ZebraNet and its theoretical analysis on distribution functions of data gathering times

We theoretically investigated a general property of data gathering times in a wireless communication system with randomly moving sensors which share data only with nearby ones. We proposed a stochastic model of the system to analyse distribution functions of data gathering times. We found that the time distribution asymptotically obeys a power-law decay in infinite space, while it becomes exponential in finite space. Mean and variance of the time distributions become finite as the number of sensors is sufficiently large, meaning efficient data gathering can be accomplished by deploying a large number of sensors when sensors are spreading data epidemically. In the finite space, moreover, both power-law and exponential distributions coexist in general. We proposed a truncated power-law distribution for a least-square fitting of the time distribution on the whole range to estimate their accurate mean and variance.