Propagation properties for a message in a Brownian sensor network

A wireless multi-hop sensor network, in which node positions are fixed, may fail to transmit a message over longer distances. This could occur, for example, due to low node density or small node transmission range. In mobile systems where nodes are allowed to move, it is natural to expect a better reachability, with the condition that messages are not time-critical and longer propagation delays are permitted. In order to understand the relation of mobility to node density and node transmission range, we study a simple network model where active sensors move according to independent Brownian motions. In the one-dimensional case, the propagation of a message can be viewed as a Brownian growth process among Poisson points on the real line. We investigate the distributional properties of the mobile nodes and show that the system grows linearly at a remarkably uniform rate. For the spatial model where planar Brownian motions transport and transfer the message to those nodes which eventually come within transmission range of active messenger nodes, we provide a discussion and some insight based primarily on simulations.