Alternative system: the virtual queue is for free; every 15 minutes, there are only a limited amount of virtual queue tickets available for a specific 15 minute

Alternative system: the virtual queue is for free; every 15 minutes, there are only a limited amount of virtual queue tickets available for a specific 15 minute slot significantly later (eg. +2hr) in the day. If that also goes to capacity, your capacity is too low for the amount of folks you let in. Increase capacity on this ride, increase attractiveness of other rides with more capacity, build new rides, or create other things eating up time other than rides.