Network Kriging

Network service providers and customers are often concerned with aggregate performance measures that span multiple network paths. Unfortunately, forming such network-wide measures can be difficult, due to the issues of scale involved. In particular, the number of paths grows too rapidly with the number of endpoints to make exhaustive measurement practical. As a result, it is of interest to explore the feasibility of methods that dramatically reduce the number of paths measured in such situations while maintaining acceptable accuracy. We cast the problem as one of statistical prediction--in the spirit of the so-called `kriging' problem in spatial statistics--and show that end-to-end network properties may be accurately predicted in many cases using a surprisingly small set of carefully chosen paths. More precisely, we formulate a general framework for the prediction problem, propose a class of linear predictors for standard quantities of interest (e.g., averages, totals, differences) and show that linear algebraic methods of subset selection may be used to effectively choose which paths to measure. We characterize the performance of the resulting methods, both analytically and numerically. The success of our methods derives from the low effective rank of routing matrices as encountered in practice, which appears to be a new observation in its own right with potentially broad implications on network measurement generally.Comment: 16 pages, 9 figures, single-space

On Delays in Management Frameworks: Metrics, Models and Analysis

Management performance evaluation means assessment of scalability, complexity, accuracy, throughput, delays and resources consumptions. In this paper, we focus on the evaluation of management frameworks delays through a set of specific metrics. We investigate the statistical properties of these metrics when the number of management nodes increases. We show that management delays measured at the application level are statistically modeled by distributions with heavy tails, especially the Weibull distribution. Given that delays can substantially degrade the capacity of management algorithms to react and resolve problems it is useful to get a finer model to describe them.We suggest theWeibull distribution as a model of delays for the analysis and simulations of such algorithms

Practical Approach to Identifying Additive Link Metrics with Shortest Path Routing

© 2015 IEEE. We revisit the problem of identifying link metrics from end- to-end path measurements in practical IP networks where shortest path routing is the norm. Previous solutions rely on explicit routing techniques (e.g., source routing or MPLS) to construct independent measurement paths for efficient link metric identification. However, most IP networks still adopt shortest path routing paradigm, while the explicit routing is not supported by most of the routers. Thus, this paper studies the link metric identification problem under shortest path routing constraints. To uniquely identify the link metrics, we need to place sufficient number of monitors into the network such that there exist m (the number of links) linear independent shortest paths between the monitors. In this paper, we first formulate the problem as a mixed integer linear programming problem, and then to make the problem tractable in large networks, we propose a Monitor Placement and Measurement Path Selection (MP-MPS) algorithm that adheres to shortest path routing constraints. Extensive simulations on random and real networks show that the MP- MPS gets near-optimal solutions in small networks, and MP- MPS significantly outperforms a baseline solution in large networks

Sparsity without the Complexity: Loss Localisation using Tree Measurements

We study network loss tomography based on observing average loss rates over a set of paths forming a tree -- a severely underdetermined linear problem for the unknown link loss probabilities. We examine in detail the role of sparsity as a regularising principle, pointing out that the problem is technically distinct from others in the compressed sensing literature. While sparsity has been applied in the context of tomography, key questions regarding uniqueness and recovery remain unanswered. Our work exploits the tree structure of path measurements to derive sufficient conditions for sparse solutions to be unique and the condition that $\ell_1$ minimization recovers the true underlying solution. We present a fast single-pass linear algorithm for $\ell_1$ minimization and prove that a minimum $\ell_1$ solution is both unique and sparsest for tree topologies. By considering the placement of lossy links within trees, we show that sparse solutions remain unique more often than is commonly supposed. We prove similar results for a noisy version of the problem

A network tomography approach for traffic monitoring in smart cities

Various urban planning and managing activities required by a Smart City are feasible because of traffic monitoring. As such, the thesis proposes a network tomography-based approach that can be applied to road networks to achieve a cost-efficient, flexible, and scalable monitor deployment. Due to the algebraic approach of network tomography, the selection of monitoring intersections can be solved through the use of matrices, with its rows representing paths between two intersections, and its columns representing links in the road network. Because the goal of the algorithm is to provide a cost-efficient, minimum error, and high coverage monitor set, this problem can be translated into an optimization problem over a matroid, which can be solved efficiently by a greedy algorithm. Also as supplementary, the approach is capable of handling noisy measurements and a measurement-to-path matching. The approach proves a low error and a 90% coverage with only 20% nodes selected as monitors in a downtown San Francisco, CA topology --Abstract, page iv

Network Monitoring: it depends on your points of view

End-to-end active network monitoring infers network characteristics by sending and collecting probe packets from the network edge, while probes traverse the network through multicast trees or a mesh of unicast paths. Most reported methods consider given source and receiver locations and study the path selection and the associated estimation algorithms. In this paper, we show that appropriately choosing the number of sources and receivers, as well as their location, may have a significant effect on the accuracy of the estimation; we also give guidelines on how to choose the best “points of view” of a network for link loss monitoring purposes. Though this observation applies across all monitoring methods, we consider, in particular, networks where nodes are equipped with network coding capabilities; our framework includes as special cases the scenarios of pure multicast and network coding. We show that, in network-coding enabled networks, multiple source active monitoring can exploit these capabilities to estimate link loss rates more efficiently than purely tomographic methods. To address the complexity of the estimation problem for large networks, we also propose efficient algorithms, including the decomposition into smaller multicast inference problems, belief-propagation, and a MINClike algorithm