Analysis of the GI/Geo/c Queue with Working Vacations

Author:

Gao Yan1,Liu Wen Fen1

Affiliation:

1. Zhengzhou Information Science and Technology Institute

Abstract

Working vacation queue models are well applied in the modeling and analysis of the router in optical networks. The GI/Geo/c queue with working vacations is studied in this paper. Through establishing two-dimensional Markov chain and using matrix-geometric solution method, the stability condition is derived. Adopting UL-type RG-factorization of irreducible Markov chain, the stationary distribution is given. Based on these, the probability distribution of queue-length and PGF of waiting time are obtained in the end.

Publisher

Trans Tech Publications, Ltd.

Reference9 articles.

1. L. D. Servi and L. G. Finn, M/M/1 queues with working vacations (M/M/1/WV), Performance Evaluation, vol. 50 (2002), pp.41-52.

2. A. Y. Liu, N. S. Tian and M. M. Guo, Geo/Geo/ 1 queue with working vacations, Chinese journal of engineering mathematics, vol. 25 (2008), pp.1059-1064.

3. J. H. Li and N. S. Tian, Analysis of the discrete time Geo/Geo/1 queue with single working vacation, Quality Technology & Quantitative Management, Vol. 5 (2008), pp.77-89.

4. Cosmika Goswami and N. Selvaraju, The discrete-time MAP/PH/1 queue with multiple working vacations, Applied Mathematical Modelling, Vol. 34 (2010), pp.931-946.

5. X. L. Xu, C. P. Liu, G. Y. Lu and X. H. Zhao, Stationary analysis for the bulk input Geom[X]/Geom/1 queue with working vacation, Informatioin Journal of Management Science and Engineering Management, Vol. 4 (2008), pp.118-128.

Cited by 2 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Analysis of $GI^{[X]}/D$-$MSP/1/\infty$ queue using $RG$-factorization;Journal of Industrial & Management Optimization;2021

2. Modelling and analysis of D-BMAP/D-MSP/1 queue using RG-factorization;Quality Technology & Quantitative Management;2020-12-28

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