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

Jerim Kim; Bara Kim; Hsing Luh

doi:10.1007/s10479-018-2917-9

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

Jerim Kim, Bara Kim, Hsing Luh

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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.

Original language	English
Pages (from-to)	137-159
Number of pages	23
Journal	Annals of Operations Research
Volume	277
Issue number	2
DOIs	https://doi.org/10.1007/s10479-018-2917-9
State	Published - 30 Jun 2019

Keywords

Feedback queue
Queue size
Round-robin
Sojourn time
Weighted round-robin

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10.1007/s10479-018-2917-9

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

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.",

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N2 - 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.

AB - 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.

KW - Feedback queue

KW - Queue size

KW - Round-robin

KW - Sojourn time

KW - Weighted round-robin

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

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Keywords

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