Consensus is one of the key problems in fault-tolerant distributed computing. Although the solvability of consensus is now a well-understood problem, comparing different algorithms in terms of efficiency is still an open problem. In this paper, we address this question for round-based consensus algorithms using communication predicates, on top of a partial synchronous system that alternates between good and bad periods (synchronous and nonsynchronous periods). Communication predicates together with the detailed timing information of the underlying partially synchronous system provide a convenient and powerful framework for comparing different consensus algorithms and their implementations. This approach allows us to quantify the required length of a good period to solve a given number of consensus instances. With our results, we can observe several interesting issues, such as the number of rounds of an algorithm is not necessarily a good metric for its performance.
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