This is exactly the kind of problem NetLOGO is geared toward modelling and solving. It is very much like the LOGO (turtle graphics) you might have learned as a tween, but multi-agent, so you can model the behaviour of several types of cars (fast, slow, hesitant, etc), design a few multi-lane obstacles and traffic conditions, and let 'r rip. Of course you can click to observe from any particular vehicle's POV as well.
There are 3D and 2D versions, but your problem will quite suit the 2D version. It has been used to model the "coil spring" pattern of stop-and-go traffic already.
Check it out. I'd love to see the results, as your subject is one of very common interest.
https://ccl.northwestern.edu/netlogo/