Regarding the host railroad, you can see a map for each route. Go to the train performance page and click any route:
http://www.amtrak.com/historical-on-time-performance
For example, here's a link to the
Crescent's performance page:
http://www.amtrak.com/crescent-train&mode=perf&overrideDefaultTemplate=OTPPageVerticalRouteOverview
The
Crescent travels from New York to Washington on Amtrak tracks; from Washington to Alexandria on CSX; and from Alexandria to New Orleans on Norfolk Southern.
The
Silver Meteor travels from New York to Washington on Amtrak tracks; from Washington to West Palm on CSX; and from West Palm to Miami on Florida DOT.