The Line and Social Mobility

Standing in a line at a fast food restaurant, I realized that the front of the line is the optimal place to be at any given point assuming that cutting was not a viable option (or was kept to a minimum) because the front of the line allows you the most mobility. You can move backwards in the line, but you cannot move forward in the line unless you someone up front wanted to move back and was willing to trade you for a position behind the line. The other thing that could move you up front as Zafar stated, is if someone in the back of the line offers something else, in Zafar's example: CASH. This model of the line immediately creates other influences to think about. Zafar brought up that someone up front could continually sell his position for one that is only slightly behind, and continuously make money with his monopoly. (This would give that person a natural monopoly because no two things can occupy the same space at once, meaning that someone always has to either be behind you in the line, or in front of you, again assuming there is only one line and you have to be in the line at all times). What else would naturally occur in this scenario? More importantly, What would happen if there was no regulation of the line and people could cheat and cut all they wanted to?