Little’s Law or Little’s Formula is a way to relate the average length of a queue and the average waiting time in a queue. It was proved by John Little in 1960 while Little was at the Case Institute of Technology. The paper proving the result is one of the most cited in the field of Operations Research.

Let be the average time a customer spends waiting in a queue. Let be the average length of the queue. Let be the arrival rate to the queue—the average number of people that arrive per unit time. Then the three quantities can be related by the simple formula .

This result holds no matter the arrival process (Poisson, deterministic, etc.), the service process (Poisson, deterministic, etc.), the queueing discipline (first come first served, last in first out, etc.), and the number of servers. It also holds for total time in the system, if you instead use and as the average number of people in the system –combining those in queue and those in service—and the average time in system, respectively. .

Prospect Theory, created by Kahneman and Tversky, is a way to quantify utility functions for people. In traditional economics, a dollar is a dollar and people are expected to maximize their wealth. In reality, people have biases. The two major biases shown in prospect theory are diminishing sensitivity and loss aversion.

Diminishing sensitivity makes people notice $1 changes in their wealth less the farther that they get from their reference point. $1 means a lot more to someone who is close to breaking even than to someone else who has already made a million dollars.

Loss aversion refers to the fact that people feel losses more strongly than equal sized gains. A loss of $100, relative to your reference point, feels worse than a gain of $100 feels good.

The effects can be seen in the following pictures. (a) isolates diminishing sensitivity and (b) isolates loss aversion. Their combined effects are shown in (c).