一类休假的Geo~X/G/1可修排队的可靠性分析

考虑单重休假、Bernoulli反馈和可变输入率的离散时间Geo~X/G/1可修排队.顾客的批到达速率与服务器的休假有关.刚服务完的顾客以概率1-θ进入队列寻求下次服务.服务器在服务过程中可能故障需修复后再继续工作.借助更新过程理论、z变换和一种分解法,研究了时刻n+位于服务器忙期的条件概率、服务器的瞬态和稳态不可用度以及(0~+,n~+]时间内服务器的平均故障次数和稳态故障频度,揭示了这类离散时间可修排队中服务器可靠性指标的结构,得到了一些特殊可修排队的可靠性结果.最后通过数值实例分析了系统参数对服务器可靠性指标的影响.

Reliability analysis of a kind of GeoX/G/1 repairable queue with vacation

This paper considers a discrete-time Geo^X/G/1 repairable queue with single vacation, Bernoulli feedback and variable input rate. The batch arrival rate of the customers has something to do with server vacation. The customer who has just been served may come back to the queue with probability 1-θ for a next service. The server may break down in the process of service and does not continue to work until it is repaired. By the theory of renewal process, z-transform and a decomposition method, the reliability indices of server, including the conditional probability that the epoch n⁺ is in server busy period, the transient and steady state availabilities, the expected failure number during (0⁺,n⁺] and steady-state failure frequency, are studied. The structure of server reliability indices in this type of discrete-time repairable queue is revealed. The reliability results for some special repairable queues are obtained. Finally, by means of numerical examples, the effects of system parameters on the reliability indices of server are analyzed.