I used to be a lift technician a little while ago...
Just how accurate do you want to make this project? It would probably be easier for you to model your project off the older "three stage" lift design.
Basically the lift is called to whatever floor, when the lift approaches a "floor zone" the motor halves its speed, and when it reaches the "door zone", the speed is reduced effectively to a crawl until the carriage is at the right level. This process is reversed when the carriage is leaving a level. You need of course to provide some kind of limits to let the controller know where the carriage is.
You also need to work out the calling system, so if a person is on the second floor wanting to go down, if the lift is travelling down from the top floor, it will stop at the second, but not if it is travelling upwards.