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Article

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

1
Department of Applied Mathematics, Vologda State University, 160000 Vologda, Russia
2
Institute of Informatics Problems of the Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, 119333 Moscow, Russia
3
Vologda Research Center of the Russian Academy of Sciences, 160014 Vologda, Russia
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(8), 678; https://doi.org/10.3390/math7080678
Received: 29 June 2019 / Revised: 22 July 2019 / Accepted: 28 July 2019 / Published: 30 July 2019
(This article belongs to the Special Issue Stochastic Processes: Theory and Applications)
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. View Full-Text
Keywords: queueing systems; rate of convergence; non-stationary; Markovian queueing models; limiting characteristics queueing systems; rate of convergence; non-stationary; Markovian queueing models; limiting characteristics
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MDPI and ACS Style

Satin, Y.; Zeifman, A.; Kryukova, A. On the Rate of Convergence and Limiting Characteristics for a Nonstationary Queueing Model. Mathematics 2019, 7, 678. https://doi.org/10.3390/math7080678

AMA Style

Satin Y, Zeifman A, Kryukova A. On the Rate of Convergence and Limiting Characteristics for a Nonstationary Queueing Model. Mathematics. 2019; 7(8):678. https://doi.org/10.3390/math7080678

Chicago/Turabian Style

Satin, Yacov, Alexander Zeifman, and Anastasia Kryukova. 2019. "On the Rate of Convergence and Limiting Characteristics for a Nonstationary Queueing Model" Mathematics 7, no. 8: 678. https://doi.org/10.3390/math7080678

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