Towards a meaningful MRA of traffic matrices

Abstract

Most research on traffic matrices (TM) has focused on finding models that help with inference, but not with other important tasks such as synthesis of TMs, traffic prediction, or anomaly detection. In this paper we approach the problem of a general model for traffic matrices, and argue that such a model must be sparse, i.e., have a small number of parameters in comparison to the size of the TM. A Multi-Resolution Analysis (MRA) of TMs can provide such a sparse representation. The Diffusion Wavelet (DW) transform is a good choice as a MRA tool here, because it inherently adapts to the structure of the underlying network. The paper describes our construction of the two-dimensional version of the DW transform and shows how to use it for our proposed MRA of TMs. The results obtained with operational networks confirm the sparseness of the DW-based TM analysis approach and its applicability to other TM-related tasks.