I’m always excited when life presents us with ready made natural experiments. A couple days ago, I wrote about the dedicated line manager at the cafeteria where I work and how I thought that his salary is probably more costly than the benefits he provides (efficiently moving lines). Well today, just my luck, the line manager was no where to be found. Lunch goers would have to navigate to the cash registers by ourselves.
Did the cafeteria devolve into a den of chaos?
The answer is no! People where just about as good at creating order spontaneously, as when managed by a central planner. Well this isn’t exactly true. The cashiers themselves called out to whoever was next on line, notifying that they were free, and could accept a new customer.
I did make one interesting observation, which may or may not be significant. The only major difference between the outcomes of the two scenarios is that the line manager would generally arrange for two customers to be waiting at a register at a time. Without the manager, people waited for the cash register to completely clear before walking up to it. At higher volumes of traffic it *may be* that this would slow down the flow, but I didn’t notice a difference in practice.
I think this hesitation could be traced back to a customer’s self interested behavior. We’ve all gone through times at the grocery store where you get behind a short line, only to wait behind a really slow person while people waiting on longer lines pass you by. At the cafeteria, perhaps people wanted to make sure that a short line would also be the quickest, by avoiding slow people.
I would like to see a mathematical model of this, because I can’t reason out whether this would cause an overall increase or decrease in the customer flow rate. On the one hand, cashiers have more work to do and spend longer without customers in front of them. On the other hand, new customers direct themselves behind the fastest payers (whereas, the line manager doesn’t know how fast the paying customer will be, before putting a new customer behind them). I don’t know which effect would dominate.
Maybe I could work out this model for a fall project (graphical model to come soon?)