Earlier quoted context omitted.
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…
1) If your roads are being overused you can easily ration that by raising the dollar price. 2) What is wrong with wealth accumulation? If credit recipients would rather do that than drive on roads they should be able to do so. They's how they get less poor! 3) If they credits are transferable then you are effectively giving people money. Just in an ass-backwards and overly confusing way.
IMO, the problem is "how do we allocate road so that high utility use gets precedent over low value use, without defining high/low value as 'rich/poor person wants to get from a to b'"
Expiring credits is an idea, as are a lot of options. Designed markets are a devil-in-the-detail endevours. A market is a good tool for this job, that's why economists and wonks like tolls. But, not every market needs to be the market. In this case, The Market is probably worse than the no market free-for-all.