A maritime vessel communications system may include a satellite communications network, and maritime communications terminals associated with maritime vessels and operable over the satellite communications network. The system may also include a communications management server to obtain vessel geographic position and heading data associated with the maritime vessels, and obtain historical vessel travel route data associated with the maritime vessels. The server may also use machine learning to determine predicted vessel travel routes based upon the vessel geographic position and heading data, and the historical vessel travel route data, and obtain historical satellite communications network usage data associated with the maritime communications terminals. The server may also use machine learning to determine predicted network usage for the terminals based upon the historical network usage data and the predicted vessel travel routes, and operate at least one of the satellite communications network and the terminals based upon the predicted usage.