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

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)1-23
Number of pages23
JournalAnnals of Operations Research
DOIs
Publication statusAccepted/In press - 2018 Jun 4

Fingerprint

Queue
Response time
Functional equation
Stationary distribution

Keywords

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

ASJC Scopus subject areas

  • Decision Sciences(all)
  • Management Science and Operations Research

Cite this

@article{2ad6f1089cd243eb91ec7bf5120a2d96,
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.",
keywords = "Feedback queue, Queue size, Round-robin, Sojourn time, Weighted round-robin",
author = "Jerim Kim and Bara Kim and Hsing Luh",
year = "2018",
month = "6",
day = "4",
doi = "10.1007/s10479-018-2917-9",
language = "English",
pages = "1--23",
journal = "Annals of Operations Research",
issn = "0254-5330",
publisher = "Springer Netherlands",

}

TY - JOUR

T1 - Analysis of a Markovian feedback queue with multi-class customers and its application to the weighted round-robin queue

AU - Kim, Jerim

AU - Kim, Bara

AU - Luh, Hsing

PY - 2018/6/4

Y1 - 2018/6/4

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

UR - http://www.scopus.com/inward/record.url?scp=85047999494&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85047999494&partnerID=8YFLogxK

U2 - 10.1007/s10479-018-2917-9

DO - 10.1007/s10479-018-2917-9

M3 - Article

AN - SCOPUS:85047999494

SP - 1

EP - 23

JO - Annals of Operations Research

JF - Annals of Operations Research

SN - 0254-5330

ER -