A theory of clock synchronization

We consider the problem of clock synchronization with uncertain message delays and bounded clock drifts. To analyze this classical problem we introduce a characterization theorem for the tightest achievable estimate of the readings of a remote clock in any given execution of the system. Using this theorem, we obtain the first optimal on-line distributed algorithms for clock synchronization. The algorithms are optimal for all executions, rather than only worst cases. The general algorithm for systems with drifting clocks has high space overhead, which is unavoidable, as we show. For systems with different clocks (i. e., clocks that run at the rate of real time), we present a remarkably simple and efficient algorithm. The discussion focuses on the variant where one of the clocks shows real time, but we present results also for the case where real time is not available from within the system. Our approach encompasses various models, such as point-To-point or broadcast channels, perfect or faulty communication links, and it has fault-detection capabilities.