I would've preferred an auction; institute a cap of x entrances/day, and run an auction the day before to efficiently allocate the limited slots to those who are most willing to pay for it. Last-minute entrants who will need to get in for whatever reason and missed the auction will pay large premium above the market clearing price. Given that vehicle traffic is non-uniform throughout the day, maybe it would make sens…
Another way to do it would be to look at historical data and predict demand in advance. You could then do custom prices by day, but scheduled a month in advance or more. You could also split the day into two or three periods with different pricing.