Analysis of a Markovian feedback queue with multi-class customers and its application to the weighted round-robin queue

Analysis of a Markovian feedback queue with multi-class customers and its application to the... Ann Oper Res https://doi.org/10.1007/s10479-018-2917-9 S.I.: QUEUEING THEORY AND NETWORK APPLICATIONS Analysis of a Markovian feedback queue with multi-class customers and its application to the weighted round-robin queue 1 2 3 Jerim Kim · Bara Kim · Hsing Luh © Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract We consider an M/G/1 Markovian feedback queue with multi-class customers. We derive functional equations for the stationary distribution of the queue size and the total response time. A system of linear equations is also derived for the moments of the queue size and the total response time distributions. The mean and the variance of the queue size and the total response time can be computed by solving the system of linear equations. By using the Markovian feedback queue with multi-class customers, we also investigate the M/PH/1 weighted round-robin queue. Numerical examples are given to show that moments of the queue sizes and of the total response times can be easily computed for the weighted round-robin queue. As the service quantum shrinks to zero, the moments of the queue sizes and the total response times converge to some limits which should be the moments of the corresponding discriminatory processor sharing queue. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Annals of Operations Research Springer Journals

Analysis of a Markovian feedback queue with multi-class customers and its application to the weighted round-robin queue

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Publisher
Springer US
Copyright
Copyright © 2018 by Springer Science+Business Media, LLC, part of Springer Nature
Subject
Business and Management; Operations Research/Decision Theory; Combinatorics; Theory of Computation
ISSN
0254-5330
eISSN
1572-9338
D.O.I.
10.1007/s10479-018-2917-9
Publisher site
See Article on Publisher Site

Abstract

Ann Oper Res https://doi.org/10.1007/s10479-018-2917-9 S.I.: QUEUEING THEORY AND NETWORK APPLICATIONS Analysis of a Markovian feedback queue with multi-class customers and its application to the weighted round-robin queue 1 2 3 Jerim Kim · Bara Kim · Hsing Luh © Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract We consider an M/G/1 Markovian feedback queue with multi-class customers. We derive functional equations for the stationary distribution of the queue size and the total response time. A system of linear equations is also derived for the moments of the queue size and the total response time distributions. The mean and the variance of the queue size and the total response time can be computed by solving the system of linear equations. By using the Markovian feedback queue with multi-class customers, we also investigate the M/PH/1 weighted round-robin queue. Numerical examples are given to show that moments of the queue sizes and of the total response times can be easily computed for the weighted round-robin queue. As the service quantum shrinks to zero, the moments of the queue sizes and the total response times converge to some limits which should be the moments of the corresponding discriminatory processor sharing queue.

Journal

Annals of Operations ResearchSpringer Journals

Published: Jun 4, 2018

References

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