Systems and Means of Informatics
2015, Volume 25, Issue 3, pp 44-59
ON THE METHOD OF CALCULATING THE STATIONARY DISTRIBUTION IN THE FINITE TWO-CHANNEL SYSTEM WITH ORDERED INPUT
- I. S. Zaryadov
- L. A. Meykhanadzhyan
- T. A. Milovanova
- R. V. Razumchik
Abstract
This paper considers a queueing system with ordered input and two servers (labelled by numbers 1 and 2). Each server has a buffer of finite capacity in front of it. Queues capacities are different. Customers arrive according to a Poisson process with constant rate. Upon arrival, a new customer goes to the server with label 1 or, if it is busy, occupies a place in the queue in front of it. If upon arrival a customer sees the queue in front of the server 1 full, it goes to the server with label 2 or, if it is busy, enters the queue in front of it.
If upon arrival of a new customer the system is full, the new customer is lost. Customers from both queues are served according to the FIFO (first in, first out) discipline and each server serves customers exponentially distributed times with the same parameter. A new method for recursive computation of the joint stationary distribution of queues is proposed.
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[+] About this article
Title
ON THE METHOD OF CALCULATING THE STATIONARY DISTRIBUTION IN THE FINITE TWO-CHANNEL SYSTEM WITH ORDERED INPUT
Journal
Systems and Means of Informatics
Volume 25, Issue 3, pp 44-59
Cover Date
2015-09-30
DOI
10.14357/08696527150303
Print ISSN
0869-6527
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
queueing system; special functions; two-dimensional Markov chain; joint distribution
Authors
I. S. Zaryadov  , L. A. Meykhanadzhyan ,
T. A. Milovanova , and R. V. Razumchik , 
Author Affiliations
Peoples' Friendship University of Russia, 6 Miklukho-Maklaya Str., Moscow 117198, Russian Federation
Institute of Informatics Problems, Federal Research Center "Computer Science
and Control", Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation
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