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Avtomatika i Telemekhanika, 2022, Issue 7, Pages 33–48
DOI: https://doi.org/10.31857/S0005231022070029 (Mi at15997) 		 
Stochastic Systems

Asymptotic diffusion analysis of $MMP P |M|N$ queuing systems with feedback

A. A. Nazarov, E. A. Pavlova

Tomsk State University, Tomsk, 634050 Russia
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DOI: https://doi.org/10.31857/S0005231022070029
Abstract: We present the results of the study of an $ N $-linear queuing system with feedback. The input flow is a Markov modulated Poisson process (MMPP). We use asymptotic diffusion analysis to find the probability distribution of the number of requests in the orbit and the number of busy servers in the system. Simulation results, as well as a numerical comparison of our method with asymptotic analysis method, are presented.
Keywords: multichannel queuing system, orbit, instantaneous feedback, delayed feedback, asymptotic diffusion analysis.
Presented by the member of Editorial Board: A. I. Lyakhov

Received: 02.11.2021
Revised: 02.02.2022
Accepted: 31.03.2022
English version:
Automation and Remote Control, 2022, Volume 83, Issue 7, Pages 1036–1049
DOI: https://doi.org/10.1134/S0005117922070025
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: A. A. Nazarov, E. A. Pavlova, “Asymptotic diffusion analysis of $MMP P |M|N$ queuing systems with feedback”, Avtomat. i Telemekh., 2022, no. 7, 33–48; Autom. Remote Control, 83:7 (2022), 1036–1049
Citation in format AMSBIB
\Bibitem{NazPav22}
\by A.~A.~Nazarov, E.~A.~Pavlova
\paper Asymptotic diffusion analysis of $MMP P |M|N$ queuing systems with feedback
\jour Avtomat. i Telemekh.
\yr 2022
\issue 7
\pages 33--48
\mathnet{http://mi.mathnet.ru/at15997}
\crossref{https://doi.org/10.31857/S0005231022070029}
\edn{https://elibrary.ru/ADTPEA}
\transl
\jour Autom. Remote Control
\yr 2022
\vol 83
\issue 7
\pages 1036--1049
\crossref{https://doi.org/10.1134/S0005117922070025}
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