| Erlang消失系统空闲服务台的利用 |
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| 引用本文： | 田乃硕,马占友,刘洺辛. Erlang消失系统空闲服务台的利用[J]. 工程数学学报, 2007, 24(4): 677-684 |
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| 作者姓名： | 田乃硕 马占友 刘洺辛 |
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| 作者单位： | 燕山大学理学院,秦皇岛,066004;燕山大学信息科学与工程学院,秦皇岛,066004 |
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| 摘 要： | 本文研究Erlang消失系统中空闲服务台的利用,该系统中有两类顾客,一类有抢占型优先权,并且是消失的;另一类可排队等待,并有无限等待空间。使用拟生灭过程和矩阵几何解,给出系统稳定的充分必要条件,第一类顾客消失概率、第二类顾客的队长和等待时间分布。数值例子解释了系统性能指标与参数之间的关系。
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| 关 键 词： | 消失系统 抢占型优先权 拟生灭过程 矩阵几何解 等待时间 |
| 文章编号： | 1005-3085（2007）04-0677-08 |
| 修稿时间： | 2005-06-28 |
The Utilization of Idle Servers in Erlang's Loss Queueing System |
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| TIAN Nai-shuo,MA Zhan-you,LIU Ming-xin. The Utilization of Idle Servers in Erlang's Loss Queueing System[J]. Chinese Journal of Engineering Mathematics, 2007, 24(4): 677-684 |
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| Authors: | TIAN Nai-shuo MA Zhan-you LIU Ming-xin |
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| Affiliation: | 1. College of Sciences, Yanshan University, Qinhuangdao 066004; 2. College of Information Science and Engineering, Yanshan University, Qinhuangdao 066004 |
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| Abstract: | In this paper, we study the utilization of idle servers in Erlang's loss queueing system. In the system, there are two kinds of customers. The first kind of customers with the preemptive priority is lossy and the second kind of customers has infinite waiting space for queueing. By applying the quasi birth and death process and matrix geometric solution, the necessary and sufficient conditions are derived for the stationarity of the system and the loss probability of the first kind of customers. Meanwhile, we get the queue length distribution and the waiting time distribution of the second kind of customers. Finally, we explain the relationship of system performance indices and parameters by numerical examples. |
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| Keywords: | loss queueing system preemptive priority quasi birth and death process matrix geometric solution the waiting time |
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