# Little’s Law (LL)

“LL states that the long-term average number of customers in a stable system L is equal to the long-term average effective arrival rate, λ, multiplied by the average time a customer spends in the system, W.

Expressed algebraically, LL appears quite simple: L = λ W

The law provides a simple and intuitive approach for the assessment of the efficiency of queuing systems.”

Example of Little’s Law

“John owns a small coffee shop. He wants to know the average number of customers queuing in his coffee shop to decide whether he needs to add more space to accommodate more clients. Currently, his queuing area can accommodate no more than eight customers.

John measured that on average, 40 customers arrive at his coffee shop every hour. He also determined that on average, a customer spends around 6 minutes in a store (or 0.1 hours). Given the inputs, John can find the average number of the customers queuing in his coffee shop by applying the Little’s Law:

L = 40 x 0.1 = 4 customers

The LL shows that on average, there are only four customers queuing in John’s coffee shop. Therefore, he does not require to create more space in the store to accommodate more queuing customers.”

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