James,
I played with the circuit a bit last night and was able to get parts of it working. Based on the calculations of the components, it appears that your first timer is setup for a ~3 second mono-stable pulse to light the bottom light of the crossing. I had to change the timing cap to 0.1uf to get the circuit to work. I'm guessing this is just a quirk with Multisim in the way the timer simulation occurs. I also changed the capacitor for the 3rd stage to get them to blink (and connecting the VCC line to 9V to debug each section independently). I did this to get the simulation working to an extent. When you build it, replace the caps with the calculated values. I couldn't figure out a good way to get the 3rd stage to start once the 1st stage completes. I tried SCRs, flip-flops, etc. and things just kept getting more compicated. There is also no way to get both of the 3rd stage lights on at the same time to fully simulate the crossing.
If you are designing this circuit as a learning experience, then by all means, keep experimenting. If you actually want to build the circuit for use, the way I would do it would be to use a small PIC microcontroller. You should be able to find one that has enough I/O and features for about the same price as a single 555 chip.
Tom
