Lower bounds for convergence function based clock synchronization

The second requirement says that for any time interval of length 1, the clock of a correct process can drift from rerdtime by at most p. 1+ D, where the constant D, accounting for clock adjustments, is called the rnazimum discontinuity. These requirements imply that the adjustments applicable to correct clocks is bounded by a constant, the so-called maximum correction. We sssume that each process has access to a local hardware clock and that the drift of correct hardware clocks is bounded by a given constant p <1. Since we are in this paper only interested in internal clock synchronization algorithms capable of masking arbitrary failures, when we talk about a synchronization algorithm, we mean an internal clock synchronization algorithm tolerant of arbitraxy failures. Many synchronization algorithms can be described as instances of a generic clock synchronization algorithm using the notion of a convergence function [10]. This generic algorithm can be succinctly described as follows: at the end of each synchronization round each process reads the clocks of all processes and then adjusts its clock value for the next round by applying a convergence function to the clock readings of the current round. A convergence function is a mapping that has a process p and p’s clock readings as parameters and returns a clock value. A synchronization algorithm which can be described as an instance of the above generic algorithm using any convergence function will be termed a convergence junction based algorithm. Convergence function based synchronization algorithms can use the following assumptions to provide internally synchronized clocks: