We consider a single server queueing-inventory system under (s,Q) replenishment strategy with working vacations, vacation interruptions and lost sales. The server provides service at a lower rate during working vacations than while in normal mode of service. If a working vacation realizes while providing service in that mode, then the server continues in the present status until the current service is completed. Upon that it switches to the normal mode of service, provided there is at least one customer waiting. If no customer is waiting at this point of time, it goes for vacation. We also assume that if there are customers in the system at a service completion epoch during a working vacation, the server will come back to the normal working mode, otherwise the server will stay in the working vacation mode. With the system having infinite capacity, the stability condition for the system is obtained, followed by computation of the steady-state probability vector and discussion. Various performance measures are evaluated. In addition, the busy period analysis is provided and the stationary waiting time distribution in the queue is derived. Numerical illustrations are provided to illustrate the system performance, and an optimization problem is also discussed.

我们考虑（s，Q下的单个服务器排队库存系统）具有工作假期，假期中断和销售损失的补货策略。与在正常服务模式下相比，服务器在工作假期期间以较低的速率提供服务。如果在以该模式提供服务的同时实现了工作假期，则服务器将继续处于当前状态，直到当前服务完成为止。如果有至少一位客户在等待，它将切换到正常服务模式。如果此时没有客户在等待，那就去度假。我们还假定，如果在工作休假期间系统中有客户处于服务完成时期，则服务器将恢复到正常工作模式，否则服务器将保持工作休假模式。利用容量无限的系统，可以获得系统的稳定性条件，然后计算稳态概率向量并进行讨论。评估了各种性能指标。另外，提供繁忙时段分析，并得出队列中的固定等待时间分布。提供了数字插图以说明系统性能，并讨论了优化问题。