Synchronization of strongly pulse-coupled oscillators with refractory periods and random medium access

  • Authors:
  • Julius Degesys;Prithwish Basu;Jason Redi

  • Affiliations:
  • BBN Technologies, Cambridge, MA;BBN Technologies, Cambridge, MA;BBN Technologies, Cambridge, MA

  • Venue:
  • Proceedings of the 2008 ACM symposium on Applied computing
  • Year:
  • 2008

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Abstract

The weakly pulse-coupled oscillator framework has proven to be a valuable resource for the development of peer-to-peer synchronization algorithms [9]. 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" pulse-coupled. 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).