基于指标比对串联排队系统平均排队时间的近似方法

串联排队系统是构成排队网络的基本结构,但是除了满足马尔可夫性或服务时间为常数的串联排队系统外,一般的串联排队系统的平均排队时间难以精确计算。为了刻画串联排队系统各个站之间的关联性,本文提出指标比的概念,基于指标比对系统的平均排队时间进行研究;通过分析指标比的数值特性,得到指标比的拟合表达式,进而对系统下游工作站的平均排队时间提出近似方法。数值实验结果显示,本文提出的近似方法对串联排队系统平均排队时间的估计效果较好。

Mean Waiting Time Approximation of Tandem Queueing Systems Based on Performance Ratio

The tandem queueing system is a basic structure of queueing networks. However, it is hard to accurately calculate the mean waiting time of the general tandem queueing system except for the tandem queues with the Markov property or constant service times. To characterize the dependence among stations in the tandem queues, this paper proposes the concept of performance ratio to study the mean waiting time. By analyzing the numerical properties of performance ratio, the fitting function of the performance ratio is achieved with which the mean waiting time of the downward station in the tandem queue is approximated. As a result, numerical experiments show that the approximation method based on the performance ratio performs well.