. & Satin, Y. & Kiseleva, K. & Korolev, V. & Panfilova, T., 2019. "On limiting characteristics for a non-stationary two-processor heterogeneous system," Applied Mathematics and Computation, Elsevier, vol. 351(C), pages 48-65.
    2. Zeifman, A.I. & Korolev, V.Yu., 2014. "On perturbation bounds for continuous-time Markov chains," Statistics & Probability Letters, Elsevier, vol. 88(C), pages 66-72.
    3. Schwarz, Justus Arne & Selinka, Gregor & Stolletz, Raik, 2016. "Performance analysis of time-dependent queueing systems: Survey and classification," Omega, Elsevier, vol. 63(C), pages 170-189.
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