Wireless Sensor Network Design via Interacting Particles

We consider a design problem in which a one-dimensional array of sensors, connected via a wireless network, is used to track a moving vehicle. Individual sensors occasionally lose the vehicle, but can relocate it with aid from neighboring sensors. Communication between sensors is costly, so we accordingly optimize the communication protocol within a class of broadcast-type protocols to maximize the amount of time that the network as a whole tracks the target, subject to a bound on the total rate of communication between sensors. The solution to the optimization problem is heavily influenced by a phase transition exhibited by the network, which we reveal by appealing to existing results from interacting particle systems. We extend these results in the course of solving our optimization problem to address the novel problem of “designing an interacting particle system.”