Games Theory for Queues
According to this article, waiting in one long single file line is a very inefficient way to wait in line. According to two Danish researchers, it is actually a lot more efficient to serve those who entered the line more recently first. This may seem counterintuitive but by taking into consideration the costs and benefits of these methods, it becomes more apparent that the “last-come, first-serve system” is more efficient.
For example, say there is 40 people waiting in line. If all 40 of those people start waiting in line between the time of 1 and 2 then there will be a bottleneck effect. There will be high traffic during that hour. This is like if all the cars on a highway decides to take one route and all the other routes are empty. However, if this line is “last-come, first-serve” less people will come at once because the probability that they will be served first is slim. This system deters people into all coming at once and spreads them out over other time slots. In this sense, it’s a traffic equilibrium by spreading people over different timeslots so that every timeslot has the same wait time. The nodes are the beginning and end of the line and each route or path is a different time of day (not the different queues). And the time it takes to get through all the different “paths” are x/a where x is the amount of people waiting in line and a is the speed factor of the line.
However, a difference between this and traffic equilibrium is that the “last-come, first-serve system” is very unlikely to happen as stated in the article. This is because people care more about justice and fairness than efficiency. No one will be willing to leave a line and come back later. One way to implement something similar to this “last-come, first-serve system” is by using appointments so that each timeslot has the same amount of people coming and going.
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