基于矩阵分析方法的具有双阶段休假的排队系统驱动的流模型性能分析

Stationary Analysis of a Fluid Queue Driven by M/M/1 Queue with Two-stage Vacations

基于矩阵分析方法研究了具有单重工作休假和多重休假策略M/M/1排队系统驱动的流模型.首先建立了控制该流模型的微分方程组,利用矩阵分析方法,得出了系统平稳库存量的laplace变换(LT)的矩阵阶乘表达式.进而利用LaplaceStieltjes变换(LST)得出了平稳库存量的期望.最后,通过数值例子展示了系统性能指标与参数的关系.

In this paper,we analyze a fluid queue driven by M/M/1 queue subject to twostage vacations policy that comprises single working vacation and multiple vacations.For such a fluid queue,we first establish sets of differential equations that governs this process,using the matrix geometric solution,we gain the Laplace transform of the joint steady state distribution of the fluid model in matrix factorial form.Then,we derive the explicit expression of the mean buffer content.At last,we present some numerical examples to illustrate the effects of system parameters on the stationary buffer content.