延迟多重休假离散时间的Geom^x/G/1可修排队系统的可靠性指标

Some reliability indices in discrete time Geom^x/G/1 repairable queueing system with delayed multiple vacations

首次考虑延迟多重休假离散时间成批到达的Geom^x/G/1可修排队系统的可靠性指标,在假定到达间隔时间和服务台的寿命服从几何分布,而服务时间、延迟休假时间、休假时间和服务台失效后的修理时间均服从一般离散分布下,使用一种新的分解方法讨论了服务台如下的可靠性问题:1)在时刻n服务台处于"广义忙期"的概率;2)服务台的瞬态和稳态不可用度;3)服务台在(0,n]时间内的平均失效次数;4)服务台在"广义忙期"内的平均失效次数.得到了一系列重要的可靠性结果.

This paper firstly considers some reliability problems in the discrete time Geom^x/G/1 repairable queueing system with delayed multiple vacations. It＇s assumed that both the inter-arrival times and the life of the service station are independent random variables with geometric distribution, while the service time, the delayed vacation time, the vacation time and the .repair time have general discrete distribution. By using a new kind of analytic approach-the decomposition method the following reliability indices of the service station are discussed： 1） The probability that the service station is during the ＂generalized busy period＂; 2）The point unavailability at timenand the steady unavailability; 3） The expected failure number during （0, n]; 4） The expected failure number during the ＂generalized busy period＂. A series of important reliability results are obtained.