Solution space and its impact on loss tomography

Loss tomography aims to obtain the loss rate for each link in a network by end-to-end measurement. Based on loss rates we can understand the traffic flows and identify bottlenecks in a network. All methods proposed in the past rely on statistical inference to obtain loss rates from observations conducted at end nodes, and most of them are based on the maximum likelihood estimate to find a solution. However, there is a lack of studying the solution space of the statistical inference, which creates uncertainty for the loss rates identified by this approach since the solution could trap to a local maximum. In this paper, we reformulate the inference processing into a nonlinear programming problem and concentrate on the solution space of the nonlinear programming problem. We find that when losses occurred on a link are modelled as a Bernoulli process, the solution space is concave, which ensures an iterative approximating algorithm can locate global maximum.