Extremal Properties of Three Dimensional Sensor Networks with Applications

In this paper, we analyze various critical transmitting/sensing ranges for connectivity and coverage in three-dimensional sensor networks. As in other large-scale complex systems, many global parameters of sensor networks undergo phase transitions: For a given property of the network, there is a critical threshold, corresponding to the minimum amount of the communication effort or power expenditure by individual nodes, above (resp. below) which the property exists with high (resp. a low) probability. For sensor networks, properties of interest include simple and multiple degrees of connectivity/coverage. First, we investigate the network topology according to the region of deployment, the number of deployed sensors and their transmitting/sensing ranges. More specifically, we consider the following problems: Assume that $n$ nodes, each capable of sensing events within a radius of $r$, are randomly and uniformly distributed in a 3-dimensional region $\mathcal{R}$ of volume $V$, how large must the sensing range be to ensure a given degree of coverage of the region to monitor? For a given transmission range, what is the minimum (resp. maximum) degree of the network? What is then the typical hop-diameter of the underlying network? Next, we show how these results affect algorithmic aspects of the network by designing specific distributed protocols for sensor networks

Connectivity, Coverage and Placement in Wireless Sensor Networks

Wireless communication between sensors allows the formation of flexible sensor networks, which can be deployed rapidly over wide or inaccessible areas. However, the need to gather data from all sensors in the network imposes constraints on the distances between sensors. This survey describes the state of the art in techniques for determining the minimum density and optimal locations of relay nodes and ordinary sensors to ensure connectivity, subject to various degrees of uncertainty in the locations of the nodes

Resource Management in Heterogeneous Wireless Sensor Networks

We propose a first approach in the direction of a general framework for resource management in wireless sensor networks (WSN). The basic components of the approach are a model for WSNs and a task model. Based on these models, a first version of an algorithm for assigning tasks to a WSN is presented. The models and the algorithm are designed in such a way that an extension to more complex models is possible. Furthermore, the developed approach to solve the RM problem allows an easy adaptation, to fit more complex models. In this way, a flexible approach is achieved, which may form the base for many RM approaches.\ud The possibilities and limitations of the presented approach are tested on randomly generated instances. The aim of these tests is to show that the chosen models and algorithm form a proper starting point to design RM tools

Distributed optimization algorithms for multihop wireless networks

Recent technological advances in low-cost computing and communication hardware design have led to the feasibility of large-scale deployments of wireless ad hoc and sensor networks. Due to their wireless and decentralized nature, multihop wireless networks are attractive for a variety of applications. However, these properties also pose significant challenges to their developers and therefore require new types of algorithms. In cases where traditional wired networks usually rely on some kind of centralized entity, in multihop wireless networks nodes have to cooperate in a distributed and self-organizing manner. Additional side constraints, such as energy consumption, have to be taken into account as well. This thesis addresses practical problems from the domain of multihop wireless networks and investigates the application of mathematically justified distributed algorithms for solving them. Algorithms that are based on a mathematical model of an underlying optimization problem support a clear understanding of the assumptions and restrictions that are necessary in order to apply the algorithm to the problem at hand. Yet, the algorithms proposed in this thesis are simple enough to be formulated as a set of rules for each node to cooperate with other nodes in the network in computing optimal or approximate solutions. Nodes communicate with their neighbors by sending messages via wireless transmissions. Neither the size nor the number of messages grows rapidly with the size of the network. The thesis represents a step towards a unified understanding of the application of distributed optimization algorithms to problems from the domain of multihop wireless networks. The problems considered serve as examples for related problems and demonstrate the design methodology of obtaining distributed algorithms from mathematical optimization methods

Optimum Node Placement in Wireless Opportunistic Routing Networks

In recent years there has been a growing interest in opportunistic routing as a way to increase the capacity of wireless networks by exploiting its broadcast nature. In contrast to traditional uni-path routing, in opportunistic routing the nodes overhearing neighbor¿s transmissions can become candidates to forward the packets towards the destination. In this paper we address the question: What is the maximum performance that can be obtained using opportunistic routing? To answer this question we use an analytical model that allows to compute the optimal position of the nodes, such that the progress towards the destination is maximized. We use this model to compute bounds to the minimum expected number of transmissions that can be achieved in a network using opportunistic routing.This work was supported by the Spanish Ministerio de Ciencia e Innovacion through the Projects TIN2010-21378-C02-01 and TIN2010-21378-C02-02 and by the Generalitat de Catalunya through Project 2009-SGR-1167.Cerdá Alabern, L.; Darehshoorzadeh, A.; Pla, V. (2013). Optimum Node Placement in Wireless Opportunistic Routing Networks. Ad Hoc Networks. 11(8):2273-2287. https://doi.org/10.1016/j.adhoc.2013.05.010S2273228711

The power of quasi-shortest paths and the impact of node mobility on dynamic networks

The objective of this thesis is to investigate three important aspects of dynamic networks: the impact of node mobility on multihop data transmission, the effect of the use of longer paths on the relative importance of nodes and the performance of the network in the presence of failure on central nodes. To analyze the first aspect, this work proposes the (κ, λ)-vicinity, which extends the traditional vicinity to consider as neighbors nodes at multihop distance and restricts the link establishment according to the relative speed between nodes. This proposal is used later on the development of three forwarding strategies. The relative speed restriction imposed on these strategies results in significant reduction of resources consumption, without incurring significant impact on the average packet delivery ratio. To analyze the second aspect, we propose the ρ-geodesic betweenness centrality, which uses shortest and quasi-shortest paths to quantify the relative importance of a node. The quasishortest paths are limited by a spreadness factor, ρ. The use of non-optimal paths causes the reranking of several nodes and its main effect is a reduced occupation of the most central positions by articulation points. Lastly, the network performenace in presence of failures is investigated through simulations, in which failures happen on nodes defined as the most central according to distinct centrality metrics. The result is a severe reduction of the average network throughput, and it is independent of the metric used to determine which nodes are the most central. The major strength of the proposed metric, then, is that, despite the severe reduction of the throughput, there is a high probability of maintaining the network connected after a failure, because it is unlikely that a failing node in the most central position is also an articulation point.O objetivo desta tese é investigar três aspectos importantes das redes dinâmicas: o impacto da mobilidade dos nós na transmissão de dados em múltiplos saltos, o efeito do uso de caminhos mais longos na importância relativa dos nós, e o desempenho da rede na presença de falha em nós centrais. Para analisar o primeiro aspecto, este trabalho propõe a (κ, λ)-vizinhança, que estende a vizinhança tradicional para considerar como vizinhos nós a múltiplos saltos de distância e restringe o estabelecimento de enlaces de acordo com a velocidade relativa entre os nós. Essa proposta é usada posteriormente no desenvolvimento de três estratégias de encaminhamento. A restrição de velocidade relativa imposta nessas estratégias resulta em uma redução significativa do consumo de recursos, sem que ocorra impacto significativo na taxa média de entrega de pacotes. Para analisar o segundo aspecto, propõe a centralidade de intermediação ρ-geodésica, que usa caminhos mais curtos e quase mais curtos para quantificar a importância relativa dos nos. Os caminhos quase mais curtos são limitados por um fator de espalhamento ρ. O uso de caminhos não ótimos provoca o reranqueamento de diversos nós e tem como principal efeito uma menor ocupação de posições mais centrais por pontos de articulação. Por fim, o desempenho da rede em presença de falha é investigado através de simulações nas quais as falhas atingem nós definidos como os mais centrais de acordo com métricas de centralidade distintas. O resultado é uma redução brusca da vazão média da rede, independentemente da métrica usada para determinar quais são os nós mais centrais. O grande trunfo da métrica proposta é que, apesar da severa redução na vazão, é grande a probabilidade de manter a rede conectada após a falha, uma vez que é pouco provável que um nó em falha nas posições mais centrais seja também um ponto de articulação