Informatics and Applications
2018, Volume 12, Issue 3, pp 42-47
ON THE INSENSITIVITY OF THE STATIONARY DISTRIBUTION OF THE LIMITED RESOURCES QUEUING SYSTEM WITH STATE-DEPENDENT ARRIVAL AND SERVICE RATES
- E. S. Sopin
- V. A. Naumov
- K. Å. Samouylov
Abstract
The authors consider further generalization ofthe queuing systems, in which customers require not only a server but also a certain amount of limited resources. In the considered queuing system, arrival and serving intensities depend on the statå of the system. The authors assume an arbitrary distribution of the service time.
The authors prove that the stationary distribution of the system has product form in the case of Poisson arrivals.
Moreover, it was shown that the steady-state probability distribution of number of customers in the system and volumes of occupied resources depends on the service time distribution only through its mean.
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[+] About this article
Title
ON THE INSENSITIVITY OF THE STATIONARY DISTRIBUTION OF THE LIMITED RESOURCES QUEUING SYSTEM WITH STATE-DEPENDENT ARRIVAL AND SERVICE RATES
Journal
Informatics and Applications
2018, Volume 12, Issue 3, pp 42-47
Cover Date
2018-08-30
DOI
10.14357/19922264180306
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
queueing system; limited resources; insensitivity; service time
Authors
E. S. Sopin  ,  , V. A. Naumov  ,
and K. Å. Samouylov ,
Author Affiliations
Peoples' Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya Str., Moscow 117198, Russian Federation
Institute of Informatics Problems, Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation
Service Innovation Research Institute (PIKE), 8A Annankatu, Helsinki 00120, Finland
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