In this article, we study a discrete-time MAP/PH/1 queue with finite system capacity and two-stage vacations. The two-stage vacations policy which comprises single working vacation and multiple vacations is featured by that once the system is empty during the regular busy period, the system first takes the working vacation during which the server can still provide the service but at a lower service rate. After this working vacation, if the system is empty, the server will take a vacation during which the server stops its service completely, otherwise, the server resumes to the normal service rate. For this queue, using the matrix-geometric combination solution method, we obtain the stationary probability vectors when the traffic intensity is not equal to one. In addition, we discuss the spectrum properties of the key matrices and give their decomposition results that can be used to reduce the computation loads. Further, waiting time is derived by constructing an absorbing Markov chain. Various performance measures are obtained. At last, some numerical examples are presented to show the impacts of system parameters on performance measures.

中文翻译：

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系统容量有限且两阶段休假的MAP / PH / 1队列的算法计算

在本文中，我们研究了具有有限系统容量和两阶段休假的离散时间MAP / PH / 1队列。包含单个工作休假和多个假期的两阶段休假策略的特征在于，一旦系统在正常繁忙时段内为空，系统将首先执行工作休假，在此期间服务器仍然可以提供服务，但服务水平较低率。在此工作休假后，如果系统为空，则服务器将休假，在此期间服务器将完全停止其服务，否则，服务器将恢复到正常的服务费率。对于此队列，使用矩阵-几何组合求解方法，获得交通强度不等于1时的平稳概率矢量。此外，我们讨论了关键矩阵的频谱特性，并给出了可用于减少计算负荷的分解结果。此外，通过构建吸收性马尔可夫链来得出等待时间。获得了各种性能指标。最后，通过一些数值例子说明了系统参数对性能指标的影响。