On the Variance Reduction Property of Buffered Leaky Bucket

Abstract

In this paper, we formalize the intuition that the Leaky Bucket (LB) smooths traffic. By sample path comparisons we show that the interdeparture times of the traffic through a LB are more even than the interarrival times of the original traffic in terms of majorization. We also prove that in steady state, the inter- departure time is smaller than the interarrival time in the sense of convex ordering. This leads to the conclusion that the coefficient of variation of the inter-departure time is smaller than that of the inter-arrival time.