Revisiting joint stationary distribution in two finite capacity queues operating in parallel

The paper revisits the problem of the computation of the joint stationary probability distribution pij in a queueing system consisting of two single-server queues, each of capacityN ≥ 3, operating in parallel, and a single Poisson flow. Upon each arrival instant, one customer is put simultaneously into each system. When a customer sees a full system, it is lost. The service times are exponentially distributed with different parameters. Using the approach based on generating functions, the authors obtain a new system of equations of a smaller size than the size of the original system of equilibrium equations (3N -2 compared to (N +1)2). Given the solution of the new system, the whole joint stationary distribution can be computed recursively. The new system gives some insights into the interdependence of pij and pnm. If relations between pi-1,N and pi,N for i = 3, 5, 7, · · · are known, then the blocking probability can be computed recursively. Using the known results for the asymptotic behavior of pij as i, j → ∞, the authors illustrate this idea by a simple numerical example.

Издательство
Федеральный исследовательский центр "Информатика и управление" РАН
Номер выпуска
3
Язык
Английский
Страницы
106-112
Статус
Опубликовано
Том
11
Год
2017
Организации
  • 1 School No. 281 of Moscow, 7 Raduzhnaya Str., Moscow, 129344, Russian Federation
  • 2 Peoples' Friendship University of Russia, RUDN University, 6 Miklukho-Maklaya Str., Moscow, 117198, Russian Federation
  • 3 Institute of Informatics Problems, Federal Research Center Computer Science and Control, Russian Academy of Sciences, 44-2 Vavilova Str., Moscow, 119333, Russian Federation
Ключевые слова
Generating function; Paired customers; Stationary distribution; Two queues
Дата создания
19.10.2018
Дата изменения
19.10.2018
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/6008/