At quieter times there may well be two aircraft equidistant from the airfield (or more accurately a 10 mile final) and it’s a toss of the coin decision who is first. If one of the aircraft has declared minimum fuel then of course he’s No.1 and the other will be instructed to ‘...decreased speed to minimum clean...’
I do struggle to understand in that scenario why an aircraft with no delay is minimum fuel.
-Although I have had an A320 once declare minimum fuel just after I’d given him a 40 mile shortcut and straight in!
If the delay is excessive or likely to get worse elect to divert earlier than later. If your destination is closed due emergency or below limits it can often take 10-20 minutes for the alternate to accept you and this often leads to multiple fuel maydays. (The system doesn’t work!)