I don't do the tarp run myself, but I'll contribute what I believe is the case.
There are two lines. One for Town Park/Warner Field, and one for condo's/down valley campers. Numbers are handed out some time very early morning. Whether the numbers are random or not I'm not real sure, as it may change.
They let a group of about 20 people from each line at a time to do the tarp run, and wait a few minutes before the next group is let go.
I'm sure some of the regular runners can contribute a little more information.