本文研究了$\left({s, S}\right)$ 库存策略的多服务台排队库存系统, 其中库存为空时有部分服务台同步多重休假, 休假时间服从指数分布。顾客到达为泊松过程, 每个服务台的服务时间和补货时间均服从指数分布。利用拟生灭过程和矩阵几何解法, 计算了系统稳态概率和一些性能指标, 并给出了系统单位时间的平均费用函数。最后, 通过数值算例分析了参数对费用函数的影响, 并得到最优库存策略和最优平均费用。

In this paper, we consider a Markovian $\left({s, S}\right)$ queueing-inventory system in which only partial servers take multiple synchronous vacations when the on-hand inventory level is zero. It is assumed that the vacation time follows an exponential distribution. The customers arrive according to a Poisson process, and the service time of the customers is distributed exponentially. The lead times for the orders are assumed to have independent and identical exponential distributions. Using the theory of quasi-birth-and-death process, the matrix-geometric solution of the steady-state probability is derived. On this basis, the steady-state performance measures and cost function of the system are obtained. Finally, the effect of the parameters on cost function is analyzed by numerical examples, and the optimal inventory policy and the optimal expected cost are also computed.