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I'm attempting to create a simulation of car traffic and to model the flow, it seems like Poisson Distribution would be useful here. I'm still trying to get my head around the variables I would incorporate, but at the moment I know what I want the arrival rate at a certain point to be, the speed limit, and the minimum gap (time) between cars.

Currently, cars spawn on one end of the road after a preset amount of time and accelerate to the speed limit, checking for cars in front and slowing down if necessary so as to keep at least a the minimum gap between the two of them.

I'm not sure how to incorporate variables such as acceleration into the Poisson Distribution. Does anybody have any experience implementing something similar?

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  • \$\begingroup\$ @tom10 You're right. I was thinking about this incorrectly but your insight put me back on track, thanks a lot. \$\endgroup\$
    – rafvasq
    Commented Apr 10, 2018 at 18:58
  • \$\begingroup\$ Great. Since it is an answer to your question, I wrote it up as one. \$\endgroup\$
    – tom10
    Commented Apr 10, 2018 at 19:21

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Unless cars are created or destroyed between the two ends of the road, your average arrival rate will be the same as your average creation rate. Therefore, all you need to do is adjust the parameters of your Poisson distribution to match your desired arrival rate.

The other variables you mention, such as acceleration, etc, aren't going to change the average arrival rate. These other variables may change the dynamics of traffic flow, and small details of the arrival, like bunching and other fluctuations about the average. But they won't change the average arrival rate.

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