The significance of finite buffer edge effects in histogram measurements of queues

Abstract

The empirically oberved “fractal” or “self-similar” nature of packet traffic implies heavy tailed queue processes for such traffic. However, based on our simulation analysis using real network data as well as standard models, we have found that the actual losses sustained are remarkably lower than those suggested by the heavy tail distribution. This can be explained by an effect observed in the tail of the histogram of a finite buffer queue process, which we call “tail-raising”, which contains information pertinent to performance estimation. This effect is also responsible for a significant reduction in packet losses for finite buffer systems, than would be otherwise predicted by the buffer overflow probability for heavy-tailed queues. We define a new parameter X _B on the histogram of a queue process for a finite buffer system, to calculate the tail of the queue process based on the information available in the histogram on the finite buffer. We propose an estimator that approximates X _B , namely, X _min, which is measurable because of the tail-raising effect and has a robust measurement method. The proposed estimator shows promise as a good predictor for performance metrics of queueing systems. We propose an innovative packet loss ratio estimation technique which uses histogram measurements combined with a virtual buffer scheme to find and extrapolate the objective packet loss rate using a binning strategy for histogram measurement, namely, Symmetric Logarithmic Binning (SLB).