Self-synchronizing properties of CSMA wireless multi-hop networks

We show that CSMA is able to spontaneously synchronize transmissions in a wireless network with constant-size packets, and that this property can be used to devise efficient synchronized CSMA scheduling mechanisms without message passing. Using tools from queuing theory, we prove that for any connected wireless networks with arbitrary interference constraints, it is possible to implement self-synchronizing TDMA schedules without any explicit message passing or clock synchronization besides transmitting the original data packets, and the interaction can be fully local in that each node decides when to transmit next only by overhearing its neighbors' transmissions. We also provide a necessary and sufficient condition on the emergence of self-synchronization for a given TDMA schedule, and prove that such conditions for self-synchronization can be checked in a finite number of steps for a finite network topology.