Bernoulli机制下具有不耐烦顾客和多重休假的排队系统

On a queue with impatient customers and multiple vacations under Bernoulli schedule

考虑Bernoulli机制下具有两类穷尽多重休假的M/M/1排队系统。当正规服务结束且系统变空时,服务台总是进行经典多重休假或多重工作休假。在经典休假期内,由于得不到服务,顾客会选择几何放弃的方式离开系统。对于该系统,首先得到了平稳概率分布和一些性能测度;其次讨论了系统队长的随机分解性;第三分析了在正规忙期开始时刻系统队长分布和忙循环。

This paper treats an M/ M/ 1 queue with two types of exhaustive multiple vacations under Bernoulli schedule. The server always takes classical multiple vacations or multiple working vacations when the system becomes empty after a normal service completion. Moreover, during classical vacation period, customers may choose to leave the system according to geometric abandon-ments because of no service available. For this model, we firstly obtain the stationary probability distribution and some performance measures of interest. Secondly, we discuss the stochastic decomposition of the system size. Thirdly, we analyze the system size dis-tribution at the initial epoch of a regular busy period and busy cycle.