This paper investigates a discrete-time GI/D-MSP/1/\infty queueing system under N-policy with renewal input. The service process is correlated and its structure is constructed through discrete-time Markovian service process. The idle server resumes to serve the customers as soon as the number of waiting customers in the queue reaches a predefined threshold value N and serves the customers exhaustively until the system becomes empty. We use the matrix-geometric method to derive the system-length distribution at prearrival epoch. Employing the Markov renewal theory, we obtain the system-length distribution at random epoch. We also carried out the system-length distributions at outside observer’s, intermediate and post-departure epochs. Further, we find the waiting-time distribution in the queue measured in slots of an arrival customer. An expected linear cost function per unit time is considered to determine the optimal value of N, which minimises the expected cost function. Some numerical results are demonstrated to measure the effects of N, interarrival-time distributions and other model parameters.

本文研究了具有更新输入的N策略下的离散时间GI / D-MSP / 1 / \ infty排队系统。服务过程是相关的，其结构是通过离散时间马尔可夫服务过程构造的。队列中等待的客户数量达到预定义的阈值N时，空闲服务器即恢复为客户服务，并彻底为客户服务，直到系统变空。我们使用矩阵几何方法来得出到达前时期的系统长度分布。利用马尔可夫更新理论，我们获得了随机纪元的系统长度分布。我们还在外部观察者，中间和出发后时期进行了系统长度分布。此外，我们在到达客户的插槽中找到的队列中找到等待时间分布。考虑每单位时间的预期线性成本函数来确定N的最佳值，这将使预期成本函数最小化。一些数值结果被证明可以测量N的影响，到达时间的分布和其他模型参数。