Time Scales in Probabilistic Models of Wireless Sensor Networks

We consider a stochastic model of clock synchronization in a wireless network consisting of N sensors interacting with one dedicated accurate time server. For large N we find an estimate of the final time sychronization error for global and relative synchronization. Main results concern a behavior of the network on different time scales $t=t_N \to \infty$, $N \to \infty$. We discuss existence of phase transitions and find exact time scales on which an effective clock synchronization of the system takes place.