Preface

It has been shown by Freris, Graham and Kumar that clocks in distributed networks cannot be synchronized precisely in the presence of asymmetric time delays even in idealized situations. Motivated by that impossibility result, we test under similar settings the performance of some existing clock synchronization protocols and show that the synchronization errors between neighboring nodes can be bounded within an acceptable level of accuracy that is determined by the degree of asymmetry in time delays. After studying the basic case of synchronizing two clocks in the two-way message passing process, we first analyze the directed ring networks, in which neighboring clocks are likely to experience severe asymmetric time delays. We then discuss connected undirected networks with two-way message passing between each pair of adjacent nodes. In the end, we expand the discussions to networks with directed topologies that are strongly connected

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

About time

Time has historically been a measure of progress of recurrent physical processes. Coordination of future actions, prediction of future events, and assigning order to events are three practical reasons for implementing clocks and signalling mechanisms. In large networks of computers, these needs lead to the problem of synchronizing the clocks throughout the network. Recent methods allow this to be done in large networks with precision around 1 millisecond despite mean message exchange times near 5 milliseconds. These methods are discussed