Analysis and optimization of highly reliable systems

In the field of network design, the survivability property enables the network to maintain a certain level of network connectivity and quality of service under failure conditions. In this thesis, survivability aspects of communication systems are studied. Aspects of reliability and vulnerability of network design are also addressed. The contributions are three-fold. First, a Hop Constrained node Survivable Network Design Problem (HCSNDP) with optional (Steiner) nodes is modelled. This kind of problems are N P-Hard. An exact integer linear model is built, focused on networks represented by graphs without rooted demands, considering costs in arcs and in Steiner nodes. In addition to the exact model, the calculation of lower and upper bounds to the optimal solution is included. Models were tested over several graphs and instances, in order to validate it in cases with known solution. An Approximation Algorithm is also developed in order to address a particular case of SNDP: the Two Node Survivable Star Problem (2NCSP) with optional nodes. This problem belongs to the class of N P-Hard computational problems too. Second, the research is focused on cascading failures and target/random attacks. The Graph Fragmentation Problem (GFP) is the result of a worst case analysis of a random attack. A fixed number of individuals for protection can be chosen, and a non-protected target node immediately destroys all reachable nodes. The goal is to minimize the expected number of destroyed nodes in the network. This problem belongs to the N P-Hard class. A mathematical programming formulation is introduced and exact resolution for small instances as well as lower and upper bounds to the optimal solution. In addition to exact methods, we address the GFP by several approaches: metaheuristics, approximation algorithms, polytime methods for specific instances and exact methods in exponential time. Finally, the concept of separability in stochastic binary systems is here introduced. Stochastic Binary Systems (SBS) represent a mathematical model of a multi-component on-off system subject to independent failures. The reliability evaluation of an SBS belongs to the N P-Hard class. Therefore, we fully characterize separable systems using Han-Banach separation theorem for convex sets. Using this new concept of separable systems and Markov inequality, reliability bounds are provided for arbitrary SBS

A Case for Time Slotted Channel Hopping for ICN in the IoT

Recent proposals to simplify the operation of the IoT include the use of Information Centric Networking (ICN) paradigms. While this is promising, several challenges remain. In this paper, our core contributions (a) leverage ICN communication patterns to dynamically optimize the use of TSCH (Time Slotted Channel Hopping), a wireless link layer technology increasingly popular in the IoT, and (b) make IoT-style routing adaptive to names, resources, and traffic patterns throughout the network--both without cross-layering. Through a series of experiments on the FIT IoT-LAB interconnecting typical IoT hardware, we find that our approach is fully robust against wireless interference, and almost halves the energy consumed for transmission when compared to CSMA. Most importantly, our adaptive scheduling prevents the time-slotted MAC layer from sacrificing throughput and delay

Topological Design of Survivable Networks

In the field of telecommunications there are several ways of establishing links between different physical places that must be connected according to the characteristics and the type of service they should provide. Two main considerations to be taken into account and which require the attention of the network planners are, in one hand the economic effort necessary to build the network, and in the other hand the resilience of the network to remain operative in the event of failure of any of its components. A third consideration, which is very important when quality of services required, such as video streaming or communications between real-time systems, is the diameter constrained reliability. In this thesis we study a set of problems that involve such considerations. Firstly, we model a new combinatorial optimization problem called Capacitated m-Two Node Survivable Star Problem (CmTNSSP). In such problem we optimize the costs of constructing a network composed of 2-node-connected components that converge in a central node and whose terminals can belong to these connected 2-node structures or be connected to them by simple edges. The CmTNSSP is a relaxation of the Capacitated Ring Star Problem (CmRSP), where the cycles of the latter can be replaced by arbitrary 2-node-connected graphs. According to previous studies, some of the structural properties of 2-node-connected graphs can be used to show a potential improvement in construction costs, over solutions that exclusively use cycles. Considering that the CmTNSSP belongs to the class of NP-Hard computational problems, a GRASP-VND metaheuristic was proposed and implemented for its approximate resolution, and a comparison of results was made between both problems (CmRSP and CmTNSSP) for a series of instances. Some local searches are based on exact Integer Linear Programming formulations. The results obtained show that the proposed metaheuristic reaches satisfactory levels of accuracy, attaining the global optimum in several instances. Next, we introduce the Capacitated m Ring Star Problem under Diameter Constrained Reliability (CmRSP-DCR) wherein DCR is considered as an additional restriction, limiting the number of hops between nodes of the CmRSP problem and establishing a minimum level of network reliability. This is especially useful in networks that should guarantee minimum delays and quality of service. The solutions found in this problem can be improved by applying some of the results obtained in the study of the CmTNSSP. Finally, we introduce a variant of the CmTNSSP named Capacitated Two-Node Survivable Tree Problem, motivated by another combinatorial optimization problem most recently treated in the literature, called Capacitated Ring Tree Problem (CRTP). In the CRTP, an additional restriction is added with respect to CmRSP, where the terminal nodes are of two different types and tree structures are also allowed. Each node in the CRTP may be connected exclusively in one cycle, or may be part of a cycle or a tree indistinctly, depending on the type of node. In the variant we introduced, the cycles are replaced by 2-node-connected structures. This study proposes and implements a GRASP-VND metaheuristic with specific local searches for this type of structures and adapts some of the exact local searches used in the resolution CmTNSSP. A comparison of the results between the optimal solutions obtained for the CRTP and the CTNSTP is made. The results achieved show the robustness and efficiency of the metaheuristi

Controlled open-cell two-dimensional liquid foam generation for micro- and nanoscale patterning of materials

Liquid foam consists of liquid film networks. The films can be thinned to the nanoscale via evaporation and have potential in bottom-up material structuring applications. However, their use has been limited due to their dynamic fluidity, complex topological changes, and physical characteristics of the closed system. Here, we present a simple and versatile microfluidic approach for controlling two-dimensional liquid foam, designing not only evaporative microholes for directed drainage to generate desired film networks without topological changes for the first time, but also microposts to pin the generated films at set positions. Patterning materials in liquid is achievable using the thin films as nanoscale molds, which has additional potential through repeatable patterning on a substrate and combination with a lithographic technique. By enabling direct-writable multi-integrated patterning of various heterogeneous materials in two-dimensional or three-dimensional networked nanostructures, this technique provides novel means of nanofabrication superior to both lithographic and bottom-up state-of-the-art techniques

Separability in Stochastic Binary Systems

A Stochastic Binary System (SBS) is a mathematical model of multi-component on-off systems subject to random failures. SBS models extend classical network reliability models (where the components subject to failure are nodes or links of a graph) and are able to represent more complex interactions between the states of the individual components and the operation of the system under study. The reliability evaluation of stochastic binary systems belongs to the class of NP-Hard computational problems. Furthermore, the number of states is exponential with respect to the size of the system (measured in the number of components). As a consequence, the representation of an SBS becomes a key element in order to develop exact and/or approximation methods for reliability evaluation. The contributions of this paper are three-fold. First, we present the concept of separable stochastic binary systems, showing key properties, such as an efficient representation and complexity in the reliability evaluation. Second, we fully characterize separable systems in two ways, using a geometrical interpretation and minimum-cost operational subsystems. Finally, we show the application of separable systems in network reliability models, specifically in the all-terminal reliability model, which has a wide spectrum of applications. Index Terms—Stochastic Binary System, Network Reliability, Computational Complexity, Chernoff Inequality

Synchronization in complex networks

Synchronization processes in populations of locally interacting elements are in the focus of intense research in physical, biological, chemical, technological and social systems. The many efforts devoted to understand synchronization phenomena in natural systems take now advantage of the recent theory of complex networks. In this review, we report the advances in the comprehension of synchronization phenomena when oscillating elements are constrained to interact in a complex network topology. We also overview the new emergent features coming out from the interplay between the structure and the function of the underlying pattern of connections. Extensive numerical work as well as analytical approaches to the problem are presented. Finally, we review several applications of synchronization in complex networks to different disciplines: biological systems and neuroscience, engineering and computer science, and economy and social sciences.Comment: Final version published in Physics Reports. More information available at http://synchronets.googlepages.com