Rude railway-trains, with all your noise and smoke,
I love to see you wheresoe'er ye move :
Though Nature seems such trespass to reprove :
Though ye the soul of old romance provoke,
I thank you, that from misery ye unyoke
Thousands of panting horses.
[Richard Howitt, from "Railway Sonnets," Hood's Magazine, March 1845]
Railway time "standard time adopted throughout a railway system" is by 1847.
1757, from rail (n.1) + road. Originally "road laid with rails for heavy wagons" in mining operations. The process itself (but not the word) seems to have been in use by late 17c. Application to passenger and freight trains dates from 1825, tending to be replaced in this sense in England by railway.
"serving as a model; worthy to serve as an exemplar," 1844, from model (n.). Model railway is by 1864.