If you're not sure where to start, you're probably going to need to start with some slightly simpler problems that you can combine together to get you to a final solution.
Perhaps the best place to start would be by trying to predict how many cars arrive at a light in one cycle? In such a case, you're going to need to know something about probability distributions and for low numbers that need to greater than or equal to 0, poisson distributions specifically.
If you're trying to predict which choice may be made by the driver of a car sitting at any given set of lights, based on measurements, the easiest approach may be to generate a discrete probability distribution (if drivers choices are uncorrelated) or Markov Chains (if they are correlated).
If you're trying to work out how single lights change colour (Green -> Amber, Amber -> Red, Red -> Green), you could model that as a State machine.
If you're trying to manage multiple sets of lights, particularly when those transitions can be driven by asynchronous events, your best bet is something like a discrete event simulation. If you're looking for a more formal description of the system as a whole you may need to move to Petri nets
If you care about the positions of the individual cars you may be able to model their positions (and transitions between positions) on a graph, where vertices are associated with a location. If you need to incorporate detailed information about geometry, dynamics, kinematics you are going to need detailed models of the cars and their interactions with the road surface (and potentially each other). This would be important if you wanted to model crashes within an intersections.