Pretty much all larger cities and sprawls in the Empire have an rapid underground rail system. These trains are entirely autonomous (with security and technical personnel on board). It is public-owned, and the fares do not pay for its upkeep - inner-city commuters, students and seniors use the rail free of charge, and everyone else pays a varying rate depending on current usage to counteract congestion. Top speed is around 50m/s (180km/h). Average speed varies depending on the density of stations.
Some of the larger city-sprawls have express lines that use sliding cabins to minimize delays at the stop. People at the station enter the cabins; people leaving at the next stop do the same on the train; the train slows down just long enough to swap the compartments.
Long-distance and intercontinental transit uses a vacuum-tube mag-lev train that runs underground or along the ocean floor. Top speed is 2000m/s (7200km/h, or the equivalent of Mach 5.88 in air). The equatorial line can go around the world in a little over six hours.
