Efficient Two-Dimensional Self-Stabilizing Byzantine Clock Synchronization in WALDEN

For tolerating Byzantine faults of both the terminal and communication components in self-stabilizing clock synchronization, the two-dimensional self-stabilizing Byzantine-fault-tolerant clock synchronization problem is investigated and solved. By utilizing the time-triggered (TT) stage provided in the underlying networks as TT communication windows, the approximate agreement, hopping procedure, and randomized grandmasters are integrated into the overall solution. It is shown that with partitioning the communication components into $3$ arbitrarily connected subnetworks, efficient synchronization can be achieved with one such subnetwork and less than $1/3$ terminal components being Byzantine. Meanwhile, the desired stabilization can be reached for the specific networks in one or several seconds with high probabilities. This helps in developing various distributed hard-real-time systems with stringent time, resources, and safety requirements.