On truncation of the matrix-geometric stationary distributions

In this paper, we study queueing systems with an infinite and finite number of waiting places that can be modeled by a Quasi-Birth-and-Death process. We derive the conditions under which the stationary distribution for a loss system is a truncation of the stationary distribution of the Quasi-Birth-and-Death process and obtain the stationary distributions of both processes. We apply the obtained results to the analysis of a semi-open network in which a customer from an external queue replaces a customer leaving the system at the node from which the latter departed. © 2019 by the authors.

Авторы
Журнал
Издательство
MDPI AG
Номер выпуска
9
Язык
Английский
Статус
Опубликовано
Номер
798
Том
7
Год
2019
Организации
  • 1 Service Innovation Research Institute, Helsinki, 00120, Finland
  • 2 Department of Applied Informatics and Probability, Peoples' Friendship University of Russia (RUDN University), Miklukho-Maklaya St. 6, Moscow, 117198, Russian Federation
  • 3 Institute of Informatics Problems, Federal Research Center 'Computer Science and Control' of the Russian Academy of Sciences, Vavilov St. 44-2, Moscow, 119333, Russian Federation
Ключевые слова
Matrix-geometric solution; Quasi-Birth-and-Death process; Truncated distribution
Дата создания
24.12.2019
Дата изменения
16.02.2021
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/55075/
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