中文摘要：

本文考虑Ⅳ策略单重休假M／G／1排队系统，通过引进“服务员忙期”和使用全概率分解技术，从任意初始状态出发，研究了队长的瞬态分布和稳态分布，首次导出了在任意时刻t瞬态队长分布的L变换的递推表达式和稳态队长分布的递推表达式，以及平稳队长的随机分解,特别地，通过本文可直接获得一些特殊排队系统相应的结果．

英文摘要：

We consider the M/G/1 queue with N- policy and single vacation. We study the transient and equilibrium distribution of the queue length from arbitrary initial condition. By introducing the server busy period and using the total probability decomposition technique we firstly derive the recursion expressions of the L- transformation of the transient queue length distribution and the equilibrium queue length distribution at any time t, and also stochastic decomposition of the queue length at a random point in equilibrium. Especially we can obtain some corresponding results under some especial cases.