Little’s Law : Overview, Formula and Practical Example

A study of Little's Law may give you insight into your business's queuing process or help you improve a project's workflow. Discover how to use Little's Law in your organization.

Little's Law : 

According to Little's Law, a stationary queueing system has an average number of items. The theorem was first published in 1961 by John Little, a professor at the Massachusetts Institute of Technology

In queueing theory, a discipline within the mathematical theory of probability, Little's result, theorem, lemma, law, or formula is a theorem by John Little which states that the long-term average number L of customers in a stationary system is equal to the long-term average effective arrival rate λ multiplied by the average time W that a customer spends in the system. Expressed algebraically the law

L = λ x W

In spite of the fact that it appears intuitively simple, the relationship is quite remarkable, since it does not take into account the distribution of arrival processes, service distributions, service orders, or practically any other factor.

To improve workflow and avoid bottlenecks, the Little's Law formula is frequently used in business development and project management systems such as kanban (a popular visual project tracking system). In addition to using Little's Law in a grocery store line or software tasks, you can use it in any situation in which there is a queue.

Here’s what each of the variables means:

1. L is the average number of items in a queuing system. 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.

2. 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.

3. W is the average waiting time an item spends in a queuing system. In project management, it’s referred to as lead time.

Example of Little's Law

In order to understand Little's Law in the real world, you may need some context, unless you are a mathematician. The following is an example of Little's Law applied to business development:

Consider an ice cream shop that you own in the heat of summer. If you want to ensure you have enough employees and enough room in your store to handle business, you need to know the average number of customers you will have in your store at any given time.

The number of customers arriving every hour is about 20. The average time it takes for a customer to choose a flavor, pay, and leave with their ice cream is 15 minutes (or 0.25 hours). The Little's Law methodology can be used to answer your question in the following ways:

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

On average, you will have five customers in your store at any given time, according to the formula. The metrics can be used to calculate essential business decisions, such as the need to hire more staff and expand the company to meet customer demands.

Reference: Masterclass