Little’s Law: Definition, Formula and Example

Little’s Law is a mathematical theorem in queueing theory that determines the average number of items in a stationary queuing system. John Little, a professor at the Massachusetts Institute of Technology (MIT), created the theorem in 1954 and formally published it in 1961.

The Little’s Law formula is frequently used in business development and project management systems such as kanban (a popular visual system used to keep track of project activity) to improve workflow and avoid bottlenecks. You can also use Little’s Law in any situation wherever there’s a queue, whether it’s the number of people in line at the grocery store or tasks executed by software.

Little’s Law states that the average number of items within a system equals the average arrival rate of items into and out of the system multiplied by the average amount of time an item spends in the system. The Little’s Law formula is: L = λ x W

Here’s what each of the variables means:

• L is the average number of items in a queuing system. In project management, it’s known as work in progress (WIP). If you use Little’s Law for project management, remember that for precise measurement, you must have a steady-state condition where the variables are unchanging in time.
  
• λ is the average number of items arriving at the system per unit of time. Also known as the long-term average effective arrival rate or throughput, it’s the rate items go in and out of the system.
• W is the average waiting time an item spends in a queuing system. In project management, it’s referred to as lead time.

Unless you’re a mathematician, you might need more context to understand how Little’s Law works in the real world. Here’s an example of Little’s Law in a business development situation:

Let’s say it’s a hot summer, and you own an ice cream shop. You want to know the average number of customers you’ll have in your store at any given time to ensure you have enough employees to handle business and the room in your store to serve them.

You have about 20 customers arriving every hour. It takes each customer an average time of about 15 minutes (or 0.25 hours) to pick a flavor, pay, and leave with their ice cream. Here’s how to use the Little’s Law methodology to answer your question:

The formula is: L= λ x W

λ = 20 (people arriving at the store per hour)

W = 0.25 (hours in one cycle time)

20 x 0.25 = 5

According to the formula, on average, there will be five customers in your store at any time. You can use these metrics to make essential calculations about your business, such as increased staffing and company expansion to meet customer demand.

Get the MasterClass Annual Membership for exclusive access to video lessons taught by science luminaries, including Terence Tao, Bill Nye, Neil deGrasse Tyson, Chris Hadfield, Jane Goodall, and more.