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I wanted to build a model with a probability problem with the following.

Consider the intersection of two roads controlled by a traffic light. The model should consider probabilistic the arrival of automobiles in each direction. Then evaluate how you would set the timing for the length that the light is green in each direction.

These are some Factors that could be consider (Not all needed):

What if the traffic is very light in one road and very heavy in the other?

What if there are sensors to detect the presence of automobiles at the intersection?

What if there are no sensors?

What possible criteria could you use to determine the "goodness" of alternative timing schemes?

How does the optimal timing of the traffic light depend on different evaluation criteria?

What if you had to consider network effects such as two or more traffic lights relatively near each other, so that the timing at one light affects the arrival rates and optimal timing at others?

This is what I think so far

Maybe all modern roads with heavy traffic require sensors now, so probability of traffic flow would not be relevant.

So if I have a two minute cycle with the lights and section the two minutes according to the probabilities assigned to the two roads. For example, if the probability that a car will arrive next in road A is P(A) = a, then the probability that a car will arrive next in road B is P(B) = 1 - a.

I could assign the lights "2a" for road A and "2(1-a)" for road B, then I think I need to decide about how long I will allow yellow/amber light from the green.

Any ideas of how I can set it up? Or maybe any different ideas about a model involving traffic lights and those 2 roads?

Any help/thoughts will be much appreciated.

Thanks!

Ps. Not sure if its necessary to use mathlab or if I could use excel