On the effect of asymmetric communication on distributed time synchronization

Several distributed algorithms have been recently proposed to estimate clock offsets and skews in a network of processors from a set of noisy measurements of the difference between clock offsets and of the ratios of clock skews. These algorithms are designed to converge to the optimal, i.e., the best linear unbiased, estimates even in the presence of node and link failures. However, they require symmetric communication between nodes for convergence. We examine the case when communication is asymmetric, i.e., when a node can receive information from another node but not vice versa. We first show that in the presence of asymmetric communication links, these algorithms converge to an unbiased but suboptimal estimate. In fact, we show that with a distributed algorithm that is constrained to use only local information, it is generally impossible to converge to the optimal estimate when communication is asymmetric. We characterize the resulting estimate that these algorithms converge to in the presence of asymmetry, and node and link failures, and its error covariance.