So here’s my airport question for the day:
I spent 40 minutes in the queue for the bag drop. When I left, the line was exactly the same length as when I arrived, so clearly the airport is capable of keeping pace with the volume of passengers.
So WHY IS THERE A FUCKING QUEUE?
OK, I think it might be analogous to how spiral arms in galaxies form :-)
For fluctuations in bag check rate, there is an asymmetry. Imagine that at the beginning, there is no queue, and passengers are arriving at a constant rate. The first fluctuation "bag check takes longer than necessary for 1/
constant flow" creates a bit of a proto-queue. In time, there will be a fluctuation where "bag check takes less time than necessary for constant flow", but that will not compensate the queue when the "sound speed" at which fluctuations propagate through the queue is slower than the way the 2/
passengers would move unhindered. That asymmetry contributes to the build-up of a queue. Less easy to explain why the queue reaches a steady state, but may be the fact that passengers can see what is going on in front of them, and not just react to the local density drop in front of them, makes 3/
It’s Little’s law: (length of queue) =(arrival rate) x (service time)
The equilibrium position isn’t a zero length queue, and here is governed by average time to find and retrieve your luggage
en.wikipedia.org/wiki/Little%...
I guess I don’t understand why: if people are being processed at the same rate at which they arrive, the system is in equilibrium whatever the length of the queue.
Little’s law is a deceptively simple result from quite a complex proof. Joining and leaving the queue are independent events rather than being in lock-step, so it’s not “one in, one out”. Arrivals can happen at any point during the service time period, not necessarily at the end of it.
I can see that would lead to noise, but not a long-term average. Maybe it’s the asymmetry that comes from never having a negative number of people waiting.
