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| Performance of the（BMAP1, BMAP2 ）/（PH1, PH2 ）/N Retrial Queueing System with Finite Buffer | |
| 作者姓名： | Zong-hao ZHOU Shi-xing LI Yi-jun ZHU |
| 作者单位： | [1]School of Mathematics and Statistics, Huangshan University, Huangshan 245041, China [2]School of Mathematics and Statistics, Zhe]iang University of Finance and Economics, Hangzhou 310018~ China [3]Faculty of Science, Jiangsu University, Zhenjiang 212013, China |
| 基金项目： | Supported by the Natural Science Research Foundation for Higher Education of Anhui Province of China （No. KJ2013B272）, and Fundamental Research Funds for the Huangshan University （No. 2012xkjq008）. |
| 摘 要： | This paper consider the （BMAP1, BMAP2）/（PH1, PH2）/N retrial queue with finite-position buffer. The behavior of the system is described in terms of continuous time multi-dimensional Markov chain. Arriving type I calls find all servers busy and join the buffer, if the positions of the buffer are insufficient, they can go to orbit. Arriving type II calls find all servers busy and join the orbit directly. Each server can provide two types heterogeneous services with Phase-type （PH） time distribution to every arriving call （including types I and II calls）, arriving calls have an option to choose either type of services. The model is quite general enough to cover most of the systems in communication networks. We derive the ergodicity condition, the stationary distribution and the main performance characteristics of the system. The effects of various parameters on the system performance measures are illustrated numerically. |
| 关 键 词： | 排队系统 缓冲性能 PH2 Markov链 服务器 连续时间 时间分布 通信网络 |
Performance of the (BMAP1, BMAP2)/(PH1, PH2)/N retrial queueing system with finite buffer |
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| Zong-hao ZHOU,Shi-xing LI,Yi-jun ZHU.Performance of the (BMAP1, BMAP2)/(PH1, PH2)/N retrial queueing system with finite buffer[J].Acta Mathematicae Applicatae Sinica,2014,30(2):429-446. | |
| Authors: | Zong-hao Zhou Shi-xing Li Yi-jun Zhu |
| Institution: | 1. School of Mathematics and Statistics, Huangshan University, Huangshan, 245041, China 2. School of Mathematics and Statistics, Zhejiang University of Finance and Economics, Hangzhou, 310018, China 3. Faculty of Science, Jiangsu University, Zhenjiang, 212013, China |
| Abstract: | This paper consider the (BMAP1, BMAP2)/(PH1, PH2)/N retrial queue with finite-position buffer. The behavior of the system is described in terms of continuous time multi-dimensional Markov chain. Arriving type I calls find all servers busy and join the buffer, if the positions of the buffer are insufficient, they can go to orbit. Arriving type II calls find all servers busy and join the orbit directly. Each server can provide two types heterogeneous services with Phase-type (PH) time distribution to every arriving call (including types I and II calls), arriving calls have an option to choose either type of services. The model is quite general enough to cover most of the systems in communication networks. We derive the ergodicity condition, the stationary distribution and the main performance characteristics of the system. The effects of various parameters on the system performance measures are illustrated numerically. |
| Keywords: | retrial queue batch Markov arrival process PH distribution buffer |
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