Mean Waiting Time Approximation Analysis Of Tandem Queueing Systems Based On Performance Ratio

A typical system in queueing theory of tandem queueing system is the basic structure of queueing network.However,it is difficult to accurately calculate the mean queueing time of a tandem queueing system whose service time follows the general distribution,except for the tandem queueing system with Markov property or constant service time.In real life,the service time of the tandem queueing system is generally distributed.In order to accurately approximate the mean queueing time of each station in the tandem queueing systems,we propose to characterize the dependence between the stations in the tandem queueing systems with performance ratio.By observing the relationship between the performance ratio and system parameters of the system,the numerical characteristics of the performance ratio is figured out.An approximate fitting expression of the performance ratio for the tandem queue with general service times is obtained by a linear combination of the theoretical value of the performance ratio with constant service times and exponential distributed service time.Then,an approximation method is proposed for the mean queueing time of the bottleneck stations in the system,and finally the average queue time of each station is estimated.Numerical experiments show that the approximation method based on the performance ratio performs well to estimate the mean queueing time of the tandem queue system.