Apologies if there is a better place to post this question (wasn't sure if riddles stackexchange or this would be more appropriate). I assume it is a graph theory type question.
Pretend you are autonomous vehicle, dropped on a random point on a random US road. You have infinite fuel. Your programming is simple - every time you encounter an intersection, you take the path that has been most travelled (you can pretend that there is historical traffic data loaded into the mapping system). For example, if you encounter a four way stop, and 70% of the time drivers go straight, you will go straight.
If you ever "re-encounter" an intersection and you are driving the same direction, you can stop (safely assuming you are in a loop state)
Has anyone ran this type of simulation before?
A few questions in this hypothetical situation:
- What kind of roads would the autonomous cars most likely end up? I was originally thinking highways, since more cars would choose to not take an exit and go straight (most of the time), but thinking about it more, unless the highway is a complete loop, the last exit of a highway would probably be taken.
- If you ran a simulation Monte Carlo style, would there be a specific road(s) in the US that would be most encountered? Would that be likely the most travelled road period in the US?
- There would be many short "loops" clearly, but I can imagine a few long ones. I wonder if there would be a strategy to find the longest loop?
Also, I am not a mathematician, but is this type of problem a graph problem or something else?