A-Train was created in Japan by Artdink, and is the first game that Maxis has published that was developed outside of the company. (We have huge egos and think we're pretty good game designers, so if we publish someone else's game, it means we're really impressed.)
This game is actually Artdink's third complete version of A-Train, which was released as Take the A-Train III in Japan.
The first version of A-Train was released in Japan in April 1986 for the Fujitsu FM-series computer. It was later available for all the major home computers in Japan.
A-Train II was released in Japan in July 1988, and was published in the U.S. by Seika Corp. under the name Railroad Empire.
Take the A-Train III was first released in Japan in December 1990 and since then has been a consistent top-ten seller, winning the Best Simulation of the Year Award from Login magazine (well, actually it tied for first with SimCity), and winning reader polls as their favorite simulation game.
The impression, it would seem, was mutual. How much, I wonder, was this game influenced by Simcity? The previous game in the series, the abovementioned Railroad Empire, was still purely a railroad sim similar to Sid Meier's Railroad Tycoon, where you lay tracks across the country and worry about little but resources and your budget. This third installment takes place on a smaller scale, on city level, and you not only want your railroad to flourish, you want the city to flourish. The way you lay out tracks will determine whether or not you get the tallest buildings.
On the other hand, I do wonder how much A-Train influenced SimCity 2000, which was released less than two years later. The two games look rather similar. SimCity 2000 was maybe graphically more advanced, since it ran in 256 colors on all platforms, but A-Train already had day and night cycles (including short dusk and dawn periods), something that would take the Simcity series ten more years to implement, and seasons.
The Take the A-Train
series, of which this game is
the third, is immensely popular in Japan. In the US, it
proved a failure, probably due to the high level of micromanagement
the game requires. All in all there have been three translations of
games of the series: Railroad Empire in 1991, A-Train in 1992, and
C.E.O. (sometimes known under its Japanese title AIV Network$) in
1997. None of them was very successful.
Kohsuke Kawaguchi has been working on a free, open-sourced clone, FreeTrain, since 2002.

The Japanese original (A Ressha de Ikou III) was released in 1990 on the NEC PC-98, see screenshot above. It was ported to the Sharp X68 in 1991, the Turbografx PC Engine 1993-06-11, and the NES at an unknown date. Later the original PC version was ported to Windows and is still sold by Artdink.
Maxis released their localisation for three platforms: DOS, Amiga, and Macintosh. The DOS version was done in-house. It supported VGA (640×480), EGA (640×350), and Hercules. For EGA and VGA, you had the choice between 16-color and monochrome. The game runs on a 286, but it has been reported that scrolling is abominable unless you have more CPU power. You can save a PCX image of the whole map out of the main menu, which of course could take quite some time, a feature Transport Tycoon would later have too.
The Macintosh and Amiga ports were done by The Dreamer's Guild, who would later create Halls of the Dead: Faery Tales Adventure II. The Macintosh version used standard UI elements just like the first two games of the Simcity series and SimTower, fitting even more smoothely into the Maxis program. It will also take advantage of any resolution the hardware supports.
In 1996 there was a Playstation version that came with a pack of SimCity Collectible Trading Card game cards. While published under the same title A-Train, it was already based on the next game of the series.

The Amiga version was created mainly for the European market, but was published in the US in 1993 by Brøderbund. It came in a hi-res and a lo-res version on seperate disks. Both were needed to play the game, but you had to boot from the one with the resolution you wanted. The lo-res version needs a 1MB Amiga, the hi-res version an additional 512kB Fast RAM.
The hi-res version is interesting because it is one of the few Amiga games at the time to use the interlaced mode (the only other one I know is the shareware, meanwhile freeware, artillery game BattleDuel), though only for the main window. As the screenshot above shows, there were up to three different resolutions on one screen: lo-res for the message window at the top, interlaced for the main screen, and the somewhat more common (Hannibal, Dark Seed) non-interlaced hi-res mode for the status bar at the bottom.