Hierarchical Traffic Matrices: Axiomatic Foundations to Practical Traffic Matrix Synthesis

The traffic matrix of a network is useful in a variety of applications: network planning and forecasting, traffic engineering and anomaly detection. Much work has focused on estimating traffic matrices, but methods are often tested on limited data. There is then the possibility of unrepresentativeness of the datasets, and the lack of generalizability of the subsequent results. Synthesis can help alleviate this problem. In this paper, we examine a fundamental question: what constitutes a good class of statistical models for traffic matrix synthesis? The results of our study is the definition of a set of axioms specifying structure on traffic matrix models, including the incorporation of organizational structure (hierarchies) in network traffic. We introduce the Hierarchical Traffic Matrix (HTM) which satisfies these requirements. We then study the hierarchical structure of the GEANT network, a research network based in Europe, to validate our ideas. Finally, we illustrate how structure in traffic matrices can affect network topology design.