Little’s Law: Understanding the Fundamentals of Queueing Theory

You’ve read all the books, you’ve checked the web, but you’re still struggling to find the perfect way to make your project more efficient. Meet Little’s Law theorem, one effective way to streamline your project that you might not have heard of yet. (Tools like Basecamp time tracking can also complement such project management strategies, ensuring that team activities are aligned with expected timelines).

With Little’s law formula, you can estimate and turn the queuing processes in your business into a smooth and aligned workflow. It will show you the main system flaws and provide you with insights on how to fix them. In this article, you’ll learn:

• ✔️ What is Little’s Law;
• ✔️ How to calculate it;
• ✔️ How to apply it in your projects.

Understanding Little’s Law in Queue Management

Little’s law is a practical theory for various queuing systems, including Agile and Kanban. Once you understand it, you’ve got a secret key that helps you to estimate and improve any queuing processes.

So, whether your processes are for mobile game development or the lines of customers queued outside your store, Little’s Law is worth checking out. 

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Little’s Law Definition and History

John Little, a Massachusetts Institute of Technology (MIT) professor, invented his theorem in 1954. He called it Little’s law and first applied the formula to queues in shops. Later, it turned out that anything that can queue – and, yes, this includes software tasks – is applicable to Little’s law.

Project management, Kanban boards, software development, retail, and even manufacturing can use this handy formula.

Little’s law states that: “the average number of customers in a stationary system (L) is equal to the long term average effective arrival rate (λ) multiplied by the average time (W) that a customer spends in the system.”

But how does project management relate to “customers” and “stationary systems”? Let’s make some slight adjustments to the formula and replace some terms to make it simpler:

• L = “Customer’s in a stationary system” to “Work in Progress (WIP)” 
• λ = “Long-term average effective arrival rate” to “Throughput” 
• W = “Time customer spends in a system” to “Lead time.” 

Now, we can calculate any system’s capacity. Here’s how!

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Little’s Law Formula

Now, you’ve got the three Little’s law variables. So, what’s the formula? It’s super simple:

L = λ x W

• Work in Progress (L) is the number of items in process in any system.
• Throughput (λ) represents the rate at which items arrive in/out of the system.
• Lead time (W) is the average time one item spends in the system.

Still, seems a bit complicated? Let’s take a look at some real-life examples to add some practical knowledge and visualization to the formula.

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Practical Applications of Little’s Law

1. Imagine that you have a bookstore with 10 visitors arriving at it every hour.
2. It takes them about 30 mins (or 0.5 hours) to find the book they want, after that they pay and leave.
3. It means that you’ll have 5 customers in your shop at any given time.

But, how did we get to this result? Let’s take out our Little’s law calculator. Here is what we have:

L = λ x W = 10 x 0.5 = 5 customers

Having five customers at any given time probably means that you don’t need to re-organize your bookstore for more space to accommodate all the customers, nor to hire more sellers.

But what if five customers isn’t the number of customers that would meet your business needs? Let’s start a selling campaign. It can help you to attract more keen readers. After a day of great discounts, you managed to increase the number of customers from 10 to 20 customers every hour.

L = 20 x 0.5 = 10 customers

Great! You managed to increase the number of customers in your shop who want to make a purchase. BUT! Whoops! Your cashier can’t seem to keep up with the increase. This is where you may need to consider either hiring more staff or increasing your prices to suit demand. 

But, hiring another seller also means that now you’ll have to pay two salaries, which is another factor to consider if you are looking to increase your marginal revenue.

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Little’s Law in Project Management

We’ve seen how Little’s Law can help you decide if and when to take the next step in business development. But, how could you apply Little’s law for project management? Simple. The thing is the most popular project management strategies like Kanban and Agile are based on Little’s law principles. 

In Kanban, the main priority is to limit Work in Progress (WIP). WIP makes the lead time longer, resulting in slower task completion. In other words, reduce your WIP and it helps you meet deadlines easier.

To determine your WIP and keep it low, you need to estimate your tasks’ arrival and departure rates (a throughput) and know how long on average they stay in the system (the lead time). Now, you can calculate your WIP.

WIP = Throughput x Lead Time

If you have two values in this formula, you can always calculate the third one:

Lead time = WIP / Throughput
Throughput = WIP / Lead time

Little’s law formula can show your team members in practice how to improve their workflow and productivity.

Let’s have a look at the example.

• Imagine you manage a bakery that produces amazing apple pies. They are extremely tasty and become popular quickly.
• Five bakers are working 8 hours daily and together produce 25 pies every day.

🥧 5 bakers x 8 hours = 25 apple pies

At some point to satisfy the pie demand, you need to increase the production (throughput). How would you do this? You can double your business’s throughput by hiring 5 more bakers. As a result, you’ll get:

🥧 10 bakers x 8 hours = 50 apple pies

The second option is to improve the cooking process and invest in better equipment, making cooking more automated and convenient and cutting the manual work time in half. Then, you can keep 5 bakers, but produce twice the number of pies:

🥧 5 bakers x 4 hours = 50 apple pies

This way, you’ll improve your team’s working capacity without the need to double your salary budget.

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Little’s Law Practice Problems

When applying the Little’s law formula to your project estimation, you may run into some practical problems. To calculate your project WIP precisely, the whole Kanban system must have a steady-state condition and the three variables must be consistent. 

Daniel S., one of the participants of the first Kanban development projects recommends “to forget the equation and focus on the assumptions” that make Little’s law work. Once you follow these guidelines, you already make your project workflow stable and easy to calculate.

Here are the conditions your project needs to meet to make your project workflow predictable and applicable to  Little’s law formula:

• Before calculations make sure that you know the average values of your project: lead time (W), WIP (L), and throughput (λ).
• Your measurements should be consistent, meaning that if you have your lead time measured in weeks, your throughput, and WIP should also be measured in weeks.
• The project should be stable. This means that the total values of each parameter should be the same for the measurement period. For example, your WIP at the beginning of the week should be equal to the WIP at the end of the week. 
• The average arrival and departure rates in your project should be equal.

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In Closing

We, at Everhour, hope that now you know how to apply Little’s law in practice and it’ll help you in your future projects to better:

• Estimate the performance of your project team
• Control project WIP and keep it low to meet deadlines on time
• Explain in practical cases why multitasking is evil
• Meet deadlines
• Make accurate predictions on project workflow and workload.

If you are managing a team of 5 or more and looking to boost efficiency, Everhour is the perfect tool to keep your team on track. With seamless time tracking, you can easily estimate task durations, set clear budgets, and generate detailed reports inside Asana, Trello, Jira, or any other pm tool.

Enjoyed the article? For more tips, strategies and tools that’ll help you make more informed business decisions and better manage your team, check out these publications next:

Reference:

• Featured image credit: Velog