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

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.