服务员假期中以概率p进入的M/G/1排队系统的随机分解

The Stochastic Decomposition for M/G/1 Queue with p-Entering Discipline During Server Vacations

该文研究 M/G/1多重休假排队系统 ,其中在服务员休假中到达顾客以概率 p( 0≤p≤ 1 )进入 .通过引进“服务员忙期”和使用拉普拉斯变换或拉普拉斯——司梯阶变换 ,我们获得队长瞬态分布的拉普拉斯变换和稳态分布的递推表达式 ,进一步得到稳态队长分布的随机分解和在特殊情况下相应的一些结果 .

This paper considers the M/G/1 queueing system with server vacations in which the customers who arrive during server vacations enter the system with probability p(0≤p≤1) . By introducing the server busy period and using the Laplace or Laplace Stieltjes transform, both the recursion expression of the Laplace transform of the transient distribution and the recursion expression of the equilibrium distribution for the queue length are obtained. Furthermore, the stochastic decomposition of the queue length at a random point in equilibrium and some corresponding results under special cases are also given.