When I was a boy I remember watching a couple of model railroading shows on public television (rare occurences) that showed men wiring up their railroads to a computer of some kind and running schedules, times and speeds from there on the layout. It seemed to work pretty flawlessly.
Do such programs exist today and what is the hardware required if they do? Where to purchase?
SMS
Actually, I think that PC via DCC would be a more appropriate title. DCC is the electronic protocol that gets the PC-generated control signals to the devices that need them.
You might look into this website:
http://www.jlcenterprises.net
They sell parts and information on Bruce Chubb’s CMRI (Computer - Model Railroad Interface) system.
I’m sure you could program a computer to automatically run a layout. The PC would need lots of input so you would need train detectors all over the place so it could keep track of where things were. Switches could be thrown automatically and the locos signalled to move. The problem with all this is that once you have the program and controls in place, you are going to get the same output everytime. To me, that would get boring. To run a different operating scheme, you would have to reprogram it. Someone told me a long time ago that a computer is a great tool to do one thing a million times. It is a terrible inefficient tool to do anything once.
This subject comes up from time to time. There are several systems on the market. One is http://www.trainpriority.com/ . All share high cost and geekinness and none are very popular. Better yet is to get 3rd planet or train sim and not even have a physical layout. 
Fred
Do they have programs to connect with a DCC system to run signals and maybe a dispatch computer to run the signals on a layout like a real railroad would have? I would like to do that one day if I can ever build my own layout. I would like to run a CTC system.