具有N个有限容量服务节点的 Jackson 排队网络

The Jackson Queueing Networks with N Service Nodes of Finite Capacity

对于多级（Ｎ＞２）串联排队系统，在一般文章中都是在有关分布全是指数分布的假设下，用近似的方法求出有关排队指标分布的近似解．而在周家良和贾波已发表的文章中，在有关分布都是相位型分布的假设下，运用马尔可夫过程的状态空间及Ｑ矩阵的递推表示方法，富有技巧性地求得了多级串联、串联反馈、并联排队系统有关排队指标稳态分布的显式精确解．文中将此技巧进一步推广用来求出具有Ｎ个有限容量服务节点的Ｊａｃｋｓｏｎ排队网络有关排队指标的稳态分布显式精确解，由于显式解的计算只涉及矩阵运算，适合于在计算机上计算，故便于应用．

For multistage(N>2) tandem queueing system, the approximate solution of the distribution of the related queueing index is usually obtained in literatures, by the method of approximation, under the assumption that all relavant distributions are exponential. But in the papers written by the present authors under the assumptions that all relavant distributions are phasetype, the precise explicit solution of the stable distribution of the multistage tandem queue, the tandem queue feedback and the parallel queueing system is provided by using the techniques of the vecursive expression of the statespace and the generator matrix of Markov process. This technique is further generalized in this paper to solve the precise explicit solution of the stable distribution of the Jackson queueing networks with N service nodes. Since the operation of matrix and recursion is easy to perform on computers, the method proposed in this paper can be conveniently applied.