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中文摘要：
研究N-策略多重休假下，顾客是批量到达的M^x（G，Gm）／1排队模型。一旦系统空闲服务台就开始一个随机长度的休假，休假结束后，如果发现顾客数达到或超过N，就立即对顾客进行服务直到系统空闲，如果发现顾客数小于N，就进行下一阶段随机长度休假。服务台提供两阶段服务：第一阶段初步服务和第二阶段m种选择服务。在第一阶段初步服务结束后，顾客可以回到队列要求重新服务，也可以立即离开系统，或接受第二阶段m种选择服务中某一种服务。通过补充变量法得到了稳态下系统队长的概率母函数和其随机分解性质。进一步计算出系统稳态的队长及其他性能指标。
英文摘要：
The M^X/（G,Gm）/1 queue model with N-policy,multiple vacations and the feedback is investigated. Once the system empties, the server will leave for a vacation with random length. When the vacation is finished, and if the queue length is greater than N, the server will immediately begin to serve the customer until the system becomes empty. Otherwise the server will leave for another vacation. The server can provide two stage services,i, e. the first elementary service and the second multi-optional service. After the first elementary service ,the customer may rejoin the queue for re-service, or leave the system forever, or receive the second multi-optional services. A supplementary variable technique is used to obtain the probability generation function of the stationary queue size distribution and its decomposition law, the queue size and other performance index.
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