With the current update, all flight activity sometimes stops @ INN. The first plane waiting to depart stops at the hold short line, and never enters the runway. All arrival activity stops, and the other departures just stack up.
Try tapping the “RWY PRIORITY” and make it 3:1 by tapping the 
(land) icon
Yea, I tried that when it happened, but nothing changed.
That happened to me too. I personally have a suspicion that it randomly glitches when you Opt out of the landing mini-game for one of your own planes.
It doesn’t always do it. But I had noticed that the flight that wasn’t landing was one of my own.
THIS IS AN UNSCIENTIFIC GUESS. Just to be clear.