A count of twelve and an arrival rate of one every three minutes gives a wait nobody in the line is actually experiencing.
ArithmeticAnswered507 views
Coffee place on the ground floor. I counted twelve people in the queue and watched the door for fifteen minutes and got five arrivals, so about one every three minutes.
L over lambda gives twelve times three, which is thirty six minutes, call it forty. Nobody in that queue is waiting forty minutes. I stood in it myself on Friday and it took under ten.
What am I doing wrong? The equation is two variables and I have measured both of them.
Marked as the answer
Your arithmetic is right and your boundary is wrong, which is failure number two from Monday. You counted twelve people in the queue, and then counted arrivals at the door. Some of those twelve did not come through the door in the window you were watching, and some of the people who came through the door went straight to a shelf without joining. Draw the box first, then count only what crosses it.
That is exactly it. I was counting the room and timing the door. Redid it with the box drawn at the end of the line and got eleven minutes, which matches what I get if I just follow somebody with a stopwatch.
Good. Keep the eleven and keep the forty. The gap between a wrong answer and a right one is the most useful paragraph you will write in The Measured Queue, and almost nobody includes it.
Filing this for later because I am about to make the same mistake at a bus stop where the queue and the shelter are different shapes.