Spatial networks with wireless applications

Many networks have nodes located in physical space, with links more common between closely spaced pairs of nodes. For example, the nodes could be wireless devices and links communication channels in a wireless mesh network. We describe recent work involving such networks, considering effects due to the geometry (convex,non-convex, and fractal), node distribution, distance-dependent link probability, mobility, directivity and interference.Comment: Review article- an amended version with a new title from the origina

More is less: Connectivity in fractal regions

Ad-hoc networks are often deployed in regions with complicated boundaries. We show that if the boundary is modeled as a fractal, a network requiring line of sight connections has the counterintuitive property that increasing the number of nodes decreases the full connection probability. We characterise this decay as a stretched exponential involving the fractal dimension of the boundary, and discuss mitigation strategies. Applications of this study include the analysis and design of sensor networks operating in rugged terrain (e.g. railway cuttings), mm-wave networks in industrial settings and vehicle-to-vehicle/vehicle-to-infrastructure networks in urban environments.Comment: 5 page

Fundamentals of Large Sensor Networks: Connectivity, Capacity, Clocks and Computation

Sensor networks potentially feature large numbers of nodes that can sense their environment over time, communicate with each other over a wireless network, and process information. They differ from data networks in that the network as a whole may be designed for a specific application. We study the theoretical foundations of such large scale sensor networks, addressing four fundamental issues- connectivity, capacity, clocks and function computation. To begin with, a sensor network must be connected so that information can indeed be exchanged between nodes. The connectivity graph of an ad-hoc network is modeled as a random graph and the critical range for asymptotic connectivity is determined, as well as the critical number of neighbors that a node needs to connect to. Next, given connectivity, we address the issue of how much data can be transported over the sensor network. We present fundamental bounds on capacity under several models, as well as architectural implications for how wireless communication should be organized. Temporal information is important both for the applications of sensor networks as well as their operation.We present fundamental bounds on the synchronizability of clocks in networks, and also present and analyze algorithms for clock synchronization. Finally we turn to the issue of gathering relevant information, that sensor networks are designed to do. One needs to study optimal strategies for in-network aggregation of data, in order to reliably compute a composite function of sensor measurements, as well as the complexity of doing so. We address the issue of how such computation can be performed efficiently in a sensor network and the algorithms for doing so, for some classes of functions.Comment: 10 pages, 3 figures, Submitted to the Proceedings of the IEE

Analysis of a Cone-Based Distributed Topology Control Algorithm for Wireless Multi-hop Networks

The topology of a wireless multi-hop network can be controlled by varying the transmission power at each node. In this paper, we give a detailed analysis of a cone-based distributed topology control algorithm. This algorithm, introduced in [16], does not assume that nodes have GPS information available; rather it depends only on directional information. Roughly speaking, the basic idea of the algorithm is that a node $u$ transmits with the minimum power $p_{u,\alpha}$ required to ensure that in every cone of degree $\alpha$ around $u$, there is some node that $u$ can reach with power $p_{u,\alpha}$. We show that taking $\alpha = 5\pi/6$ is a necessary and sufficient condition to guarantee that network connectivity is preserved. More precisely, if there is a path from $s$ to $t$ when every node communicates at maximum power, then, if $\alpha <= 5\pi/6$, there is still a path in the smallest symmetric graph $G_\alpha$ containing all edges $(u,v)$ such that $u$ can communicate with $v$ using power $p_{u,\alpha}$. On the other hand, if $\alpha > 5\pi/6$, connectivity is not necessarily preserved. We also propose a set of optimizations that further reduce power consumption and prove that they retain network connectivity. Dynamic reconfiguration in the presence of failures and mobility is also discussed. Simulation results are presented to demonstrate the effectiveness of the algorithm and the optimizations.Comment: 10 page

Two-Hop Connectivity to the Roadside in a VANET Under the Random Connection Model

We compute the expected number of cars that have at least one two-hop path to a fixed roadside unit in a one-dimensional vehicular ad hoc network in which other cars can be used as relays to reach a roadside unit when they do not have a reliable direct link. The pairwise channels between cars experience Rayleigh fading in the random connection model, and so exist, with probability function of the mutual distance between the cars, or between the cars and the roadside unit. We derive exact equivalents for this expected number of cars when the car density $\rho$ tends to zero and to infinity, and determine its behaviour using an infinite oscillating power series in $\rho$, which is accurate for all regimes. We also corroborate those findings to a realistic situation, using snapshots of actual traffic data. Finally, a normal approximation is discussed for the probability mass function of the number of cars with a two-hop connection to the origin. The probability mass function appears to be well fitted by a Gaussian approximation with mean equal to the expected number of cars with two hops to the origin.Comment: 21 pages, 7 figure

Multipath Key Establishment for Wireless Sensor Networks Using Just-Enough Redundancy Transmission

In random key predistribution techniques for wireless sensor networks, a relatively small number of keys are randomly chosen from a large key pool and are loaded on the sensors prior to deployment. After deployment, each sensor tries finding a common key shared by itself and each of its neighbors to establish a link key to protect the wireless communication between themselves. One intrinsic disadvantage of such techniques is that some neighboring sensors do not share any common key. In order to establish a link key among these neighbors, a multihop secure path may be used to deliver the secret. Unfortunately, the possibility of sensors being compromised on the path may render such an establishment process insecure. In this work, we propose and analyze the Just-Enough Redundancy Transmission (JERT) scheme that uses the powerful Maximum-Distance Separable (MDS) codes to address the problem. In the JERT scheme, the secret link key is encoded in (n, k) MDS code and transmitted through multiple multihop paths. To reduce the total information that needs to be transmitted, the redundant symbols of the MDS codes are transmitted only if the destination fails to decode the secret. The JERT scheme is demonstrated to be efficient and resilient against node capture. One salient feature of the JERT scheme is its flexibility of trading transmission for lower information disclosure

Lifenet: a flexible ad hoc networking solution for transient environments

In the wake of major disasters, the failure of existing communications infrastructure and the subsequent lack of an effective communication solution results in increased risks, inefficiencies, damage and casualties. Currently available options such as satellite communication are expensive and have limited functionality. A robust communication solution should be affordable, easy to deploy, require little infrastructure, consume little power and facilitate Internet access. Researchers have long proposed the use of ad hoc wireless networks for such scenarios. However such networks have so far failed to create any impact, primarily because they are unable to handle network transience and have usability constraints such as static topologies and dependence on specific platforms. LifeNet is a WiFi-based ad hoc data communication solution designed for use in highly transient environments. After presenting the motivation, design principles and key insights from prior literature, the dissertation introduces a new routing metric called Reachability and a new routing protocol based on it, called Flexible Routing. Roughly speaking, reachability measures the end-to-end multi-path probability that a packet transmitted by a source reaches its final destination. Using experimental results, it is shown that even with high transience, the reachability metric - (1) accurately captures the effects of transience (2) provides a compact and eventually consistent global network view at individual nodes, (3) is easy to calculate and maintain and (4) captures availability. Flexible Routing trades throughput for availability and fault-tolerance and ensures successful packet delivery under varying degrees of transience. With the intent of deploying LifeNet on field we have been continuously interacting with field partners, one of which is Tata Institute of Social Sciences India. We have refined LifeNet iteratively refined base on their feedback. I conclude the thesis with lessons learned from our field trips so far and deployment plans for the near future.MSCommittee Chair: Santosh Vempala; Committee Member: Ashok Jhunjhunwala; Committee Member: Michael Best; Committee Member: Nick Feamste