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Stationary analysis of a discrete-time GI/D-MSP/1 queue with multiple vacations

机译：具有多个休假的离散时间GI / D-MSP / 1队列的平稳分析

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This paper analyzes the steady-state behavior of a discrete-time single-server queueing system with correlated service times and server vacations. The vacation times of the server are independent and geometrically distributed, and their durations are integral multiples of slot duration. The customers are served one at a time under discrete-time Markovian service process. The new service process starts with the initial phase distribution independent of the path followed by the previous service process when the server returns from a vacation and finds at least one waiting customer. The matrix-geometric method is used to obtain the probability distribution of system-length at prearrival epoch. With the help of Markov renewal theory approach, we also derive the system-length distribution at an arbitrary epoch. The analysis of actual-waiting-time distribution in the queue measured in slots has also been carried out. In addition, computational experiences with a variety of numerical results are discussed to display the effect of the system parameters on the performance measures.
机译：本文分析了具有相关服务时间和服务器休假的离散时间单服务器排队系统的稳态行为。服务器的休假时间是独立的，并且是几何分布的，并且它们的持续时间是插槽持续时间的整数倍。在离散时间的马尔可夫服务过程中，一次为客户提供服务。当服务器从休假返回并找到至少一个等待的客户时，新的服务过程从初始阶段分布开始，而与初始服务过程所遵循的路径无关。矩阵几何方法用于获得到达前时期系统长度的概率分布。借助马尔可夫更新理论方法，我们还可以得出任意时期的系统长度分布。还对在时隙中测量的队列中的实际等待时间分布进行了分析。此外，还讨论了具有各种数值结果的计算经验，以显示系统参数对性能指标的影响。

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