Event Detection Time for Mobile Sensor Networks Using First Passage Processes

A new technique based on first passage processes is presented as a means for calculating the detection time of an event by wireless mobile sensors located in R^d, d = 1,2 and 3. Our proposed method is valid for any type of mobility model, and is amenable to a variety of extensions. We consider heterogenous networks in which sensor platforms have different mobility patterns. The second extension considers unreliable sensors with randomly distributed operational lifetimes. The second generalization is of paramount importance if the network is deployed in a hostile environment. Our main results are illustrated for random linear motion and Brownian motion. An approach for applying our theorems when sensors move according to a time- homogenous Markov process is also considered.