Informatics and Applications
2014, Volume 8, Issue 4, pp 3-10
JOINT STATIONARY DISTRIBUTION OF THE NUMBER OF CUSTOMERS IN THE SYSTEM AND REORDERING BUFFER IN THE MULTISERVER REORDERING QUEUE
- A. V. Pechinkin
- R. V. Razumchik
Abstract
The paper considers a continuous-time multiserver queueing system with buffer on infinite capacity and 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 whose service finished but which violated the order are kept in the reordering buffer of infinite capacity. A joint stationary distribution of the number of customers in the buffer, servers, and reordering buffer is obtained in terms of a computational algorithm and a generating function. A numerical example is provided.
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[+] About this article
Title
JOINT STATIONARY DISTRIBUTION OF THE NUMBER OF CUSTOMERS IN THE SYSTEM AND REORDERING BUFFER IN THE MULTISERVER REORDERING QUEUE
Journal
Informatics and Applications
2014, Volume 8, Issue 4, pp 3-10
Cover Date
2014-10-30
DOI
10.14357/19922264140401
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
queueing system; reordering; infinite capacity; joint distribution
Authors
A. V. Pechinkin  and R. V. Razumchik , 
Author Affiliations
Institute of Informatics Problems, Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian
Federation
Peoples' Friendship University of Russia, 6 Miklukho-Maklaya Str., Moscow 117198, Russian Federation
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