Identifiability of link metrics based on end-to-end path measurements

Abstract

We investigate the problem of identifying individual link metrics in a communication network from end-to-end path measurements, under the assumption that link metrics are additive and constant. To uniquely identify the link metrics, the number of linearly independent measurement paths must equal the number of links. Our contribution is to characterize this condition in terms of the network topology and the number/placement of monitors, under the constraint that measurement paths must be cycle-free. Our main results are: (i) it is generally impossible to identify all the link metrics by using two monitors; (ii) nevertheless, metrics of all the interior links not incident to any monitor are identifiable by two monitors if the topology satisfies a set of necessary and sufficient connectivity conditions; (iii) these conditions naturally extend to a necessary and sufficient condition for identifying all the link metrics using three or more monitors. We show that these conditions not only allow efficient identifiability tests, but also enable an efficient algorithm to place the minimum number of monitors in order to identify all link metrics. Our evaluations on both random and real topologies show that the proposed algorithm achieves identifiability using a much smaller number of monitors than a baseline solution.

Preferential Link Tomography: Monitor Assignment for Inferring Interesting Link Metrics

“…Inferring fine-grained network characteristics using aggregated measurements, as known as network tomography [1], is an effective technique to facilitate various network operations [2], [3], [4], such as network monitoring, load balance, and fault diagnosis. In communication networks, a subset of nodes with monitoring capabilities, i.e., monitors, can initiate and collect end-to-end measurements of selected cycle-free paths.…”

“…In many cases, these link metrics are additive [2], [5]. For example, delay is a typical additive metric since an end-to-end path delay is the sum of all link delays, while a multiplicative metric like packet delivery ratio can be expressed in an additive form by applying the log(·) function.…”

“…For example, delay is a typical additive metric since an end-to-end path delay is the sum of all link delays, while a multiplicative metric like packet delivery ratio can be expressed in an additive form by applying the log(·) function. In order to identify additive link metrics, we need to solve a linear system, where the unknown variables are the link metrics, and the known constants are the end-to-end path measurements, each equal to the sum of the corresponding link metrics along a path [2]. Since these end-to-end path measurements are conducted among monitors, the monitor assignment (which nodes should be assigned as monitors) becomes a key problem.…”

“…On the other hand, we usually want to minimize the number of monitors assigned, since assigning a node as a monitor usually needs non-negligible operational cost (e.g., hardware/software, human efforts). Ma et al [2] successfully solved the above problem by proposing the MMP algorithm which identifies all link metrics in the network by assigning the minimum number of monitors.…”

“…Although it is difficult to obtain the dependency between link identifiability and a particular monitor, we are able to effectively narrow down the search space by safely trimming unrelated network components. After graph trimming, Scalpel reuses the MMP algorithm [2] for monitor assignment. The preferential link tomography problem studied in this paper generalizes the problem studied in MMP in which all links are considered as interesting links.…”