Efficiency Analysis on an Information Sharing Process with Randomly Moving Mobile Sensors

For the recent remarkable developments of wireless communication technology, information communication networks between mobile sensors become possible and have been studied recently. In the networks, however, the theoretical understanding of efficient content delivery schemes for collecting information is quite primitive at present. To promote the understanding, we investigate analytically and numerically an information sharing process with mobile sensors where the motion of sensor is a random walk and each sensor exchanges possessing information with the other sensors if they are at the same position on the d-dimensional unbounded square lattice. We find that probability distribution functions for information collection times obey power laws at the tails. We introduce three classes for the characterization of information collection performance and classify the system by recursiveness of random walk and the power-law exponents. Consequently, information collection is successful in one and two dimensions, while unsuccessful in larger dimensions. It also become efficient in one and two dimensions as increasing the number of sensors sufficiently. However, the system in two dimension needs much more sensors for the efficient collection compared to that in one dimension.