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- Title
On extreme values of the queue length in some queuing systems.
- Authors
Akbash, Kateryna; Doronina, Natalia; Matsak, Ivan
- 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 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.
- Subjects
DISTRIBUTION (Probability theory); LIMIT theorems; ENGINEERING reliability theory; STATISTICAL physics; EXTREME value theory; QUEUING theory
- Publication
Georgian Mathematical Journal, 2024, Vol 31, Issue 1, p1
- ISSN
1072-947X
- Publication type
Article
- DOI
10.1515/gmj-2023-2055