Scaling Relations of Data Gathering Times in an Epidemically Data Sharing System with Opportunistically Communicating Mobile Sensors

We investigated data gathering time in an epidemically data sharing system with opportunistically communicating mobile sensors. We proposed a stochastic process of the system where N sensors moved randomly and independently on the d–dimensional square grid with size L and when meeting opportunistically at the same position on the grid, the sensors shared and stored all possessing data epidemically. We focused on three data gathering times, that is, latency times that (1) at least one sensor collects all (2) every sensor collects at least one common data (3) every sensor collects all. As a result, we found that in general the complementary cumulative distribution functions of these times decay exponentially in their asymptotic regions.We also examined a decay speed, which is also called relaxation time, of the exponential decay numerically with varying d, L, and N. Finally we showed scaling relations of the relaxation times. We think that these relations are useful for estimating the minimum required number of sensors to collect data within a certain short period of time when the sensors are densely covered on the system.