The weakly pulse-coupled oscillator framework has proven to be a valuable resource for the development of peer-topeer synchronization algorithms . But leveraging it in a practical implementation (e.g. in wireless ad hoc/sensor networks) is problematic due to the difficulty in achieving precise coordination of broadcast messages. We found that a pseudo-random medium access control (MAC) protocol produces a super-linear increase in the number of messages required per node with increasing network size, which would normally discourage its use. However, introducing a “refractory period” reduces this growth to linear with a small constant (verified by numerical simulations). Furthermore, the refractory period allows for an increase in the coupling constant, effectively making the network “strongly” pulsecoupled. We show that the combination of the refractory period, strong coupling, and probabilistic medium access results in a significant decrease in the average number of messages required per node in several practical network topologies (and as much as ∼ 90 % over the original idealistic mechanism in line topologies)
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