They must have a good idea on how many are in the queue as they are giving out numbered wristbands, so allowing for a drop out rate, they will know there are X thousand queuing.
They must also by now have a pretty good idea of the people/hour through the hall.
They'll need to account for closures for cleaning, and any planned delay due to the Princes' Vigil tonight.
But I agree they will probably try to over estimate rather than underestimate, and they need to allow for unexpected delays such as guards fainting or whatever.
At least the weather looks good.
They've just announced that tomorrow evening there will be a vigil by the 8 grandchildren.