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It's unclear to me why this is fairer than the tax we currently use, which is
A x D + queueing

Obviously this depends on how one defines "fairness".

The point isn't fairness. The point is that the road becomes more useful.

What we have is a classic tragedy of the commons situation. The road is "free". So everyone rushes to use it. Its usefulness is reduced in the sense that people spend much of their time using the road as simply a waiting area while sitting in traffic instead getting full value from it by moving along it.

Congestion pricing works by restricting access to the point where traffic continues to flow, making the road less for waiting and more for travel, while simultaneously forcing people to make a decision about whether their use of the road is really that important. So long as the road appears "free", there will be people casually using the road, creating more traffic, and forcing others that might take better advantage of the road, to wait.

Your analysis ignores the value of the road as a function congestion.

But even looking at the road strictly from a taxing standpoint, it isn't obvious that people will pay more overall in taxes or that it's even bad if they do.

If congestion taxes are used to subsidize road spending and repair, while keeping road taxes revenue neutral, then taxes on gasoline can be made lower. In effect congestion pricing allows some people to trade away their right to access by enjoying a lower tax on gas. They in effect sell their access to someone more willing to pay.

Secondly, congestion pricing opens up the possibility that people will pay more simply because traffic is reduced. They may pay the government more in taxes, but get to enjoy a less crowded and more useful road.

The point isn't fairness.

I'm not sure I agree with you, but in any event, if you're right you'd better tell that to the other guy whose argument was based on it allegedly being more fair.

The point is that the road becomes more useful. What we have is a classic tragedy of the commons situation...

This is a better argument in favor of it, yes.

Your analysis ignores the value of the road as a function [of] congestion.

With queuing, let me grant the road (as you have pointed out) becomes "less valuable" in aggregate. However the "value" of any road is different to different people. And this can raise a fairness issue, albeit not necessarily the one the other poster was talking about.

I mean, if people are priced out of certain roads, have some of their road (gas, license, whatever) taxes been stealthily converted into transfer payments? to whom? and has the government violated the social contract under which it had been collecting all those taxes previously to create the roads in the first place?

(Not that the gov't doesn't do things like that all the time, of course. I've always heard that originally the Golden Gate Bridge was supposed to be free as soon as it had paid for itself... yeah sure :)

But even looking at the road strictly from a taxing standpoint, it isn't obvious that people will pay more overall in taxes or that it's even bad if they do. If congestion taxes are used to subsidize road spending and repair, while keeping road taxes revenue neutral, then taxes on gasoline can be made lower.

To me, this is a big "if". Scratch that: it's an infinite "if". :)

Yes, gas tax "can be" made lower in accord with revenue gained some other way, but it's a near-certainty that it will not be. Thus I refuse to consider it as part of an argument for doing it.

In effect congestion pricing allows some people to trade away their right to access by enjoying a lower tax on gas.

It could be set up this way.

It will not be.

(Slight amendment here: I can certainly imagine a "deal" being struck in which, initially, a gas-tax reduction was tossed into a congestion-pricing plan, pitched as a way to offset the cost, as a benefit like you say, to sweeten the deal for some people. However, it's likely that said gas-tax discount would not last and would rise as soon and as fast as politicians were able to do so under the radar.)

Let's say I agree with this scenario. (I think I do, but it's more honest to say I have no idea. :) Is the benefit being received worth the added cost? On whom is the cost falling? How is the cost falling?

These are unavoidably political-economic questions, of course, and they inevitably raise issues of "fairness". So I guess I don't agree with you that you can fully separate "fairness" from this issue.