| PH/M/c可修排队系统 |
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| 引用本文： | 岳德权,李兰巧,祁洪娟.PH/M/c可修排队系统[J].数学的实践与认识,2010,40(8). |
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| 作者姓名： | 岳德权 李兰巧 祁洪娟 |
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| 作者单位： | 燕山大学理学院,河北秦皇岛,066004 |
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| 基金项目： | 国家自然科学基金(70671088) |
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| 摘 要： | 研究了一个修理工和c个服务台的可修排队系统.假设顾客的到达过程为PH更新过程,服务台在忙时与闲时具有不同的故障率.顾客的服务时间、服务台的寿命以及服务台的修理时间均服从指数分布.通过建立系统的拟生灭过程,得到了系统稳态分布存在的充要条件.利用矩阵几何解方法,给出了系统的稳态队长.在此基础上,得到了系统的某些排队论和可靠性指标.
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| 关 键 词： | 可修排队 拟生灭过程 矩阵几何解 稳态条件 稳态队长 PH分布 |
PH/M/c Queueing System with Unreliable Servers |
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| YUE De-quan,LI Lan-qiao,QI Hong-juan.PH/M/c Queueing System with Unreliable Servers[J].Mathematics in Practice and Theory,2010,40(8). |
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| Authors: | YUE De-quan LI Lan-qiao QI Hong-juan |
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| Institution: | YUE De-quan,LI Lan-qiao,QI Hong-juan (College of Science,Yanshan University,Qinhuangdao 066004,China) |
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| Abstract: | In this paper,we study a queueing system with a repairman and c unreliable servers.It is assumed that the arrival process of customers is a PH renewal process,and servers have different failure rates during the busy period and the idle period.The service time of customers,the lifetime and the repair time of servers follow exponential distributions. By establishing the quasi-birth-and-death process of the system,we obtain the necessary and sufficient condition that the steady state distribution of the system... |
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| Keywords: | queue with unreliable servers quasi-birth-and-death process matrix-geometric solution steady-state condition steady-state queueing length PH distribution |
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