Additive network tomography, which addresses the inference of link/node performance metrics (e.g., delays) that are additive from the sum metrics on measurement paths, represents the most well-studied branch in the realm of network tomography, upon which a rich body of seminal works have been conducted. This chapter focuses on the case in which the metrics of interest are additive and constant, which allows the network tomography problem to be cast as a linear system inversion problem. After introducing the abstract definitions of link identifiability and network identifiability using linear algebraic conditions, the chapter presents a series of graph-theoretic conditions that establish the necessary and sufficient requirements to achieve identifiability in terms of the number of monitors, the locations of monitors, the connectivity of the network topology, and the routing mechanism. It also contains extended conditions that allow the evaluation of robust link identifiability under failures and partial link identifiability when the network-wide identifiability condition is not satisfied.

This chapter completes the topic of measurement design for additive network tomography, started in Chapter 3, by discussing how to construct suitable measurement paths to identify additive link metrics using a given set of monitors. As in Chapter 3, the focus is on the design of efficient path construction algorithms that make novel use of certain graph algorithms (specifically, algorithms for constructing independent spanning trees) to find a set of paths that form a basis of the link space without enumerating all possible paths. The chapter also discusses a variation of the path construction problem when the number of measurement paths is constrained and each measurement path may fail with certain probability.

Based on the conditions for identifying additive link metrics presented in Chapter 2, this chapter addresses two network design questions: (1) Given an unbounded number of monitors, where should they be placed in the network to identify the metrics of all the links using a minimum number of monitors? (2) Given a bounded number of monitors, where should they be placed in the network to identify the metrics of the largest subset of links? The focus here is on the design of intelligent algorithms that can efficiently compute the optimal monitor locations without enumerating all possible monitor placements, achieved through strategic decomposition of the network topology based on the required identifiability conditions. Variations of these algorithms are also given to address cases with predictable or unpredictable topology changes and limited links of interest. In addition to theoretical analysis, empirical results are given to demonstrate the capability of selected algorithms for which such results are available.