On the possibility and impossibility of achieving clock synchronization

AbstractIt is known that clock synchronization can be achieved in the presence of faulty processors as long as the nonfaulty processors are connected, provided that some authentication technique is used. Without authentication the number of faults that can be tolerated has been an open question. Here we show that if we restrict logical clocks to running within some linear functions of real time, then clock synchronization is impossible without authentication when one-third or more of the processors are faulty. We also provide a lower bound on the closeness to which simultaneity can be achieved in the network as a function of the transmission and processing delay properties of the network

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

Modelling and Synchronisation of Delayed Packet-Coupled Oscillators in Industrial Wireless Sensor Networks

In this paper, a Packet-Coupled Oscillators (PkCOs) synchronisation protocol is proposed for time-sensitive Wireless Sensor Networks (WSNs) based on Pulse-Coupled Oscillators (PCO) in mathematical biology. The effects of delays on synchronisation performance are studied through mathematical modelling and analysis of packet exchange and processing delays. The delay compensation strategy (i.e., feedforward control) is utilised to cancel delays effectively. A simple scheduling function is provided with PkCOs to allocate the packet transmission event to a specified time slot, by configuring reference input of the system to a non-zero value, in order to minimise the possibility of packet collision in synchronised wireless networks. The rigorous theoretical proofs are provided to validate the convergence and stability of the proposed synchronisation scheme. Finally, the simulations and experiments examine the effectiveness of PkCOs with delay compensation and scheduling strategies. The experimental results also show that the proposed PkCOs algorithm can achieve synchronisation with the precision of $26.3\mu s$ ($1$ tick)

Comments on the "Byzantine Self-Stabilizing Pulse Synchronization" Protocol: Counter-examples

Embedded distributed systems have become an integral part of many safety-critical applications. There have been many attempts to solve the self-stabilization problem of clocks across a distributed system. An analysis of one such protocol called the Byzantine Self-Stabilizing Pulse Synchronization (BSS-Pulse-Synch) protocol from a paper entitled "Linear Time Byzantine Self-Stabilizing Clock Synchronization" by Daliot, et al., is presented in this report. This report also includes a discussion of the complexity and pitfalls of designing self-stabilizing protocols and provides counter-examples for the claims of the above protocol

An Autonomous Distributed Fault-Tolerant Local Positioning System

We describe a fault-tolerant, GPS-independent (Global Positioning System) distributed autonomous positioning system for static/mobile objects and present solutions for providing highly-accurate geo-location data for the static/mobile objects in dynamic environments. The reliability and accuracy of a positioning system fundamentally depends on two factors; its timeliness in broadcasting signals and the knowledge of its geometry, i.e., locations and distances of the beacons. Existing distributed positioning systems either synchronize to a common external source like GPS or establish their own time synchrony using a scheme similar to a master-slave by designating a particular beacon as the master and other beacons synchronize to it, resulting in a single point of failure. Another drawback of existing positioning systems is their lack of addressing various fault manifestations, in particular, communication link failures, which, as in wireless networks, are increasingly dominating the process failures and are typically transient and mobile, in the sense that they typically affect different messages to/from different processes over time