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We analyze the spatial smoothing algorithm of Solis, Borkar and Kumar [1] for clock synchronization over multi-hop wireless networks. In particular, for a model of a random wireless network we show that with high probability the error variance is O(1) as the number of nodes in the network increases. This provides support for the feasibility of time-based computing n large wireless networks. We also provide bounds on the settling time of a distributed algorithm.

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The functional lifetime of a sensor network is defined as the maximum number of times a certain data collection function or task can be carried out without any node running out of energy. The specific task considered in this paper is that of communicating a specified quantity of information from each sensor to a collector node. The problem of finding the communication scheme which maximizes functional lifetime can be formulated as a linear program, under "fluid-like" assumptions on information bits. This paper focuses on analytically solving the linear program for some simple regular network topologies.The two topologies considered are a regular linear array, and a regular two-dimensional network. In the linear case, an upper bound on functional lifetime is derived, as a function of the initial energies and quantities of data held by the sensors. Under some assumptions on the relative amounts of the energies and data, this upper bound is shown to be achievable, and the exact form of the optimal communication strategy is derived. For the regular planar network, upper and lower bounds on functional lifetime, differing only by a constant factor, are obtained.Finally, it is shown that the simple collection scheme of transmitting only to nearest neighbors, yields a nearly optimal lifetime in a scaling sense.0-7803-9201

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