服务速率呈线性增长、带休假策略的M/M/5/m排队模型

M/M/5/m Queuing Model with Linear Growth of Service Rate and Vacation Strategy

基于不同服务速率的休假排队模型在实际生活中处处可见,对它的研究具有一定的应用价值,比如银行、食堂、体检中心、加油站,售票厅、快递站等,可为提高国民经济效益和顾客服务满意度提供一定的帮助。文章运用拟生灭过程、矩阵几何解等理论方法,确立状态转移图、无穷小生成元、转移概率矩阵,建立可变服务下带休假策略的排队模型,得出模型的主要指标。

Vacation queuing model based on different service rates can be seen everywhere in real life. It has certain application value for its research, such as bank, canteen, physical examination center, gas station, ticket office, express station, etc. It can provide certain help for improving national economic benefits and customer service satisfaction. By using the theory of Quasi-Birth-Death process and matrix geometry solution, the state transition graph, infinitesimal generator and transition probability matrix were established, and the queuing model with vacation strategy under variable service were established, the main indicators of the model are obtained.