一类休假排队平稳队长的数值计算与渐近分析  

Numerical Computation and Tail Asymptotic for Queue Length of a Vacation Queue

作　　者：张宏波 史定华[2] ZHANG HONGBO SHI DINGHUA(School of Mathematics and Statistics, Henan Institute of Finance and Banking, Zhengzhou 450046, China School of College, Shanghai University, Shanghai 200444, China)

机构地区：[1]河南财政金融学院数学与统计学院,郑州450046 [2]上海大学理学院,上海200444

出　　处：《应用数学学报》2017年第5期770-780,共11页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(61174160);河南省科技攻关计划项目(172102210242);河南省高等学校青年骨干教师(2014GGJS-136);河南省高等学校重点科研(16A110002)资助项目

摘　　要：本文讨论休假时间服从T-SPH分布的M/M/1休假排队平稳附加队长分布的数值计算以及尾部渐近特征,其中T-SPH表示可数状态吸收生灭过程吸收时间的分布.在分布PGF的基础上,得到了多重休假和单重休假两种情形平稳附加队长以及队长各阶阶乘矩的迭代公式和渐近公式,并用数值例子检验了方法的有效性.This paper considers numerical computation and tail asymptotic for stationary additional queue length of M/M/1 queue with T-SPH vacation, where T-SPH denotes the continue-time phase type distribution defined on a birth and death process with countably many states. By analysis of probability generating function, for both single vacation and multiple vacations, recursive and asymptotic formulas for additional queue length and factorial moments are obtained. Moreover, numerical examples are also given to show the effectiveness of the method.

关 键 词：休假排队 无限位相分布 平稳队长 阶乘矩 渐近分析 

分 类 号：O226[理学—运筹学与控制论] O171[理学—数学]