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I'm looking for a way to model a simple road network (e.g. cars, no need for multiple transport modes), to investigate the effects of intelligent routing on congestion.

Is there any existing software that offers this functionality? Or examples I can borrow from?

This is just for a very basic proof of concept, so doesn't have to be neat.

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The one that I know is Aimsun, which is defined as a traffic modelling software that allows you to model anything from a single bus lane to an entire region. It's a professional tool and I'm pretty sure it can do what you need.

There's also an Aimsun page on Wikipedia:

Aimsun software is used by government agencies, municipalities, universities and consultants worldwide for traffic engineering, traffic simulation, transportation planning and emergency evacuation studies. It is used to improve road infrastructure, reduce emissions, cut congestion and design urban environments for vehicles and pedestrians.

It's not a free application but if you just need to get some ideas and "play" with it you should be able to request a free trial version.

Here are a few images of the software in action taken from the official website:

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