Informatics and Applications
2015, Volume 9, Issue 3, pp 2531
JOINT STATIONARY DISTRIBUTION OF m QUEUES IN THE NSERVER QUEUEING SYSTEM WITH REORDERING
 A. V. Pechinkin
 R. V. Razumchik
Abstract
The paper considers a continuoustime Nserver queueing system with a buffer of infinite capacity and customer reordering. The Poisson flow of customers arrives at the system. Service times of customers at each server are exponentially distributed with the same parameter. Each customer obtains a sequential number upon arrival. The order of customers upon arrival should be preserved upon departure from the system. Customers which violated the order form different queues in the reordering buffer which has infinite capacity. If there are n, n = 1, N, customers in servers, then the latest customer to occupy a server is called the 1st level customer, the last but one  the 2nd level customer, . . . , the first  the nth level customer. Customers in the reordering buffer that arrived between the 1st level and the 2nd level customers, form the queue number one. Customers, which arrived between the 2nd level and the 3rd level customers, form the queue number two, etc. Customers, which arrived between the Nth level and the (N  1)th level customers, form the queue number (N  l) in the reordering buffer. Mathematical relations in terms of Ztransform, which make it possible to calculate the joint stationary distribution of the number of customers in the buffer, servers, and in the 1st, 2nd, . . . , mth queues (m = 1, N  1) in the reordering buffer, are obtained.
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[+] About this article
Title
JOINT STATIONARY DISTRIBUTION OF m QUEUES IN THE NSERVER QUEUEING SYSTEM WITH REORDERING
Journal
Informatics and Applications
2015, Volume 9, Issue 3, pp 2531
Cover Date
20150230
DOI
10.14357/19922264150303
Print ISSN
19922264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
multiserver queueing system; reordering; separate queues; joint stationary distribution
Authors
A. V. Pechinkin and R. V. Razumchik ,
Author Affiliations
Institute of Informatics Problems, Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences, 442 Vavilov Str., Moscow 119333, Russian Federation
Peoples’ Friendship University of Russia, 6 MiklukhoMaklaya Str., Moscow 117198, Russian Federation
