We consider a wireless sensor network, where nodes switch between an active (on) and a sleeping (off) mode, to save energy. The basic assumptions are that the on/off schedules are completely uncoordinated and that the sensors are distributed according to a Poisson process and their connectivity ranges are larger or equal to their sensing ranges. Moreover, the durations of active and sleeping periods are such that the number of active nodes at any particular time is so low that the network is always disconnected.Is it possible to use such a network for time-critical monitoring of an area? Such a scenario requires indeed to have bounds on the latency, which is the delay elapsed between the time at which an incoming event is sensed by some node of the network and the time at which this information is retrieved by the data collecting sink. A positive answer is provided to this question under some simplifying assumptions discussed in the paper. More precisely, we prove that the messages sent by a sensing node reach the sink with a fixed asymptotic speed, which does not depend on the random location of the nodes, but only on the network parameters (node density, connectivity range, duration of active and sleeping periods). The results are obtained rigorously by using an extension of first passage percolation theory.

In this paper, performance formulae for a queue serving Gaussian traffic are presented. The main technique employed is motivated by a general form of Schilder's theorem, the large deviation result for Gaussian processes. Most probable paths leading to a given buffer occupancy are identified. Special attention is given to the case where the sample paths of the Gaussian process are smooth. The performance approximations are compared with known analytical results or by means of simulation. The approximations appear to be surprisingly accurate.

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