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Avtomatika i Telemekhanika, 2022, Issue 1, Pages 113–129
DOI: https://doi.org/10.31857/S000523102201007X (Mi at15891) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Stochastic Systems

On estimates of the mean queue length for single-channel queuing systems in terms of statistical unconditional second-order moments of the modified arrival flow

B.J. Likhttsindera, I. A. Blatova, E. V. Kitaevab

a Povolzhskiy State University of Telecommunications and Informatics, Samara, 443010 Russia
b Samara University, Samara, 443086 Russia
Full-text PDF (502 kB) First page Citations (2)
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DOI: https://doi.org/10.31857/S000523102201007X
Abstract: We consider a mathematical model of the simplest single-channel queuing system (QS) with a deterministic service time in the case of an arbitrarily correlated arrival flow. Various generalizations of the Pollaczek–Khinchine formula for the mean queue length are obtained for this QS. An interval model of the arrival flow is proposed. Within the framework of this model, an expression is obtained for the mean queue length in terms of statistical unconditional moments of the second order. All results are obtained under very general assumptions of ergodicity and stationarity. The results of numerical experiments confirming the theoretical conclusions are presented.
Keywords: queuing system, correlated arrival flow, mean queue length, Pollaczek-Khinchine formula.
Presented by the member of Editorial Board: V. M. Vishnevsky

Received: 15.09.2019
Revised: 25.08.2021
Accepted: 29.08.2021
English version:
Automation and Remote Control, 2022, Volume 83, Issue 1, Pages 92–105
DOI: https://doi.org/10.1134/S0005117922010076
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: B.J. Likhttsinder, I. A. Blatov, E. V. Kitaeva, “On estimates of the mean queue length for single-channel queuing systems in terms of statistical unconditional second-order moments of the modified arrival flow”, Avtomat. i Telemekh., 2022, no. 1, 113–129; Autom. Remote Control, 83:1 (2022), 92–105
Citation in format AMSBIB
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\pages 113--129
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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