  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.

Distributed, Parallel, and Cluster Computing