PH/M/1排队系统驱动的流模型

Fluid Model Driven by a PH/M/1 Queue

在流模型的研究中,传统的谱分析方法计算量极大,经常导致病态的数值结果.首先把PH/M/1排队系统的队长过程作为外部驱动环境,建立了一个新的流模型.其次,根据平衡条件给出流模型的稳态联合分布满足的矩阵微分方程,利用经典的Laplace变换(LT)方法给出稳态下缓冲器(库)的容量分布,进一步导出了稳态下的主要性能指标——平均缓冲器容量和空库概率的简洁表达式.最后,提出了数值例子展示了系统参数对性能指标的影响.

In the analysis of the fluid model, the conventional spectral method re- sults in ill-behaved numerical results owing to computation complexity. Firstly, a new fluid model driven by the queue length process of the PH/M/1 queue is framed. Secondly, the matrix differential equation satisfied by the stationary joint distribution of the fluid model is proposed based on the equilibrium condition. Using the classical Laplace transform （LT） method, the buffer content distribution is obtained. Further- more, the main performance indices, the expected buffer content and the probability of empty buffer content, are derived. Finally, the numerical examples are presented to demonstrate the effect of the system parameters on the performance indices.