Performance and cost analysis of a Geom/G/1 (G, SV) system

In this paper, a gate service Geom/G/1 queue system with single vacation is analyzed. Firstly, a gate service policy and single vacation are introduced in detail, the expected number of customers in the system at the beginning instant of a service period is obtained. Next, the Probability Generating Function (P.G.F.) of the stationary queue length is obtained by using regeneration cycle approach. Then the P.G.F. of the waiting time is derived under the condition of the independence between the arrival process and the waiting time. Moreover, the P.G.Fs. of the service period, the vacation period and the idle period are obtained, and the mean length of three periods are also obtained. Cost model is formulated to determine the optimal expected vacation length. Finally, based on numerical results, the relations of the performance measures and traffic intensity are discussed.     

基于 Min($N,D,V$)——策略和单重休假的 $M/G/1$ 排队系统队长分布的瞬态和稳态解

本文主要研究服务员单重休假且在休假时间中根据 Min($N,D,V$)--控制策略可立即中断休假的 $M/G/1$ 排队系统．运用全概率分解技术和拉普拉斯变换工具,讨论在任意初始状态条件下队长的瞬态和稳态性质,得到了队长分布瞬态解的拉普拉斯变换表达式．在此基础上,直接获得了便于作数值计算的队长分布稳态解的递推表达式．进一步,给出了稳态队长的随机分解结构、附加队长分布的显示表达式,以及在一些特殊情形下的相应结果．最后,通过数值实例考察了附加队长分布对系统参数的敏感性,分析参数不同取值对系统运行性能的影响．