Originally Posted by
wetrat0
This is a good observation. I discussed this above briefly, but did not give any technical reply because the model would have to get a lot more complicated. One way you could model this is at every point in time, the server can choose to work slowly or quickly, but working quickly has a higher cost. The server then chooses to work slowly or quickly at each time point based on minimizing the long run average cost (to the server and to the customers for waiting).
I'm not sure that would be a fair assumption. It doesn't cost the worker any more to process a higher number of passengers per hour, because they are doing less screening per passenger. For example, if there are 50 passengers and 6% of them get a bag check, then when there are 100 passengers only 3% of them get a bag check. The cost to the worker is the same.
Originally Posted by
wetrat0
The structure of the solution would be such that when the line exceeds N customers, the server would work quickly, but when the line is at most N, it would work slowly. Figuring out N would really require knowing a lot more about the real parameters (arrival rate, various possible service rates, costs, etc.) so it doesn't lend itself to an easy example.
My theory is that the workers adjust the rate of screening in order to keep the line at a certain length. This is similar to a nightclub, where they want there to be a line outside to make the club look popular, but not long enough to discourage people from coming in.