Quick Detection of Changes in Tra c Statistics : Application to Variable Rate Compression 1

In many communication applications, sources generate data at a variable rate. This variation can be captured by a two-level model. At a larger time scale, the source alternates between a nite number of models at the higher level, while each model represents the local uctuation at the smaller time scale. Typically the data goes through a lossy compression at the encoder, and then is entered into a buuer before being transmitted over a xed-rate or a regulated-rate (e.g., Leaky Bucket) channel. Since the buuer size is nite, the choice of compression parameters must balance the tradeoo between the distortion due to lossy compression and the distortion caused by buuer overrow. As the optimal compression parameters may be diierent for each individual model, a method is needed to detect changes from one model to another. We show via examples that for many common traac models, the problem of detecting changes in traac statistics can be reduced to the following general change point detection problem: Let A 1 ; A 2 ; : : : be a series of independent observations such that A 1 ; A 2 ; : : :; A m?1 are i.i.d. distributed according to an unknown distribution F, and A m ; A m+1 ; : : : are i.i.d. distributed according to another unknown distribution G. m is the unknown change point. The objective is to determine that a change has occurred as soon as possible, while maintaining a low rate of false alarms. In this paper we propose a sequential nonparametric change point detection algorithm using Kolmogorov-Smirnov statistics, and demonstrate that it is asymp-totically optimal, in that under the constraint Etime until a false alarm] T, our algorithm is such that Edetection delay] = O(log(T)), as T ! 1. This property is known to be the best that can be achieved. Furthermore, unlike other nonparamet-ric schemes, the performance of the algorithm is independent of the distributions F and G.