On extreme values of the queue length in some queuing systems

被引：1

作者：

Akbash, Kateryna ^{[1
]}

Doronina, Natalia ^{[2
]}

Matsak, Ivan ^{[3
]}

机构：

[1] Volodymyr Vynnychenko Cent Ukrainian State Univ, Dept Math & Methods Teaching Math, Shevchenko St 1, UA-25006 Kropyvnytskyi, Ukraine

[2] Taras Shevchenko Natl Univ Kyiv, Dept Foreign Languages Math Fac, 2-6 Academician Glushkov Ave, UA-03127 Kiev, Ukraine

[3] Taras Shevchenko Natl Univ Kyiv, Fac Comp Sci & Cybernet, 2-6 Academician Glushkovavenue, UA-03127 Kiev, Ukraine

来源：

GEORGIAN MATHEMATICAL JOURNAL | 2023年

关键词：

Extreme values; queuing systems; regenerative processes;

D O I：

10.1515/gmj-2023-2055

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 and 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.

引用

页码：1 / 16

页数：16

共 21 条

[1] EXTREME VALUE THEORY FOR A CLASS OF DISCRETE DISTRIBUTIONS WITH APPLICATIONS TO SOME STOCHASTIC PROCESSES [J].