If it is some fake currency, say, HOV-credits, that is distributed on a monthly basis, equally, to everyone, then to a first approximation, you're providing for equivalence in capacity to pay. You can choose to spend, or not spend, your HOV-credits, on any given day.
This also offers the opportunity for rationing, as it's possible to increase or decrease the allocations based on net usage.
If the credits expire after some time, say a few months, then there's the ability to bank them, but not indefinitely. This is not a form of perpetual wealth accumulation.
The argument could be made for either making the credits transferable, so that those less wealthy in other regards could sell them for other units of trade, or not, and/or to set limits on such transactions.
All of this occurs independent of actual currency, though there would be an overall budget to the programme.
And it accomplishes the goal of setting an opportunity cost to highway travel, and congestion, which could itself be varied according to circumstances (higher charges at peak hours / during high-congestion events, lower off-peak or when uncongested).
Then there's the question of interactions with alternative transit, telecommute, or similar schemes.