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Asynchronous Phase Synchronization in Uniform Unidirectional Rings
April 2004 (vol. 15 no. 4)
pp. 378-384

Abstract—This paper proposes a self-stabilizing asynchronous phase synchronization protocol for uniform unidirectional rings. Consider applications with phase bound K, i.e., the phases are phase 0, phase 1, \ldots, phase K-1, phase 0, phase 1, etc. Under the protocol, when the ring is stabilized, it satisfies the following criterion: No node begins to execute phase (k+1)mod K until all nodes have executed phase k, and after all nodes have executed their phase k, each node eventually executes phase (k+1)mod K. Besides the variable used to denote the phase that a node is working on, each node maintains only one auxiliary variable with b states, where b can be any number greater than or equal to the ring size. Provided that K and b satisfy the limitation: {\rm{K}}\times b>n(b-1), the proposed protocol is correct under the parallel model and takes at most 2({\rm{K}}\times b) rounds to stabilize.

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Index Terms:
Phase synchronization, self-stabilization, transient fault, uniform ring.
Shing-Tsaan Huang, Tzong-Jye Liu, Su-Shen Hung, "Asynchronous Phase Synchronization in Uniform Unidirectional Rings," IEEE Transactions on Parallel and Distributed Systems, vol. 15, no. 4, pp. 378-384, April 2004, doi:10.1109/TPDS.2004.1271186
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