In the Internet, a statistical perspective of global traffic flows has been considered as an important key to network operations and management. Nonetheless, it is expensive or sometime difficult to measure statistics of each flow directly. Therefore, it is of practical importance to infer unobservable statistical characteristics of individual flows from characteristics of the aggregated-flows, which are easily observed at some links (e.g., router interfaces) in the network. In this paper, we propose a new approach to such inference problems based on finding an inverse function from (observable) probabilities of some states on aggregated-flows to (unobservable) probabilities of some states on flows on a discrete state model, and provide a method inferring arrival rate statistics of individual flows (the OD traffic matrix inference). Our method is applicable to cases not covered by the existing normal-based methods for the OD traffic matrix inference. We also show simulation results on several flow topologies, which indicate potential of our approach
