In-network computation in sensor networks
Sappidi, Rajasekhar Reddy
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Sensor networks are an important emerging class of networks that have many applications. A sink in these networks acts as a bridge between the sensor nodes and the end-user (which may be automated and/or part of the sink). Typically, convergecast is performed in which all the data collected by the sensors is relayed to the sink, which in turn presents the relevant information to the end-user. Interestingly, some applications require the sink to relay just a function of the data collected by the sensors. For instance, in a fire alarm system, the sinks needs to monitor the maximum of the temperature readings of all the sensors. For these applications, instead of performing convergecast, we can let the intermediate nodes process the data they receive, to significantly reduce the volume of traffic transmitted and increase the rate at which the data is collected and processed at the sink: this is known as in-network computation. Most of the current literature on this novel technique focuses on asymptotic results for large networks and for very elementary functions. In this dissertation, we study a new class of functions for which we want to compute explicit solutions for networks of practical size. We consider the applications where the sink is interested in the first M statistical moments of the data collected at a certain time. The k-th statistical moment is defined as the expectation of the k-th power of the data. The M=1 case represents the elementary functions like MAX, MIN, MEAN, etc. that are commonly considered in the literature. For this class of functions, we are interested in explicitly computing the maximum achievable throughput including routing, scheduling and queue management for any given network when in-network computation is allowed. Flow models have been routinely used to solve optimal joint routing and scheduling problems when there is no in-network computation and they are typically tractable for relatively large networks. However, deriving such models is not obvious when in-network computation is allowed. Considering a single rate wireless network and the physical model of interference, we develop a discrete-time model for the real-time network operation and perform two transformations to obtain a flow model that keeps the essence of in-network computation. This model gives an upper bound on the maximum achievable throughput. To show the tightness of that upper bound, we derive a numerical lower bound by computing a feasible solution to the discrete-time model. This lower bound turns out to be close to the upper bound proving that the flow model is an excellent approximation to the discrete-time model. We then adapt the flow model to a wired multi-rate network with asynchronous transmissions on links with different capacities. To compute the lower bound for wired networks, we propose a heuristic strategy involving the generation of multiple trees and effective queue management that achieves a throughput close to the one computed by the flow model. This cross validates the tightness of the upper bound and the goodness of our heuristic strategy. Finally, we provide several engineering insights on what in-network computation can achieve in both types of networks.