Analysis of M/G/1 Queue Model with Priority

Pan Quanru

doi:doi:10.11648/j.pamj.20130202.16

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Analysis of M/G/1 Queue Model with Priority

Pan Quanru

Published in Pure and Applied Mathematics Journal (Volume 2, Issue 2)

Received: 17 March 2013 Accepted: Published: 2 April 2013

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Abstract

Due to the queue phenomenon different customers needing different service quality, a model is established as follows: there are two types of customers in the system and their arrival rates are different; first-class customers have no preemptive priority, the different service time for the different customers and all the service time obeys the general distribution. The following conclusions are drawn: the Laplace - Steele Kyrgyz transform of the low-priority customers’ waiting time stationary distribution; the average waiting time in the system of low priority customers; the Laplace - Steele Kyrgyz transform of the low-priority customers’ staying time stationary distribution; At last, this paper points out the problems to be solved.

Published in	Pure and Applied Mathematics Journal (Volume 2, Issue 2)
DOI	10.11648/j.pamj.20130202.16
Page(s)	94-97
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Non-Preemptive, Priority, General Distribution

References

[1]	Douglas R Miller. Computation of steady-state probability of priority queue[J]. Operation Research, 1981, 29(5):945-948.
[2]	Gelenbe E. Product Form Network with Negative and Positive Customers[J]. J Appl Prob, 1991,28:656-663.
[3]	Xu Zurun ,Zhu Yiju, Bernoulli feedback queue with slow service period and impatient customers[J],Journal of jiang su university(Nature science Edition) ,2010,31(6):740-744.
[4]	LIU Jian-min,A heavy traffic diffiusion approximation for preemptive resume priority queueing with heavy tailed service,Pure and Applied Mathematics[J],2010,26(4):559-566.
[5]	WANG Ye-qun,Queuing System M/M/1/T with Priority Mechanism Based on Living Time,Journal of Beijing University of Posts and Telecommunications[J],2010,33(3):80-83.
[6]	Douglas R Miller. Computation of steady-state probability of priority queue[J]. Operation Research, 1981,29(5):945-948.

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APA Style

Pan Quanru. (2013). Analysis of M/G/1 Queue Model with Priority. Pure and Applied Mathematics Journal, 2(2), 94-97. https://doi.org/10.11648/j.pamj.20130202.16

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ACS Style

Pan Quanru. Analysis of M/G/1 Queue Model with Priority. Pure Appl. Math. J. 2013, 2(2), 94-97. doi: 10.11648/j.pamj.20130202.16

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AMA Style

Pan Quanru. Analysis of M/G/1 Queue Model with Priority. Pure Appl Math J. 2013;2(2):94-97. doi: 10.11648/j.pamj.20130202.16

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@article{10.11648/j.pamj.20130202.16,
  author = {Pan Quanru},
  title = {Analysis of M/G/1 Queue Model with Priority},
  journal = {Pure and Applied Mathematics Journal},
  volume = {2},
  number = {2},
  pages = {94-97},
  doi = {10.11648/j.pamj.20130202.16},
  url = {https://doi.org/10.11648/j.pamj.20130202.16},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20130202.16},
  abstract = {Due to the queue phenomenon different customers needing different service quality, a model is established as follows: there are two types of customers in the system and their arrival rates are different; first-class customers have no preemptive priority, the different service time for the different customers and all the service time obeys the general distribution. The following conclusions are drawn: the Laplace - Steele Kyrgyz transform of the low-priority customers’ waiting time stationary distribution; the average waiting time in the system of low priority customers; the Laplace - Steele Kyrgyz transform of the low-priority customers’ staying time stationary distribution; At last, this paper points out the problems to be solved.},
 year = {2013}
}

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TY  - JOUR
T1  - Analysis of M/G/1 Queue Model with Priority
AU  - Pan Quanru
Y1  - 2013/04/02
PY  - 2013
N1  - https://doi.org/10.11648/j.pamj.20130202.16
DO  - 10.11648/j.pamj.20130202.16
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 94
EP  - 97
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20130202.16
AB  - Due to the queue phenomenon different customers needing different service quality, a model is established as follows: there are two types of customers in the system and their arrival rates are different; first-class customers have no preemptive priority, the different service time for the different customers and all the service time obeys the general distribution. The following conclusions are drawn: the Laplace - Steele Kyrgyz transform of the low-priority customers’ waiting time stationary distribution; the average waiting time in the system of low priority customers; the Laplace - Steele Kyrgyz transform of the low-priority customers’ staying time stationary distribution; At last, this paper points out the problems to be solved.
VL  - 2
IS  - 2
ER  -

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Author Information

Pan Quanru

School of Mathematics and Physics, Jiangsu University of Science and Technology, Zhenjiang, Jiangsu 212003, China

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Plain Text BibTeX RIS

APA Style

Pan Quanru. (2013). Analysis of M/G/1 Queue Model with Priority. Pure and Applied Mathematics Journal, 2(2), 94-97. https://doi.org/10.11648/j.pamj.20130202.16

Copy | Download

ACS Style

Pan Quanru. Analysis of M/G/1 Queue Model with Priority. Pure Appl. Math. J. 2013, 2(2), 94-97. doi: 10.11648/j.pamj.20130202.16

Copy | Download

AMA Style

Pan Quanru. Analysis of M/G/1 Queue Model with Priority. Pure Appl Math J. 2013;2(2):94-97. doi: 10.11648/j.pamj.20130202.16

Copy | Download

@article{10.11648/j.pamj.20130202.16,
  author = {Pan Quanru},
  title = {Analysis of M/G/1 Queue Model with Priority},
  journal = {Pure and Applied Mathematics Journal},
  volume = {2},
  number = {2},
  pages = {94-97},
  doi = {10.11648/j.pamj.20130202.16},
  url = {https://doi.org/10.11648/j.pamj.20130202.16},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20130202.16},
  abstract = {Due to the queue phenomenon different customers needing different service quality, a model is established as follows: there are two types of customers in the system and their arrival rates are different; first-class customers have no preemptive priority, the different service time for the different customers and all the service time obeys the general distribution. The following conclusions are drawn: the Laplace - Steele Kyrgyz transform of the low-priority customers’ waiting time stationary distribution; the average waiting time in the system of low priority customers; the Laplace - Steele Kyrgyz transform of the low-priority customers’ staying time stationary distribution; At last, this paper points out the problems to be solved.},
 year = {2013}
}

Copy | Download

TY  - JOUR
T1  - Analysis of M/G/1 Queue Model with Priority
AU  - Pan Quanru
Y1  - 2013/04/02
PY  - 2013
N1  - https://doi.org/10.11648/j.pamj.20130202.16
DO  - 10.11648/j.pamj.20130202.16
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 94
EP  - 97
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20130202.16
AB  - Due to the queue phenomenon different customers needing different service quality, a model is established as follows: there are two types of customers in the system and their arrival rates are different; first-class customers have no preemptive priority, the different service time for the different customers and all the service time obeys the general distribution. The following conclusions are drawn: the Laplace - Steele Kyrgyz transform of the low-priority customers’ waiting time stationary distribution; the average waiting time in the system of low priority customers; the Laplace - Steele Kyrgyz transform of the low-priority customers’ staying time stationary distribution; At last, this paper points out the problems to be solved.
VL  - 2
IS  - 2
ER  -

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