How Can Traffic Flow Simulation Impact Motorway Speeds in Major Cities?

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Traffic flow simulation tools can effectively model the impact of reduced speed limits in urban areas. Slower speed limits generally lead to increased traffic congestion, as fewer vehicles pass a given point over time due to longer gaps between cars. Maintaining a two-second following distance further illustrates how a higher speed limit can enhance traffic flow by reducing the time it takes for vehicles to cross intersections. Additionally, higher speed limits enable drivers to better navigate common traffic disruptions, such as lane changes and merging. For optimal traffic management, synchronizing traffic signals is crucial, and resources on traffic signal synchronization algorithms can be found online. Furthermore, traffic flow can be mathematically modeled using a first-order hyperbolic partial differential equation, derived from the principle of conservation of vehicles.
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Has anyone seen a traffic flow simulator, or used a program similar to this?

I would like to simulate the effects of slowing traffic speed limit in a major city, and see what effect it would have on the motorways, maybe the software is all ready in use some where?
 
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In general, a slower speed limit will result in higher traffic. This is because the number of cars passing by any specific cross section of a street / highway is reduced with a slower speed limit (or larger gaps time wise).

In theory, even if all drivers maintain a 2 second following distance, the flow with a faster speed limit is increased slightly by the reduced time it takes for a car to pass across a cross section of a street.

In practice, a higher speed limit allows for cars to compensate more for the normal impedances to traffic flow, like lane changes or cars merging into traffic from side streets.

The best way to improve traffic flow is to synchronize the street signals. Do a web search for "traffic signal synchronization algorithm", and you'll find a lot of hits, probably including some simulations. It's easier to synchronize signals if all streets are one way.
 
There's a simple first order hyperbolic partial differential equation which can model traffic flow. You can derive it from conservation of cars. Search for 'traffic flow pde' or something like that.
 
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