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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2015, Vol. 32 ›› Issue (3): 391-396.doi: 10.3969/j.issn.1005-3085.2015.03.008

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用于求解休假排队网络稳态分布的预处理GMRES法

杨淑伶   

  1. 广东工业大学应用数学学院，广州 510090
  • 收稿日期:2013-10-24 接受日期:2014-04-03 出版日期:2015-06-15 发布日期:2015-08-15
  • 基金资助:
    国家自然科学基金 (11101095).

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

YANG Shu-ling   

  1. Faculty of Applied Mathematics, Guangdong University of Technology, Guangzhou 510090
  • Received:2013-10-24 Accepted:2014-04-03 Online:2015-06-15 Published:2015-08-15
  • Supported by:
    The National Natural Science Foundation of China (11101095).

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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．

关键词: 排队网络, 休假, QBD过程, 预处理GMRES法

Abstract:

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 triangular 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.

Key words: queueing network, vacation, QBD process, preconditioner GMRES method

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