# Algebraic method for approximating joint stationary distribution in finite capacity queue with negative customers and two queues [АЛГЕБРАИЧЕСКИЙ МЕТОД ПРИБЛИЖЕННОГО РАСЧЕТА СТАЦИОНАРНОГО РАСПРЕДЕЛЕНИЯ В СИСТЕМЕ ОБСЛУЖИВАНИЯ КОНЕЧНОЙ ЕМКОСТИ С ОТРИЦАТЕЛЬНЫМИ ЗАЯВКАМИ И ДВУМЯ ОЧЕРЕДЯМИ]

Consideration is given to the single-server queueing system (QS) with a Poisson flow of (ordinary) customers and Poisson flow of negative customers. There is a queue of capacity k (0 < k < ∞), where ordinary customers wait for service. If an ordinary customer finds the queue full upon an arrival, it is considered to be lost. Each negative customer upon arrival moves one ordinary customer from the queue, if it not empty, to another queue (bunker) of capacity r (0 < r < ∞) and after that it leaves the system. If upon arrival of a negative customer the queue is not empty and the bunker is full, the negative customer and one ordinary customer from the queue leave the system. In all other cases, an arrival of a negative customer has no effect on the system. Customers from bunker are served with relative priority (i. e., a customer from bunker enters server if only there are no customers in the queue to be served). Service times of customers from both the queue and the bunker are exponentially distributed with the same parameter. Purely algebraic method based on generating functions, Chebyshev and Gegenbauer polynomials for approximate calculation of joint stationary probability distribution is presented for the case k = r. Numerical examples, showing both pros and cons of the method are provided. © 2015 Federal Research Center "Computer Science and Control" of Russian Academy of Sciences. All rights reserved.

Авторы
Razumchik Rostislav V.
Издательство
Федеральный исследовательский центр "Информатика и управление" РАН
Номер выпуска
4
Язык
Английский
Страницы
68-77
Статус
Опубликовано
Ссылка
Том
9
Год
2015
Организации
• 1 Institute of Informatics Problems, Federal Research Center “Computer Science and Control”, The Russian Academy of Sciences, 44-2 Vavilov Str., Moscow, 119333, Russian Federation
• 2 Peoples' Friendship University, 6 Miklukho-Maklaya Str., Moscow, 117198, Russian Federation
Ключевые слова
Approximation; Gegenbauer polynomials; Negative customers; Queueing system; Stationary distribution
Дата создания
20.07.2021
Дата изменения
20.07.2021
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/74503/
Поделиться

### Другие записи

#### METHODS AND ALGORITHMS FOR JOB SCHEDULING IN SYSTEMS WITH PARALLEL SERVICE: A SURVEY [ОБЗОР МОДЕЛЕЙ И АЛГОРИТМОВ РАЗМЕЩЕНИЯ ЗАДАНИЙ В СИСТЕМАХ С ПАРАЛЛЕЛЬНЫМ ОБСЛУЖИВАНИЕМ]

Статья
Konovalov Mikhail G., Razumchik Rostislav V.
Информатика и ее применения. Федеральный исследовательский центр "Информатика и управление" РАН. Том 9. 2015. С. 56-67

#### PHOTODYNAMIC THERAPY FOR VENOUS TROPHIC ULCERS

Статья
Tamrazova O.B., Molochkov A.V., Bagramova G.E., Pomerantsev O.N.
Клиническая дерматология и венерология. Общество с ограниченной ответственностью Издательство Медиа Сфера. Том 11. 2013. С. 62-67