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.

In wireless sensor networks, one is not interested in downloading all the data from all the sensors. Rather, one is only interested in collecting from a sink node a relevant function of the sensor measurements. This paper studies the maximum rate at which functions of sensor measurements can be computed and communicated to the sink node. It focuses on symmetric functions, where only the data from a sensor is important, not its identity. The results include the following. The maximum rate of downloading the frequency histogram in a random planar multihop network with n nodes is O(1/logn) A subclass of functions, called type-sensitive functions, is maximally difficult to compute. In a collocated network, they can be computed at rate O(1/n), and in a random planar multihop network at rate O(1/logn). This class includes the mean, mode, median, etc. Another subclass of functions, called type-threshold functions, is exponentially easier to compute. In a collocated network they can be computed at rate O(1/logn), and in a random planar multihop network at rate O(1/loglogn). This class includes the max, min, range, etc. The results also show the architecture for processing information across sensor networks.

This paper presents the computing and communicating statistics in sensor networks. A deterministic sequence of message passing between sensors, result in the vector of function values being, communicated to the fusion center, for any combination of individual measurement vectors. A wireless communication model using protocols is also discussed.