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A matrix giving the traffic volumes between origin and destination in a network has tremendously potential utility for network capacity planning and management. Unfortunately, traffic matrices are generally unavailable in large operational IP networks. On the other hand, link load measurements are readily available in IP networks. In this paper, we propose a new method for practical and rapid inference of traffic matrices in IP networks from link load measurements, augmented by readily available network and routing configuration information. We apply and validate the method by computing backbonerouter to backbone-router traffic matrices on a large operational tier-1 IP network -a problem an order of magnitude larger than any other comparable method has tackled. The results show that the method is remarkably fast and accurate, delivering the traffic matrix in under five seconds.

The search for unifying properties of complex networks is popular, challenging, and important. For modeling approaches that focus on robustness and fragility as unifying concepts, the Internet is an especially attractive case study, mainly because its applications are ubiquitous and pervasive, and widely available expositions exist at every level of detail. Nevertheless, alternative approaches to modeling the Internet often make extremely different assumptions and derive opposite conclusions about fundamental properties of one and the same system. Fortunately, a detailed understanding of Internet technology combined with a unique ability to measure the network means that these differences can be understood thoroughly and resolved unambiguously. This article aims to make recent results of this process accessible beyond Internet specialists to the broader scientific community and to clarify several sources of basic methodological differences that are relevant beyond either the Internet or the two specific approaches focused on here (i.e., scale-free networks and highly optimized tolerance networks).complex network ͉ HOT ͉ Internet topology ͉ network design ͉ scale-free network

Many basic network engineering tasks (e.g., traffic engineering, capacity planning, anomaly detection) rely heavily on the availability and accuracy of traffic matrices. However, in practice it is challenging to reliably measure traffic matrices. Missing values are common. This observation brings us into the realm of compressive sensing, a generic technique for dealing with missing values that exploits the presence of structure and redundancy in many realworld systems. Despite much recent progress made in compressive sensing, existing compressive-sensing solutions often perform poorly for traffic matrix interpolation, because real traffic matrices rarely satisfy the technical conditions required for these solutions.To address this problem, we develop a novel spatio-temporal compressive sensing framework with two key components: (i) a new technique called SPARSITY REGULARIZED MATRIX FAC-TORIZATION (SRMF) that leverages the sparse or low-rank nature of real-world traffic matrices and their spatio-temporal properties, and (ii) a mechanism for combining low-rank approximations with local interpolation procedures. We illustrate our new framework and demonstrate its superior performance in problems involving interpolation with real traffic matrices where we can successfully replace up to 98% of the values. Evaluation in applications such as network tomography, traffic prediction, and anomaly detection confirms the flexibility and effectiveness of our approach.

Traffic matrices are required inputs for many IP network management tasks: for instance, capacity planning, traffic engineering and network reliability analysis. However, it is difficult to measure these matrices directly, and so there has been recent interest in inferring traffic matrices from link measurements and other more easily measured data. Typically, this inference problem is ill-posed, as it involves significantly more unknowns than data. Experience in many scientific and engineering fields has shown that it is essential to approach such ill-posed problems via "regularization". This paper presents a new approach to traffic matrix estimation using a regularization based on "entropy penalization". Our solution chooses the traffic matrix consistent with the measured data that is informationtheoretically closest to a model in which source/destination pairs are stochastically independent. We use fast algorithms based on modern convex optimization theory to solve for our traffic matrices. We evaluate the algorithm with real backbone traffic and routing data, and demonstrate that it is fast, accurate, robust, and flexible.

A matrix giving the traffic volumes between origin and destination in a network has tremendously potential utility for network capacity planning and management. Unfortunately, traffic matrices are generally unavailable in large operational IP networks. On the other hand, link load measurements are readily available in IP networks. In this paper, we propose a new method for practical and rapid inference of traffic matrices in IP networks from link load measurements, augmented by readily available network and routing configuration information. We apply and validate the method by computing backbonerouter to backbone-router traffic matrices on a large operational tier-1 IP network -a problem an order of magnitude larger than any other comparable method has tackled. The results show that the method is remarkably fast and accurate, delivering the traffic matrix in under five seconds.

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