Estimating the Rate of Convergence of the PH/M/1 Model by Reducing to Quasi-Birth-Death Processes-Reference-Cited by-同舟云学术

Estimating the Rate of Convergence of the PH/M/1 Model by Reducing to Quasi-Birth-Death Processes

Published:2023-03-18 Issue:6 Volume:11 Page:1494
ISSN:2227-7390
Container-title:Mathematics
language:en
Short-container-title:Mathematics

Author:

Usov Ilya¹,Satin Yacov¹^ORCID,Zeifman Alexander¹²³⁴^ORCID

Affiliation:

1. Department of Applied Mathematics, Vologda State University, 15 Lenina Str., 160000 Vologda, Russia

2. Federal Research Center “Computer Sciences and Control” of the Russian Academy of Sciences, 44-2 Vavilova Str., 119333 Moscow, Russia

3. Vologda Research Center of the Russian Academy of Sciences, 556A Gorky Str., 160014 Vologda, Russia

4. Moscow Center for Fundamental and Applied Mathematics, Moscow State University, 119991 Moscow, Russia

Abstract

We are studying the quasi-birth-death process and the property of weak ergodicity. Using the C-matrix method, we derive estimates for the rate of convergence to the limiting regime for the general case of the PH/M/1 model, as well as the particular case when m=3. We provide a numerical example for the case m=3, and construct graphs showing the probability of an empty queue and the probability of p1(t).

Funder

Ministry of Science and Higher Education of the Russian Federation

Publisher

MDPI AG

Subject

General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)

Link

https://www.mdpi.com/2227-7390/11/6/1494/pdf

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