Fisher information-based experiment design for network tomography

Network tomography aims to infer the individual performance of networked elements (e.g., links) using aggregate measurements on end-to-end paths. Previous work on network tomography focuses primarily on developing estimators using the given measurements, while the design of measurements is often neglected. We fill this gap by proposing a framework to design probing experiments with focus on probe allocation, and applying it to two concrete problems: packet loss tomography and packet delay variation (PDV) tomography. Based on the Fisher Information Matrix (FIM), we design the distribution of probes across paths to maximize the best accuracy of unbiased estimators, asymptotically achievable by the maximum likelihood estimator. We consider two widely-adopted objective functions: determinant of the inverse FIM (D-optimality) and trace of the inverse FIM (A-optimality). We also extend the A-optimal criterion to incorporate heterogeneity in link weights. Under certain conditions on the FIM, satisfied by both loss and PDV tomography, we derive explicit expressions for both objective functions. When the number of probing paths equals the number of links, these lead to closed-form solutions for the optimal design; when there are more paths, we develop a heuristic to select a subset of paths and optimally allocate probes within the subset. Observing the dependency of the optimal design on unknown parameters, we further propose an algorithm that iteratively updates the design based on parameter estimates, which converges to the design based on true parameters as the number of probes increases. Using packet-level simulations on real datasets, we verify that the proposed design effectively reduces estimation error compared with the common approach of uniformly distributing probes.