I was wrong-again. Much of the issue with the park is associated with the north and northeast entrance and it seemed feasible that the balance of the entries Cody, West Yellowstone, & Jackson could remain open by weeks end. The problem is that with the north loop closed, it appears the lower loop will see more pressure because the visitors will be more concentrated. That leads to the potential for a reservation system - at least that’s the talk.

From the link:
“However, he did note during the conference that the southern portion of the park could not accommodate all of Yellowstone’s visitors, which can amount to 1 million or more per month in the summer.”

“This could mean that when the park does reopen, timed visitations or reservations might be implemented to try to handle the influx of visitors, but Sholly was not firm on this.”