Experiment Design for Link Loss Tomography

We study experiment design to infer link loss rates from end-to-end losses on selected paths using network tomography. Since the inverse Fisher information matrix (FIM) establishes a lower bound on the error of any unbiased estimator, we formulate the problem as the design of probabilities in selecting probing paths to minimize an objective function based on the FIM. We consider two widely-adopted objective functions: the determinant of the inverse FIM (D-optimality) and the trace of the inverse FIM (A-optimality), where the former characterizes the volume of error ellipsoid and the latter characterizes the sum mean square error (MSE). Using a special property of the FIM, we obtain closed-form expressions for both objective functions, which lead to closed-form solutions for the optimal path selection probabilities. In particular, we show that the D-optimal design is uniform probing, i.e., probing each path with an equal probability. We verify through simulations that the A-optimal design can reduce the MSE compared with uniform probing.