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Avtomatika i Telemekhanika, 2023, Issue 7, Pages 3–22
DOI: https://doi.org/10.31857/S0005231023070012 (Mi at16186) 		 
Stochastic Systems

Analytical investigation of a single-server queueing system with an incoming MAP event flow

A. M. Gortsev, L. A. Nezhelskaya

National Research Tomsk State University, Tomsk, Russia
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DOI: https://doi.org/10.31857/S0005231023070012
Abstract: This paper considers a single-server queueing system with an incoming Markovian Arrival Process (MAP) request flow with two states. Explicit expressions are derived for the stationary probability distribution of the states and several numerical characteristics of the system (the probability of idle time of the server, the expected number of requests in the system, and the mean queue length). The resulting numerical characteristics are presented in tables and plotted in graphical form as well. The recurrent MAP flow with two states as a special case of correlated MAP request flows is studied.
Keywords: MAP request flow, single-server queueing system, stationary probability distribution of system states, numerical characteristics.
Presented by the member of Editorial Board: V. M. Vishnevsky

Received: 27.02.2023
Revised: 25.04.2023
Accepted: 11.05.2023
English version:
Automation and Remote Control, 2023, Volume 84, Issue 7, Pages 763–777
DOI: https://doi.org/10.25728/arcRAS.2023.62.11.001
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: A. M. Gortsev, L. A. Nezhelskaya, “Analytical investigation of a single-server queueing system with an incoming MAP event flow”, Avtomat. i Telemekh., 2023, no. 7, 3–22; Autom. Remote Control, 84:7 (2023), 763–777
Citation in format AMSBIB
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\by A.~M.~Gortsev, L.~A.~Nezhelskaya
\paper Analytical investigation of a single-server queueing system with an incoming MAP event flow
\jour Avtomat. i Telemekh.
\yr 2023
\issue 7
\pages 3--22
\mathnet{http://mi.mathnet.ru/at16186}
\crossref{https://doi.org/10.31857/S0005231023070012}
\edn{https://elibrary.ru/FCERPV}
\transl
\jour Autom. Remote Control
\yr 2023
\vol 84
\issue 7
\pages 763--777
\crossref{https://doi.org/10.25728/arcRAS.2023.62.11.001}
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