That is true if the new road does is indeed the source of the new traffic. But it all falls apart if that future increase in traffic will be coming regardless of whether the road is built. that's where the paradox really breaks down.

You cannot solve the problem of an external source of new traffic, be it a new stadium at the edge of town or new machine added to the edge of a network, by not building in any new capacity. Well, you could if you simply chose not to serve that new node. Not running any new roads to a new airport is a great way to get that airport to close, just as not serving that new customer on your network is a great way to make that customer go elsewhere.

The other flipside to the pardox is that it really is applicable to any network. Sometimes the best way to improve the efficiency of mass transit is to cull bus/train routes. But try selling that in a modern city.

To put the original paradox another way, though: if you run a road out of town far enough, somebody will build an airport at the end. The airport is indeed an "external source of new traffic", but it was built because the traffic system had enough unused capacity to absorb the projected load.

I;m not convinced that the people building stadiums and airports go around looking for cities with extra traffic capacity. They are responding to forces well outside local traffic issues. The fact that they will generate increased traffic is a factor during planning and construction, but it is certainly not in any way a driving force behind the decision to build.

You kind of imply that building a new road is useless if travel time stays the same. But increased traffic bandwidth IS improvement, even if individual drivers don't feel it.

Also same thing applies to this paradox. Even if individual travel time is reduced for some, I doubt that overall traffic throughput is reduced. At worst case scenario it should stay the same.

That only appears to be the best option if you specify all trips to be made via private automobile. Road bandwidth is more efficient on bike or bus, but people will default to a car if the road is well suited and there is parking at the destination. It's not that the road is useless, it's that it perpetuates demand for driving and so can't solve congestion except by brute force saturation.

It's one of the big shifts in planning thought to get away from a simple engineering problem of moving more cars faster and try to integrate different modes and give land use a more careful impact assessment.

> Road bandwidth is more efficient on bike or bus

Not necessarily for the people on the bus. Efficiency in terms of capacity represents one of several possible optimization criteria; the distribution of transit times to various destinations represents another.

That assumes that people will change from a car to other options. At least where I live, that will not happen. They tried to do exactly what you said - instead of increasing size of roads, they broadened roads but made the new lanes only for public transport. The expected happened - everyone who used cars before, were using them after, and only thing that improved is people who ride bus reach destination a little faster. Same would be with bikes and other things - nothing will have impact, car throughput is basically only thing that matters in traffic congestion reduction.

If you expand capacity in one mode but hold the other ones steady, you're still running into Braess' paradox. It doesn't matter that there is more bus capacity if people were tolerating the existing car congestion before. People will not switch until the roads are jam-packed.

The paradox still applies when we consider the Tokyo rail network. There's lots of rail in Tokyo - it transports most of the commuters. Major lines are quite literally packed during rush hour. [0] Adding more rail will make the system even more popular, so the problem won't get better.

OTOH consider congestion charges. When interviewed[1], individuals do not believe they were significantly affected by the introduction of a charge, even though overall traffic levels go down substantially, by one fifth in the example used of Stockholm.

What we are changing when we change capacities is not speed or comfort, but a preference for what kind of congestion we get and how cheaply it will be filled. If our only goal is congestion reduction we should not be looking at the roads at all.

The San Francisco area has plenty of car traffic, but more recently, within the past decade or so, the public transit has become extremely popular. This is not because the transit has gotten substantially better by quality or speed metrics. It is because the population is making more trips and longer ones, and the public transit systems were the last resort for capacity. Demand for new trips is in turn caused by available housing being located distantly from workplaces. If newcomers were able to live where they worked, congestion would drop significantly.

[0] https://www.youtube.com/watch?v=pRBLnth4oSg [1] https://www.youtube.com/watch?v=wC33HAq--x8

My point was that in most places none of these things you mentioned actually helps reduce congestion except brute force capacity increase by building more or wider roads somewhere.

Sure, there always are some cases where fiddling with lanes, transport types and other relatively cheap means of changes makes traffic better, but in the end simply more roads are needed.

Your confusing a local optima with a global one. If you added enough rail capacity eventually you run out of people in the country to use up more capacity. Roads are something of a special case in that they scale terribly, but you really could build a rail network in a city that could handle 7 billion people per hour if cost was not an issue.

In the setup described here, all the roads have infinite throughput. There's no level of traffic at which they stop working altogether; you can push as many cars per unit time through either network, and that many cars per unit time will come out the other side. But, as with many kinds of system, you may pay a heavy price in latency if you insist on getting lots of bandwidth.

But there's something right in what you say. When you add the extra road you make travel time worse at low usage and better at high usage.

Suppose your network has an upper path with cost for x cars 1 on the left and x on the right, and a lower path with cost x on the left and 1 on the right, and the optional vertical road is free at any capacity. Then, if I've done the calculations right, average travel time with t cars is 1+t/2 without the extra road, and min(2,2t) with. So at t=1, which is the case usually used to demonstrate the paradox, the extra road increases the travel time from 1.5 to 2, but beyond that point increased traffic is free for the enlarged network but not for the original one. So, e.g., if t=10 then the extra road makes things 3x faster. The crossover point is at t=2, where both networks have average travel time 2.

So the extra road is a win if you expect t >= 2, and a loss if you expect t <= 2.

(If we measure throughput as "max traffic with such-and-such a limit to average travel time", then if the limit is <= 2 then both have finite throughput and the one with the extra road is worse, but if the limit is >= 2 then the network with the extra road has infinite bandwidth.)

The entire problem is that people look at the effect (Full roadways) and fail to see the related causes (the rent is too ed high (because we aren't building enough valid working and living (not just homes) spaces in the city)).