用于求解休假排队网络稳态分布的预处理GMRES法  

Preconditioner GMRES Method for Solving Steady State Distribution of Vacation Queueing Networks

作　　者：杨淑伶[1] 

机构地区：[1]广东工业大学应用数学学院,广州510090

出　　处：《工程数学学报》2015年第3期391-396,共6页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金青年基金(11101095)~~

摘　　要：休假排队网络的稳态分布的计算在众多应用领域具有非常重要的意义,稳态分布向量可通过求解一个奇异的线性系统来得到.但由于该线性系统维数巨大且结构复杂,不易直接求解,本文提出了一种带分块下三角预处理算子的GMRES迭代法求解该系统.该预处理GMRES法具有易于构造且快速收敛的优点.数值试验的结果验证了该算法的优越性.The determination of the steady-state distribution of the vacation queuing, network is very important in many applications. The steady-state distribution vector can be obtained by solving a singular linear system. However, it is difficult to solve this system directly due to its huge size and complicated structure. A GMRES iterative method with a block lower trian- gular matrix preconditioner is proposed in this paper to solve this system. The preconditioner GMRES method has the advantages of easy construction and rapid convergence. Numerical examples demonstrate the superiority of the proposed algorithm.

关 键 词：排队网络 休假 QBD过程 预处理GMRES法 

分 类 号：O226[理学—运筹学与控制论] O242[理学—数学]