串联排队系统中各服务站间的关联性分析

Dependence Analysis Among Service Stations in Tandem Queueing Systems

串联排队系统中站与站之间存在关联性,深入分析串联排队系统中上游服务站对下游服务站的影响对研究串联排队系统性能具有重要意义。然而,串联排队系统上游服务站的输出过程通常是非更新过程,很难从理论上分析出各个站之间的关联性。文中利用指标比研究了串联排队系统各站间的关联性,通过大量的模拟实验,分析指标比与系统参数之间的关系。研究发现,上游服务站对下游服务站的平均排队时间有扩大或缩小效应。指标比是上游服务站服务时间的平方变异系数的增函数,当指标比大于1时,指标比是上游服务站与下游服务站平均服务时间之比的增函数;当指标比小于1时,指标比是上游服务站与下游服务站平均服务时间之比的减函数。因此,可以通过调整上游服务站的服务时间或平方变异系统来改变指标比,从而有效控制串联排队系统下游服务站的排队时间。

There is dependence among stations in tandem queueing systems.Deep analysis of the influence of the upward station on the downward station is important for studying of the performance of the tandem queueing systems.However,the departure process of the upward station is usually non-renewal process,which causes the dependence among stations is difficult to be analyzed theoretically.This paper adopts performance ratio to study the dependence among stations.By simulations,the relationship between performance ratio and system parameters are analyzed.It is found that the upward station could magnify or reduce the mean waiting time of the downward station.The performance ratio increases with the square variation coefficient of the service time at the upward station.When the performance ratio is greater than 1,it increases with the ratio of the mean service time of the upward station to the downward station.When the performance ratio is less than 1,it decreases with the ratio of the mean service time of the upward station to the downward station.The mean waiting time of the downward station could be changed by adjusting mean or square variation coefficient of the service time at the upward station.