Solution space of loss tomography

Loss tomography aims to obtain the loss rate of each link in a network by end-to-end measurement. Based on loss rates we can understand the traffic flows and identify bottlenecks. All methods proposed so far rely on statistical inference to achieve this goal, and most of them are based on maximum likelihood to infer hidden information. However, there is a lack of studying the solution space of the inference, which may create uncertainty for the loss rates identified by the maximum likelihood approach since the solution identified could trap to a local maximum. In this paper, we reformulate the inference process into a nonlinear programming problem and concentrate on studying the solution space of the non-linear programming problem. We find when losses occurred on a link is modeled as Bernoulli process, the solution space is concave, which ensures an iterative approximating algorithm can identify the global maximum.