Systems and Means of Informatics
2021, Volume 31, Issue 3, pp 4-17
JOINT STATIONARY DISTRIBUTION IN THE GI/M/n/infinity QUEUE WITH GENERAL RENOVATION
- T. A. Milovanova
- I. S. Zaryadov
- L. A. Meykhanadzhyan
Abstract
Multiserver queuing system with a finite number of identical servers and one queue of unlimited capacity is being considered. Customers enter the system one by one in accordance with a recurrent flow. Service times are exponentially distributed with the same parameter. General renovation mechanism is implemented in the system: a customer, whose service has been completed, upon leaving the system removes a random number of other customers from the queue according to a given probability distribution. The method is proposed for finding the joint stationary distribution of the total number of customers in the system and the time elapsed since the last arrival. Expressions (in terms of transforms) for the calculation of the transient joint distribution are presented.
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[+] About this article
Title
JOINT STATIONARY DISTRIBUTION IN THE GI/M/n/infinity QUEUE WITH GENERAL RENOVATION
Journal
Systems and Means of Informatics
Volume 31, Issue 3, pp 4-17
Cover Date
2021-11-10
DOI
10.14357/08696527210301
Print ISSN
0869-6527
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
queueing system; general renovation; queue management
Authors
T. A. Milovanova  , I. S. Zaryadov ,  , and L. A. Meykhanadzhyan 
Author Affiliations
Peoples' Friendship University of Russia (RUDN University), 6 Miklukho- Maklaya Str., Moscow 117198, Russian Federation
Federal Research Center "Computer Science and Control", Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation
Financial University under the Government of the Russian Federation, 49 Lenin- gradsky Prosp., Moscow 125993, Russian Federation
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