Statistical Methodology for Approximating G/G/1 Queues by the Strong Stability Technique

We consider a statistical methodology for the study of the strong stability of the M=G=1 queueing system after disrupting the arrival flow. More precisely, we use nonparametric density estimation with boundary correction techniques and the statistical Student test to approximate the G=G=1 system by the M=G=1 one, when the general arrivals law G in the G=G=1 system is unknown. By elaborating an appropriate algorithm, we effectuate simulation studies to provide the proximity error between the corresponding arrival distributions of the quoted systems, the approximation error on their stationary distributions and confidence intervals for the difference between their corresponding characteristics.