On extreme values of the queue length in some queuing systems-Reference-Cited by-同舟云学术

On extreme values of the queue length in some queuing systems

Published:2023-08-25 Issue:1 Volume:31 Page:1-16
ISSN:1072-947X
Container-title:Georgian Mathematical Journal
language:en
Short-container-title:

Author:

Akbash Kateryna¹^ORCID,Doronina Natalia²^ORCID,Matsak Ivan³^ORCID

Affiliation:

1. Department of Mathematics and Methods of Teaching Math , Volodymyr Vynnychenko Central Ukrainian State University , Shevchenko street 1 , Kropyvnytskyi 25006 , Ukraine

2. Department of Foreign Languages for Mathematical Faculties , Taras Shevchenko National University of Kyiv , 2 / 6 {2/6} , Academician Glushkov avenue , Kyiv 03127 , Ukraine

3. Faculty of Computer Science and Cybernetics , Taras Shevchenko National University of Kyiv , 2 / 6 {2/6} , Academician Glushkov avenue , Kyiv 03127 , Ukraine

Abstract

Abstract In this paper, the rate of convergence to the exponential distribution in the limit theorem for extreme values of the queue length in queuing systems M / G / 1

{M/G/1}

and G / M / 1

{G/M/1}

are studied. In proving these results, we first prove one general boundary theorem for extremal values of regenerative processes, which is of independent interest. This topic is closely related to the task of the first passage times to rare sets by the regenerative process. The need for such research arises in many areas: the mathematical theory of reliability, queuing theory, some statistical problems of physics.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/gmj-2023-2055/pdf

Reference23 articles.

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