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

Idle Period Propagation in Message-Passing Applications

Idle periods on different processes of Message Passing applications are unavoidable. While the origin of idle periods on a single process is well understood as the effect of system and architectural random delays, yet it is unclear how these idle periods propagate from one process to another. It is important to understand idle period propagation in Message Passing applications as it allows application developers to design communication patterns avoiding idle period propagation and the consequent performance degradation in their applications. To understand idle period propagation, we introduce a methodology to trace idle periods when a process is waiting for data from a remote delayed process in MPI applications. We apply this technique in an MPI application that solves the heat equation to study idle period propagation on three different systems. We confirm that idle periods move between processes in the form of waves and that there are different stages in idle period propagation. Our methodology enables us to identify a self-synchronization phenomenon that occurs on two systems where some processes run slower than the other processes.Comment: 18th International Conference on High Performance Computing and Communications, IEEE, 201