We were in line to buy tickets to enter a tourist attraction. The line was accumulating, even though the place had two cashier windows open.
I inclined my ear toward the windows and heard people at each station discussing memberships. Meanwhile we, and everyone behind us, were interested in simply buying tickets for the day.
I thought it was an inefficient process to have all available windows processing memberships. My plan would be to have one window dedicated to normal tickets – the quick transaction – and one window that would take membership applications as well as sell tickets.
That would have made my experience better. But would it be better overall?
Let’s assume it takes an average of 2 minutes to buy a set of tickets. And let’s assume an average of 10 minutes to buy an annual membership.
In order to replicate my situation, let’s assume the two memberships are at the beginning of the line. So for the first 10 minutes, the line does not move as both windows are busy with memberships. Then there are 20 minutes left to sell tickets. At 2 minutes each, times 2 windows, that equals 20 sets of tickets.
So in 30 minutes, 2 windows process 20 sets of tickets and 2 memberships. How does that compare with my proposed setup?
The first window is only tickets. In 30 minutes, it processes 15 sets of tickets.
The second window is memberships and tickets. This window takes 20 minutes for memberships and then has 10 minutes for tickets, so 5 sets of tickets.
The total is still 20 sets of tickets and 2 memberships.
That doesn’t show any difference. But the difference does show up in the average wait time.
Average wait time in the first case is 0 for the memberships and then 10 + ((0 + 2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18) / 10) = 10 + 90/10 = 19 minutes per set of tickets
Average wait time in the second case is (0 + 10) / 2 = 5 minutes for memberships and then (0 + 2 + 4 + … + 26 + 28) / 15 = 210/15 = 14 minutes for the first window and (20 + 22 + 24 + 26 + 28) / 5 = 120/5 = 24 minutes for the second window.
The average is not 14 + 24 / 2 (which equals 19 minutes), since more people had the lower wait time. The average is 210 + 120 / 20 = 16.5 minutes.
So dedicating a window to the slower process results in a lower wait time for 90% of the clients.
Not only is it faster, but it also feels faster to everyone, since the main line is always moving. With the original configuration, it felt very slow because the whole line did not move at all for 10 minutes.
See, I am going to wait at the fords of the wilderness until word comes from you to inform me.
2 Samuel 15:28
This is Alpha, the first-born, when he was 2YO.
This is Beta, the second-born, when he was about 2YO.
This is Gamma, the third-born, when he was about 18MO.
