Modelling population movement within a city.

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The semester break is here and I'm working on a startup. One of the project requires me to determine the movement of population within a highly-dense city in light of variables as such time of the day, parts of a week, how large scale events affects the movement of population across different parts of the city. Why is this interesting? Take Uber as a case example: Uber slaps surge pricing on consumers if the pick-up destination of their choice experiences a greater demand than supply. While this works in the favour of Uber drivers, this certainly means more pay out to Uber drivers by Uber. More pertinently, this suggests poor allocation of resources to areas of greater demand where areas of lower demand could be experiencing a greater supply of Uber drivers.

Any suggestion as to good resources and the mathematics to get me started would be very much appreciated.

Thanks in advance.

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This is basically Sim City.

http://m.ign.com/wikis/simcity/Traffic

Traffic moves in predictable patterns. Generally speaking, your Sims leave their homes in a residential zone in the morning, and then take the nearest route to their jobs, either commercial or industrial. They'll stay there until the mid-afternoon (around 5pm), then drive back. Traffic to and from entertainment venues during their off-hours is not simulated; check out the zone relationships page for more information.

If you want to fully figure out your city's situation, watch the traffic flow during 9am and 5pm, the two “rush hours” (which in truth last more than an hour until you get mass transit in the city). Generally speaking, the more options you have between your residential and industrial neighborhoods, the better your traffic flow will be, as your Sims will be less inclined to take the exact same route as all their neighbors.

Here is some raw data for you on real cities, you can extrapolate to whatever you are investigating.

https://www.google.com/amp/www.citylab.com/amp/article/364604/?client=ms-android-hms-tmobile-us