Probability-time characteristics of MjGj1j1 queueing system with renovation

The queueing system in which the losses of incoming customers (tasks) are possible due to the introduction of a special renovation mechanism is under consideration. The renovation mechanism means that the task at the moment of the end of its service with some probability may empty the buffer and leave the system, or with an additional probability may just leave the system without emptying the buffer. The queueing system consists of the server with general service time distribution and the buffer of unlimited capacity. The incoming flow of tasks is a Poisson one. The embedded upon the end of service times Markov chain is constructed and under the assumption of the existence of a stationary regime for the embedded Markov chain the formula for the probability generation function is derived. In addition, the next probability characteristics (based on the embedded Markov chain) are obtained: The probability of the system being empty, the probability of a task in the buffer to be dropped (not to be dropped), the probability distribution of served (dropped) tasks. Also the average numbers of customers in the system, dropped customers and served customers (based on the embedded Markov chain) are derived as the service waiting time distribution for non-dropped tasks and the average service waiting time for non-dropped tasks. © Copyright 2017 for the individual papers by the papers' authors.

Авторы
Редакторы
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Сборник материалов конференции
Издательство
CEUR-WS
Номер выпуска
-
Язык
Русский
Страницы
125-131
Статус
Опубликовано
Подразделение
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Ссылка
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DOI
-
Номер
-
Том
1995
Год
2017
Организации
  • 1 Department of Applied Probability and Informatics, Peoples' Friendship University of Russia, 6 Miklukho-Maklaya St., Moscow, 117198, Russian Federation
  • 2 Federal Research Center Computer Science and Control, Institute of Informatics Problems, Russian Academy of Sciences, 44-2 Vavilova St., Moscow, 119333, Russian Federation
Ключевые слова
Embedded markov chain; General service time distribution; Queueing system; Renovation; Time-probability characteristics
Дата создания
19.07.2019
Дата изменения
19.07.2019
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/39090/