Little’s Law

Little’s Law refers to the theory that states the average time an item or individual enters the queue and exits the same. The main aim of this law is to determine the number of hours spent on the items in the queue.

The Little’s Law queuing theory is frequently practiced in restaurants, supermarkets, and cafeterias. It indicates the efficiency of the staff to serve the customers. Also, it calculates the waiting time for the customers during bank queues. However, the Little’s Law equation has various assumptions and limitations.

• Little’s Law is the queuing theory used to determine the average rate at which customers enter the outlet and purchase items. 
• It also considers the time spent and the total number of customers entering the restaurant or retail store. This law and Kanban are closely interrelated to each other.
• The concept originated in 1951 when Professor John Little explained the theory at the Massachusetts Institute of Technology (MIT). 
• The law has applications in various businesses like banks, restaurants, hotels, cafes, food joints, and others.

Little’s Law, a fundamental principle in queuing theory, helps determine the time it takes for the items or customers to arrive and exit the queue. It has widespread application in various fields. By leveraging this theory, businesses can generate more profits by identifying the waiting time and productivity curve. Conversely, individuals can benefit from quicker access to goods or services. 

The application of Little’s Law in manufacturing has been significant over the decades. It helps in analyzing material flow between processes. Additionally, it also considers the rate at which it moves. In this context, the average number of units equals the production and lead rates. However, when applied in retail outlets like restaurants, various factors come into play. These include the distribution of the service and service order. While the former refers to the staff service rate, the latter is the service sold to the customer. 

Various laws and theories in manufacturing, such as Kanban, Agile, and Lean Manufacturing, are based on this concept. However, Little’s Law equation and Kanban have an interrelation between them. The Kanban managers use this law to calculate the time the team requires to complete the work. The formula could also be used to determine the engineering lead time, representing the lead time from receiving the order to starting to produce the item.

The history of Little’s Law cycle time dates back to the mid-1900s. As a professor at the Massachusetts Institute of Technology (MIT), John Dutton Conant Little (John Little) introduced this theory in 1954. However, the formula was first developed and published by physicist Philip McCord Morse in 1958. 

However, there was no evidence to support the theory. As a result, in 1961, Little republished the law stating the possible queuing situations to deny the allegations. Therefore, it became a fundamental concept in operations management and queuing theory.

Let us look at its formula to comprehend the concept better: 

L = λW

where

• L refers to the number of items within the queue.
• λ (lambda) is the rate at which items arrive in and exit the queue.
• W refers to the average time the customers spend inside the queue. 

The working and application of this law are similar to the daily routine of the coffee shop. As customers enter, sit, and leave, the cafe correlates significantly. So, if a customer needs coffee, they will stand in the queue. As they receive their coffee, they will exit the outlet. Therefore, shop owners can identify the rate at which customers arrive daily.

Let us look at these examples for a better understanding of the concept:

Example #1

Suppose Hella wants to increase the taco franchise for her store in the state. Thus, she uses Little Law's formula to determine the average number of customers arriving at her store. In total, there are 30 customers, and every customer must wait 15 minutes to get a taco. So, let us calculate the average number of customers using Little’s Law formula:

L = λW

= 30 x 0.25

= 7.5 customers on average. 

Hella's store witnesses an average rate of 7.5 or almost eight customers at any given time.

Example #2

According to statistical data published in 2023, using the Little’s Law formula, the average number of customers for the international food chain McDonald's is 69 million daily. Additionally, the rate at which their burgers flow is 75 burgers per second. This demonstrates the immense scale and efficiency of their operations. 

This has been a guide to what is Little’s Law. Here, we explain the concept in detail along with its examples, formula, and history. You may also have a look at the following articles –

• Law Of Total Probability
• Stochastic Modeling
• Gamma Distribution