Dependence Analysis Among Service Stations in Tandem Queueing Systems

Abstract

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.

Keywords

• tandem queueing system|dependence|performance ratio|waiting time|simulation