Modeling local stationary behavior of Internet traffic

Abstract

Non-stationary behavior of aggregated IP traffic patterns was demonstrated in a number of studies. However, none of those did either consider practical aspects of this phenomenon or propose suitable model to capture it. Searching for model for IP traffic aggregates we introduce the concept of local stationarity and demonstrate that it allows to model traffic patterns measured in high-speed operational networks. The proposed model is on-line in nature and suitable for real-time estimation of the traffic state in terms of piecewise covariance stationary stochastic process. As a basic tool of the model we use change-point statistical test allowing us to dynamically and automatically determine whether statistical characteristics of the traffic pattern changes and, if so, estimate new parameters of the traffic pattern. We provide numerical examples and discuss applications of the proposed model that include but not limited to dynamic resource reservation, routing with guaranteed bandwidth, etc.