对M/T-SPH/1排队平稳指标的进一步研究——数值计算与渐近分析  

Further study for stationary indices of M/T-SPH/1 queue--numerical calculation and tail asymptotic

作　　者：张宏波 ZHANG Hong-bo(School of Statistics and Mathematics,Henan Finance University,Zhengzhou 450046,China)

机构地区：[1]河南财政金融学院统计与数学学院,河南郑州450046

出　　处：《高校应用数学学报（A辑）》2021年第1期1-8,共8页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：河南省科技攻关计划(172102210242)。

摘　　要：讨论M/T-SPH/1排队平稳队长分布的数值计算,以及平稳队长和逗留时间分布各阶矩的数值计算及渐近分析.其中T-SPH表示可数状态吸收生灭链吸收时间的分布.在分布PGF和LST的基础上,首先给出了计算平稳队长分布,平稳队长以及逗留时间分布各阶矩的数值结果的递推公式.其次还讨论了平稳队长及平稳逗留时间分布各阶矩的尾部渐近特征.结果表明当参数取不同值时,两个指标尾部具有三种不同类型的衰减方式.最后还用数值例子检验了方法的有效性.This paper considers numerical computation for stationary queue length distribution,numerical computation and tail asymptotics for moments of stationary queue length and sojourn time for M/T-SPH/1 queue,where T-SPH denotes the discrete-time phase type distribution defined on a birth and death process with countably many states.By analysis of probability function and Laplace-Stieltjes transform,recursive formulas for queue length and moments of queue length and sojourn time are given.Moreover,exact tail asymptotic characterizations for moments of queue length and sojourn time are also obtained,the results show that there are three types of exact tail asymptotics for such two indices in different regions.Finally,numerical examples are also given to show the effectiveness of the method.

关 键 词：M/T-SPH/1排队 平稳指标 尾部特征 数值计算 生成函数 

分 类 号：O226[理学—运筹学与控制论]