Computing the stationary distribution of queueing systems with random resource requirements via fast fourier transform

Queueing systems with random resource requirements, in which an arriving customer, in addition to a server, demands a random amount of resources from a shared resource pool, have proved useful to analyze wireless communication networks. The stationary distributions of such queuing systems are expressed in terms of truncated convolution powers of the cumulative distribution function of the resource requirements. Discretization of the cumulative distribution function and the application of the fast Fourier transform are a traditional way of calculating convolutions. We suggest finding truncated convolution powers of the cumulative distribution functions by calculating the convolution powers of the truncated cumulative distribution functions via fast Fourier transform. This radically decreases computational complexity. We introduce the concept of resource load and investigate the accuracy of the proposed method at low and high resource loads. It is shown that the proposed method makes it possible to quickly and accurately calculate truncated convolution powers required for the analysis of queuing systems with random resource requirements. © 2020 by the authors.

Авторы
Журнал
Издательство
MDPI AG
Номер выпуска
5
Язык
Английский
Статус
Опубликовано
Номер
772
Том
8
Год
2020
Организации
  • 1 Service Innovation Research Institute, 8 A Annankatu, Helsinki, 00120, Finland
  • 2 Applied Informatics and Probability Department, 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
Discretization; Fast fourier transform; Queueing system; Random resource requirements
Дата создания
02.11.2020
Дата изменения
16.02.2021
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/64799/