Tight Bounds for Maximal Identifiability of Failure Nodes in Boolean Network Tomography

We study maximal identifiability, a measure recently introduced in Boolean Network Tomography to characterize networks' capability to localize failure nodes in end-to-end path measurements. We prove tight upper and lower bounds on the maximal identifiability of failure nodes for specific classes of network topologies, such as trees and $d$-dimensional grids, in both directed and undirected cases. We prove that directed $d$-dimensional grids with support $n$ have maximal identifiability $d$ using $2d(n-1)+2$ monitors; and in the undirected case we show that $2d$ monitors suffice to get identifiability of $d-1$. We then study identifiability under embeddings: we establish relations between maximal identifiability, embeddability and graph dimension when network topologies are model as DAGs. Our results suggest the design of networks over $N$ nodes with maximal identifiability $\Omega(\log N)$ using $O(\log N)$ monitors and a heuristic to boost maximal identifiability on a given network by simulating $d$-dimensional grids. We provide positive evidence of this heuristic through data extracted by exact computation of maximal identifiability on examples of small real networks

Network Tomography on Correlated Links

Network tomography establishes linear relationships between the characteristics of individual links and those of end-to-end paths. It has been proved that these relationships can be used to infer the characteristics of links from end-to-end measurements, provided that links are not correlated, i.e., the status of one link is independent from the status of other links. In this paper, we consider the problem of identifying link characteristics from end-to-end measurements when links are "correlated," i.e., the status of one link may depend on the status of other links. There are several practical scenarios in which this can happen; for instance, if we know the network topology at the IP-link or at the domain-link level, then links from the same local-area network or the same administrative domain are potentially correlated, since they may be sharing physical links, network equipment, even management processes. We formally prove that, under certain well defined conditions, network tomography works when links are correlated, in particular, it is possible to identify the probability that each link is congested from end-to-end measurements. We also present a practical algorithm that computes these probabilities. We evaluate our algorithm through extensive simulations and show that it is accurate in a variety of realistic congestion scenarios

In-vehicle network delay tomography

Due to the increased complexity of new in-vehicle networking architectures, which makes direct monitoring of internal network components intractable, alternative solutions are required to tackle this issue. One solution is to leverage the end-to-end measurements to estimate the internal network performance. To this end, we propose to employ network tomography as a monitoring tool for in-vehicle networks. Network tomography can infer the overall network performance by measuring only subset of the network. We investigate the use of network tomography in in-vehicle network by analysing network identifiability of three main architectures: bus-based, central-gateway, and Ethernet-based architectures. Our analysis results indicate the applicability of network tomography in in-vehicle networks based on certain topological and monitors’ conditions. Furthermore, we validate our analytical results through simulation which shows a maximum error of only 0.174 milliseconds. Moreover, we compare the proposed approach with one of existing solutions and show that network tomography achieves better performance with minimal monitoring overhead of up to 52.2% and 782.3µs bandwidth and latency improvements, respectively. Index Terms—In-vehicle network monitoring, controller area network, network tomography, link delay inference

A Network Tomography Approach for Traffic Monitoring in Smart Cities

Traffic monitoring is a key enabler for several planning and management activities of a Smart City. However, traditional techniques are often not cost efficient, flexible, and scalable. This paper proposes an approach to traffic monitoring that does not rely on probe vehicles, nor requires vehicle localization through GPS. Conversely, it exploits just a limited number of cameras placed at road intersections to measure car end-to-end traveling times. We model the problem within the theoretical framework of network tomography, in order to infer the traveling times of all individual road segments in the road network. We specifically deal with the potential presence of noisy measurements, and the unpredictability of vehicles paths. Moreover, we address the issue of optimally placing the monitoring cameras in order to maximize coverage, while minimizing the inference error, and the overall cost. We provide extensive experimental assessment on the topology of downtown San Francisco, CA, USA, using real measurements obtained through the Google Maps APIs, and on realistic synthetic networks. Our approach provides a very low error in estimating the traveling times over 95% of all roads even when as few as 20% of road intersections are equipped with cameras

Adaptive Loss Inference Using Unicast End-to-End Measurements

We address the problem of inferring link loss rates from unicast end-to-end measurements on the basis of network tomography. Because measurement probes will incur additional traffic overheads, most tomography-based approaches perform the inference by collecting the measurements only on selected paths to reduce the overhead. However, all previous approaches select paths offline, which will inevitably miss many potential identifiable links, whose loss rates should be unbiasedly determined. Furthermore, if element failures exist, an appreciable number of the selected paths may become unavailable. In this paper, we creatively propose an adaptive loss inference approach in which the paths are selected sequentially depending on the previous measurement results. In each round, we compute the loss rates of links that can be unbiasedly determined based on the current measurement results and remove them from the system. Meanwhile, we locate the most possible failures based on the current measurement outcomes to avoid selecting unavailable paths in subsequent rounds. In this way, all identifiable and potential identifiable links can be determined unbiasedly using only 20% of all available end-to-end measurements. Compared with a previous classical approach through extensive simulations, the results strongly confirm the promising performance of our proposed approach

Incorporating Betweenness Centrality in Compressive Sensing for Congestion Detection

This paper presents a new Compressive Sensing (CS) scheme for detecting network congested links. We focus on decreasing the required number of measurements to detect all congested links in the context of network tomography. We have expanded the LASSO objective function by adding a new term corresponding to the prior knowledge based on the relationship between the congested links and the corresponding link Betweenness Centrality (BC). The accuracy of the proposed model is verified by simulations on two real datasets. The results demonstrate that our model outperformed the state-of-the-art CS based method with significant improvements in terms of F-Score

A Churn for the Better: Localizing Censorship using Network-level Path Churn and Network Tomography

Recent years have seen the Internet become a key vehicle for citizens around the globe to express political opinions and organize protests. This fact has not gone unnoticed, with countries around the world repurposing network management tools (e.g., URL filtering products) and protocols (e.g., BGP, DNS) for censorship. However, repurposing these products can have unintended international impact, which we refer to as "censorship leakage". While there have been anecdotal reports of censorship leakage, there has yet to be a systematic study of censorship leakage at a global scale. In this paper, we combine a global censorship measurement platform (ICLab) with a general-purpose technique -- boolean network tomography -- to identify which AS on a network path is performing censorship. At a high-level, our approach exploits BGP churn to narrow down the set of potential censoring ASes by over 95%. We exactly identify 65 censoring ASes and find that the anomalies introduced by 24 of the 65 censoring ASes have an impact on users located in regions outside the jurisdiction of the censoring AS, resulting in the leaking of regional censorship policies

Network tomography based on 1-D projections

Network tomography has been regarded as one of the most promising methodologies for performance evaluation and diagnosis of the massive and decentralized Internet. This paper proposes a new estimation approach for solving a class of inverse problems in network tomography, based on marginal distributions of a sequence of one-dimensional linear projections of the observed data. We give a general identifiability result for the proposed method and study the design issue of these one dimensional projections in terms of statistical efficiency. We show that for a simple Gaussian tomography model, there is an optimal set of one-dimensional projections such that the estimator obtained from these projections is asymptotically as efficient as the maximum likelihood estimator based on the joint distribution of the observed data. For practical applications, we carry out simulation studies of the proposed method for two instances of network tomography. The first is for traffic demand tomography using a Gaussian Origin-Destination traffic model with a power relation between its mean and variance, and the second is for network delay tomography where the link delays are to be estimated from the end-to-end path delays. We compare estimators obtained from our method and that obtained from using the joint distribution and other lower dimensional projections, and show that in both cases, the proposed method yields satisfactory results.Comment: Published at http://dx.doi.org/10.1214/074921707000000238 in the IMS Lecture Notes Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

Active Topology Inference using Network Coding

Our goal is to infer the topology of a network when (i) we can send probes between sources and receivers at the edge of the network and (ii) intermediate nodes can perform simple network coding operations, i.e., additions. Our key intuition is that network coding introduces topology-dependent correlation in the observations at the receivers, which can be exploited to infer the topology. For undirected tree topologies, we design hierarchical clustering algorithms, building on our prior work. For directed acyclic graphs (DAGs), first we decompose the topology into a number of two-source, two-receiver (2-by-2) subnetwork components and then we merge these components to reconstruct the topology. Our approach for DAGs builds on prior work on tomography, and improves upon it by employing network coding to accurately distinguish among all different 2-by-2 components. We evaluate our algorithms through simulation of a number of realistic topologies and compare them to active tomographic techniques without network coding. We also make connections between our approach and alternatives, including passive inference, traceroute, and packet marking