Title: A Two-step Statistical Approach for Inferring Network Traffic Demands (Revises Technical Report BUCS-2003-003) Author: Alberto Medina, Kave Salamatian, Nina Taft, Ibrahim Matta, and Christophe Diot Date: March 1, 2004 Abstract: Accurate knowledge of traffic demands in a communication network enables or enhances a variety of traffic engineering and network management tasks of paramount importance for operational networks. Directly measuring a complete set of these demands is prohibitively expensive because of the huge amounts of data that must be collected and the performance impact that such measurements would impose on the regular behavior of the network. As a consequence, we must rely on statistical techniques to produce estimates of actual traffic demands from partial information. The performance of such techniques is however limited due to their reliance on limited information and the high amount of computations they incur, which limits their convergence behavior. In this paper we study a two-step approach for inferring network traffic demands. First we elaborate and evaluate a modeling approach for generating good starting points to be fed to iterative statistical inference techniques. We call these starting points {\it informed priors} since they are obtained using actual network information such as packet traces and SNMP link counts. Second we provide a very fast variant of the EM algorithm which extends its computation range, increasing its accuracy and decreasing its dependence on the quality of the starting point. Finally, we evaluate and compare alternative mechanisms for generating starting points and the convergence characteristics of our EM algorithm against a recently proposed Weighted Least Squares approach.