So I'm trying to create a very simple mathematical model for a very idealized theoretical situation of traffic flow. In this situation I'm considering vehicles to be points (no length) each going the same speed with the same distance between them. The vehicle in front (vehicle 1) slows down and as a result each vehicle behind it slows down by the same amount, however there is a lag/reaction time in-between each consecutive vehicle slowing down. All I've got right now is a jumbled mess of variables in my head as I try to create a general model for this. I'll define them as follows:(adsbygoogle = window.adsbygoogle || []).push({});

I feel like some of the variables I've declared could be declared in a different more comprehensible way, and if so, please suggest how I should do it.

- Vehicle Speed: ##v = \frac{dx}{dt}##
- Vehicle Distance: ##x##
- Vehicle Speed after Deceleration: ##v - Δv = \frac{dx}{dt} - \frac{Δx}{Δt}## (Is there perhaps a different way of writing this that's more useful? Not sure why but I feel like there is. Probably not.)
- Lag/Reaction Time: ##t##

That aside, does anyone have any ideas for how I can start to model what I'm trying to model? I've also created a simple graphic that might be helpful, you can ignore the subscript on the vehicle distance variable.

I feel like I might just be lacking the initial intuition, as might be obvious by the jumbled manner in which I've put this post together. If anyone can give me any suggestions on creating this initial model I'd appreciate it!

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# Attempting to model traffic flow after front car decelerates

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