摘要
这篇论文从可靠性研究的观点与不可靠的加油站和多重适应推迟的假期认为排队的分离时间的 GeoX/G/1 是模型。后面的问题将被讨论：1 ) 服务者在在时间 n 的一个概括忙时期的概率；2 ) 加油站在在时间 n 的失败的概率，即，加油站的短暂 unavailability，和加油站的稳定的州的 unavailability；3 ) 加油站失败的期望的数字在时间间隔期间(0， n ] ，并且加油站的稳定的州的失败频率；4 ) 加油站故障在的期望的数字一概括的服务者忙碌时期。最后，作者证明有不可靠的加油站的一些普通分离时间的排队模型是在这篇论文讨论的模型的特殊情况。
This paper considers the discrete-time GeoX/G/1 queueing model with unreliable service station and multiple adaptive delayed vacations from the perspective of reliability research. Following problems will be discussed： 1） The probability that the server is in a ＂generalized busy period＂ at time n; 2） The probability that the service station is in failure at time n, i.e., the transient unavailability of the service station, and the steady state unavailability of the service station; 3） The expected number of service station failures during the time interval （0, hi, and the steady state failure frequency of the service station; 4） The expected number of service station breakdowns in a server＇s ＂generalized busy period＂. Finally, the authors demonstrate that some common discrete-time queueing models with unreliable service station are special cases of the model discussed in this paper.
基金
supported in part by the National Natural Science Foundation of China under Grant Nos. 71171138,70871084
the Specialized Research Fund for the Doctoral Program of Higher Education of China under Grant No.200806360001
关键词
离散时间
可靠性指标
服务站
延误休假
排队系统
自适应
延迟
排队模型
Delayed vacation policy, discrete-time queueing model, failure frequency, reliability index,total probability decomposition, unavailability, unreliable.
