Networked traffic routing apps like Waze ought to nullify the Braess' paradox; if everyone used Waze, new roads would always have a positive marginal impact.
What typically happens when a new roadway opens or a congested route is widened is that travel times first fall, as expected; but soon the reduced travel times attract drivers who previously had used other routes, or who had commuted at off-peak times, or who had used public transit. Thus the improved roadway ends up with significantly more traffic than the old roadway, and the price (in travel time) of the increased capacity is bid back up near its previous level.
Added roadway capacity can lead to a welfare improvements, but it mostly comes in the form of fewer people shifting their schedules to beat rush-hour traffic or deigning to take public transit, and not through reductions in travel times. In actual fact, as we've seen throughout the era of American suburbanization, vast new roadways have probably substantially increased average travel times [1] by markedly changing patterns of land use (i.e., by giving rise to the modern low-density, car-dependent suburb), albeit while also engendering some welfare gains (e.g., increased suburban living space).
If you want to prevent induced demand from gobbling up expected improvements in travel times when you build new roads, you pretty much either have to (a) decrease demand by deliberately increasing the financial cost of travel (e.g., through tolls or congestion charges), or (b) over-build roadway capacity in the extreme, to the extent that just about everyone in the region can fit on the roads at once, alone in his or her own car (as is the situation in cities like mine).
0. https://en.m.wikipedia.org/wiki/Induced_demand
1. I mean in comparison to a counterfactual alternative history in which the urban-suburban commuter freeway systems typical of American cities went unbuilt. Commute times in European metropolises, which mostly lack the extensive commuter roadways and concomitant suburban sprawl of their American counterparts, are broadly lower than in American metros of similar sizes, for example.
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.
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.
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.
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
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.
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.
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.)
On the other hand, with socially optimal traffic patterns there would be induced demand and more drivers would come on the roads and potentially use Waze.
It's actually difficult to know what would make Waze better off, providing socially optimal routes or individually optimal routes.
Waze might also behave like many companies and ask for subsidies from local governments for turning on the social optimization, and the local governments are ill-equiped to know how much to pay.
If it optimizes for each individual traveller, then Braess' paradox still applies even with Waze because all the travelers in Braess' paradox make the individually optimal choice.
If it optimizes for the socially optimal distribution, then it does solve the problem. But this sounds like an optimization problem that would be really hard to formulate and solve in practice, so I'd be surprised if Waze (or any other networked traffic app) did it right now. Maybe eventually?
The catch is no one knows in advance who is going to go the bar. It can be shown that no pure strategy can work for EFB.
Whether traffic moves faster or slower pollution is bound to increase.