带启动-关闭期和N策略的多重休假M/G/1排队

M/G/1 Multiple Vacation Queue with Set-up and Close-down Period and N-policy

研究多重休假带启动-关闭期和N策略的M/G/1排队系统,根据嵌入Markov链的方法推导出状态转移概率矩阵,利用M/G/1型排队系统结构矩阵解析法,得出顾客服务完离去后系统稳态队长分布及其母函数的表达式;从而由经典随机分解原理,给出稳态队长的随机分解结果.此外,利用LST变换处理卷积,得到忙期的母函数及数学期望的表达式;进而得到忙期、启动期和关闭期的母函数及在稳态下服务员处于各状态的概率.最后提出一些数值例子以验证结论.

this paper is concerned with a continuing time rnultiple vacation of M/G/1 queue with set-up and close-down period and N-policy. With regarding customer immediate leaving and the numbers of customers in the system, the Markov chain imbedded in the time that customer immediate leaving and its transition probability matrix were given. By using the analytic method of M/G/1 structure matrix, stochastic decomposition properties of the queue length and the average length were obtained. Meanwhile, we show the generating function of the busy period, set-up period and close-down period, we calculate the probability which the server is in various in the steady-state situation. Finally some numerical examples are presented.