Modeling and constructing unstructured overlay networks: Algorithms, techniques and the Smart Grid case

Abstract: Throughout its lifetime, the Internet was always associated with overlay networks; from the WorldWideWeb and peer-to-peer networks to blogs and social networking solutions, overlays built on the Internet infrastructure gave it additional value and made it more engaging to everyday users. Today, rising overlay networks such as the Smart Grid as well as a multitude of sensor, mobile and wireless networks herald a new era of unprecedented connectivity and networking. Common thread to all these developments is an ever increasing need for users and devices to connect and collaborate in a more natural way, one that reflects their existing social relations and enables them to form new ones. In this thesis we provide algorithms and techniques that enable users and overlay designers to model, construct and address practical considerations of such overlay networks. We focus our efforts on the unstructured overlay paradigm and our overarching goal is to provide methods and solutions that enable users to connect and collaborate with each other on their own terms through an overlay network, constrained by as few assumptions as possible, while providing guarantees on performance and key metrics. To pursue this goal we provide network designers with a framework for the analysis and systematic study of probabilistic techniques such as random walks in close conjunction with the unstructured overlays they are deployed on. The framework, based on a well known connection between random walks and electric circuits, is complemented by a basic set of analytical tools, a brief overview of recurring overlay problems that can be expressed within it, as well as practical algorithms and an accompanying extensive experimental study that illustrate its potential. Building further on the paradigm of the relation between electric flows and random walks, and inspired by a recently identified form of natural computation by the microorganism Physarum Polycephalum, we propose a randomized distributed algorithm that uses walkers to construct a distance-based clustered overlay. On the other hand, we address the users’ need for effortless and natural collaboration by making a connection with the b-matching with preferences problem and proposing a distributed algorithm that enables nodes with individual preferences to form an overlay, while achieving a guaranteed level of quality for their connections. While providing both one-shot and adaptive forms of the algorithm, we prove that it achieves guaranteed performance bounds. Furthermore, we prove that the algorithm always converges to a solution that provides a guaranteed approximation of the maximum total amount of a link-quality metric called satisfaction, even when the original b-matching problem did not admit a stable solution. Finally, communication overlays for power grids, collectively called Smart Grid, is an ideal application area for the above: the multitude of devices and communication technologies, the number of actors involved with individual agendas and the many protocols under standardization, all call for flexibility in the overlay formation and guarantees in key metrics that unstructured overlays can provide. In specific, based on matching and related assignment problems, we present a novel modeling on resource dispatch in power grids that takes into account node preferences and domain-related constraints. We also propose an algorithm that uses only local information to solve the problem with guaranteed performance, and we complement its presentation with simulations that demonstrate its effectiveness.