Here in Sydney, we just got a massive 'size' upgrade and well well, it slowed traffic! https://www.smh.com.au/politics/nsw/the-rozehell-interchange...

Unfortuantely maths and the real world don't always add up..

Right, as can the effect of adding bicycle lanes, smart traffic lights, buses, bus lanes, traffic calming, different road surfaces, and etc etc.

And- apparently it gets interesting if you start computing throughput in terms of per person instead of per vehicle.

It's the psychology that they don't take into account. Making travel times better in one area makes more people take more trips or change when they take trips, making it worse again until some kind of equilibrium is reached over a year or a couple of years (which is often around the same kind of travel times you had before the upgrade).

You could absolutely make traffic better by increasing lanes somewhere where the population was generally decreasing at a decent rate, of course, but population growth is another source in many places - you can't build enough new capacity in a lot of areas to keep up with the growth.

The fundamental problem is that cars are a very space inefficient way of moving people - that's why we see this problem in cities but don't tend to see it in rural areas (because they don't have many people but have plenty of space, so the volumetric inefficiency doesn't matter), and why you don't tend to see the issue much with rail other transit - since they have so much passenger capacity for the space they take up, if there's induced demand there's often scope for increasing service frequency.