Chapters 7 and 8 are designated for network tomography for stochastic link metrics, which is a more fine-grained model than the models of deterministic additive/Boolean metrics, capturing the inherent randomness in link performances at a small time scale. Referred to as stochastic network tomography, these problems are typically cast as parameter estimation problems, which model each link metric as a random variable with a (partially) unknown distribution and aim at inferring the parameters of these distributions from end-to-end measurements. Chapter 7 focuses on one branch of stochastic network tomography that is based on unicast measurements. It introduces a framework based on concepts from estimation theory (e.g., maximum likelihood estimation, Fisher information matrix, Cramér–Rao bound), within which probing experiments and parameter estimators are designed to estimate link parameters from unicast measurements with minimum errors. Closed-form solutions are given for inferring parameters of packet losses (i.e., loss tomography) and packet delay variations (i.e., packet delay variation tomography).

This chapter covers preliminary materials required to understand the presentation in the following chapters, including selected definitions from graph theory, linear algebra, and parameter estimation. We also introduce a classification of routing mechanisms based on the controllability of the routing of probes by monitors generating the probes, which will facilitate the discussion in the following chapters.