Network Tomography based on Adaptive Measurements in Probabilistic Routing

We discuss Boolean network tomography in a probabilistic routing environment. Although the stochastic behavior of routing can be found in load balancing mechanisms and normal routing protocols, it has not been discussed much in network tomography so far. In probabilistic routing, because monitoring paths are not uniquely determined, a huge number of measurements are generally required to identify the network state. To overcome this difficulty, we propose a network tomography method for efficiently narrowing down the states with a limited number of measurements by iteratively updating the posterior of the states. In this method, we introduce mutual information as a measure of the effectiveness of the probabilistic monitoring path. This enables us to prioritize measurements that are critically effective in identifying the state, thus significantly reducing the number of required measurements. We show that our method has a theoretical guarantee of the approximation ratio (1 – 1/e) on the basis of submodularity analysis. Numerical evaluations show that our method can identify the network states with far fewer measurements than existing methods.