延迟多重休假离散时间的Geom^x/G/1可修排队系统—一些排队指标

The Discrete Time Geom^x/G/1 Repairable Queueing System with Delay Multiple Vacations——Some Queueing Indices

该文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,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,通过引进"服务员忙期"和使用全概率分解技术,从任意初始状态i(i=0,1,…)出发,研究了系统在任意时刻队长的瞬态性质,导出了队长瞬态分布的Z-变换,其次研究了系统在任意时刻队长的稳态分布,获得了稳态分布的递推表达式,进一步也得出了系统稳态队长的随机分解结果.特别地,通过该文可直接获得一系列特殊的离散时间排队系统相应的结果.

This paper firstly considers the discrete time Geom^x｜G｜1 repairable queue system with delay 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 introducing the server busy period and using the total probability decomposition technique we discuss the transient properties of the queue length from the beginning of any initial state i（i=0,1,…）,and obtain the z-transformation of the transient distribution of the queue length.Furthermore,we obtain the recursion expressions of the steady distribution and the stochastic decomposition of the queue length at a random point in equilibrium.Especially we can obtain some corresponding results of the discrete queue system under some special cases.