On the M/G/1 queueing system with multiclass customers and fixed feedback

doi:1005-8885 (2008) 02-0114-08

中国邮电高校学报(英文) ›› 2008, Vol. 15 ›› Issue (2): 114-121.doi: 1005-8885 (2008) 02-0114-08

On the M/G/1 queueing system with multiclass customers and fixed feedback

张奇支

School of Computer, South China Normal University, Guangzhou 510631, China

收稿日期:2007-10-08 修回日期:1900-01-01 出版日期:2008-06-30
通讯作者: 张奇支

On the M/G/1 queueing system with multiclass customers and fixed feedback

ZHANG Qi-zhi

School of Computer, South China Normal University, Guangzhou 510631, China

Received:2007-10-08 Revised:1900-01-01 Online:2008-06-30
Contact: ZHANG Qi-zhi

摘要/Abstract

摘要：

The M/G/1 queueing system with multiclass customer arrivals, fixed feedback, and first come first served policy is considered, where different classes of customers have different arrival rates, service-time distributions, and feedback numbers. The joint probability generation function of queue size of each class and the Laplace-Stieltjes transform of the total sojourn time of a customer in each class are presented, which extended the results obtained by Choi B D. The mean queue size of each class and mean total sojourn time of a customer in each class are obtained with this result. The results can be used in computer and communication networks for their performance analysis.

关键词:

M/G/1;queueing;system,;feedback,;multiclass;customers,;queue;size,;sojourn;time

Abstract:

Key words:

M/G/1 queueing system;feedback;multiclass customers;queue size;sojourn time

中图分类号:

ZHANG Qi-zhi. On the M/G/1 queueing system with multiclass customers and fixed feedback[J]. Acta Metallurgica Sinica(English letters), 2008, 15(2): 114-121.

参考文献

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3. Choi B D, Kim B, Choi S H. On the M/G/1 Bernoulli feedback queue with multi-class customers. Computer and Operation Research, 2000, 27(3): 269-286

4. Takagi H. Queueing analysis: a foundation of performance evaluation: Vol 1 vacation and priority systems: Part 1. Amsterdam, The Netherland: Elsevier Science, 1991

5. Takine T, Takagi H, Hasegawa T. Sojourn times in vacation and polling systems with Bernoulli feedback. Journal of Applied Probability, 1991, 28(2): 422-432

6. Wortman M A, Disney R L. The M/GI/1 Bernoulli feedback queue with vacations. Queueing System, 1991, 9(4): 353-64

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9. Berg J L, Boxma O J, Groenendijk W P. Sojourn times in the M/G/1 queue with deterministic feedback. Communications in Statistics-Stochastic Models, 1989, 5(1): 115-29

10. Adve V S, Nelson R. The relationship between Bernoulli and fixed feedback policies for the M/G/1 queue. Operations Research, 1994, 42(2): 380-385

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12. Zhang Qi-zhi, Liao Jian-xin, Zhu Xiao-min. On queue sizes of M/G/1 queueing system with fixed times of feedbacks. Journal of Beijing University of Posts and Telecommunications, 2005, 25(3): 17-19 (in Chinese)

13. Zhang Qi-zhi, Liao Jian-xin, Xu Tong. On sojourn time of M/G/1 queueing system with fixed times of feedback. Journal of Beijing University of Posts and Telecommunications, 2005, 25(6): 61-64 ( in Chinese)

14. Simon B. Priority queues with feedback. Journal of the Association for Computing Machinery, 1984, 31(1): 134-149

15. Takacs L. Introduction to the theory of queues. New York, NY, USA: Oxford University Press, 1962

16. Yuan Zhao-rui, Yang Fang-chun. A study of feature interactions in intelligent networks. The Journal of China Universities of Posts and Telecommunica, 2002, 9(1): 77-78

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On the M/G/1 queueing system with multiclass customers and fixed feedback

On the M/G/1 queueing system with multiclass customers and fixed feedback

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