Stable Systems: Little’s Law and Kanban
When discussing Agile methodology and Kanban, one equation makes frequent appearances: Little’s Law. But what does this formula have to do with project management?
While originating from queuing theory, Little’s Law has been found to apply to all kinds of different systems – from retail to design to development. In Kanban, Little’s Law links the three basic metrics – throughput, cycle time, and work in progress – in one simple formula.
Understanding how these Kanban metrics are connected allows you to analyze your work processes and see how changing one metric will affect the other two.
The History of Little’s Law
John Little came up with a theorem that connects the number of customers in a store with the rate that they arrive and the average time each customer spends there. This looks like this:
Average number of customers = Average arrival rate * Average time in the store
Consider a store where each customer spends on average 12 minutes (0.2 hours), with 10 customers arriving per hour.
Average number of customers = 10* 0.2 = 2
Little’s Law states that on average, 2 customers are in the store at any one time.
Little’s Law and Kanban
Remarkably, Little’s Law was found to apply to any number of other systems, including Kanban systems.
In Kanban, WIP limits are applied to each process state – outstanding tasks must be completed before new tasks can enter a process state. Limiting work in progress allows the arrival and departure rate of tasks (throughput) to stay roughly the same in order to apply Little’s Law and get accurate results.
In Kanban terms, Little’s Law is expressed a little differently, but the idea is the same:
WIP = Throughput * Cycle Time
If we imagine the Kanban board as the store, WIP is equivalent to the number of customers inside at any one time, throughput is the rate of customers passing through the store and cycle time measures how long each one spends inside the system.
This means that if two of the three values are known, the third value can be calculated – without knowing anything else about the tasks, team or project:
WIP = Throughput * Cycle Time
Cycle Time = WIP/Throughput
Throughput = WIP/Cycle Time
Little’s Law Assumptions in a Kanban System
There are several assumptions needed to make the law work:
- The average Arrival Rate is equal to the average Departure Rate
- All tasks entering the system will eventually exit the system once completed
- There should not be large variances in WIP between the beginning and the end of the time period examined
- The WIP average age should remain the same, neither increasing nor decreasing
- Consistent units must be used to measure Cycle Time, WIP, and Throughput
Little’s Law is not influenced by the arrival process distribution, the service distribution, the service order, or practically anything else. As these assumptions become more inaccurate, the process behavior becomes more and more unpredictable.
It’s important to remember that Little’s Law only deals with average values. Even if the assumptions do not hold for the entire time period under consideration, Little’s Law can still be applied. However, the more these assumptions are violated, the more the accuracy of the equation breaks down.
Little’s Law in Action
Imagine you manage a widget-crafting project. You have four team members, and each team member has a widget-crafting capacity of one widget every two days – the average cycle time for the team is 2 days. Each team member works alone on their widget, giving a WIP of 4. This configuration gives your team an average throughput of 2 widgets/day.
What happens if we raise our WIP? As long as the assumptions hold, Little’s Law will still apply. However, this does not mean that doubling WIP will magically double your throughput while cycle time remains the same. It simply means that the formula will balance out – a change to WIP will cause cycle time or throughput or both to change and keep obeying the law.
Making Predictions With Little’s Law
In order for the Law to be valid, we need to have all of its assumptions valid. So one prerequisite for the Law to work is to guarantee that all the assumptions won’t be violated in the future.
Even if that’s the case, the Little’s Law is still a relationship of averages as each component in the relationship is an average. This calculation will produce an average. We cannot make any probabilistic forecasts using this approach.
Making predictions based on an average can land you in some hot water. Forecasts based on averages would make sense only if you know something about the shape of the underlying distribution of your data. If you don’t there is no way to associate any percentile with the average value – there can be exactly 50% or much more than 50% or significantly less than 50% chance of that goal being achieved.
If we don’t know the distribution, then we cannot give a probability of where the average falls. And if we don’t know a probability, then we cannot make a forecast.
Little’s Law is an unreliable method of making future predictions. If you really want to get accurate delivery forecasts, then you should use tools like the Cycle Time Scatterplot or Monte Carlo Simulation.
Analyze Process Performance
So long as the five assumptions are accurate, Little’s Law applies to both the system as a whole and to its component parts. This allows you to get a deeper understanding of the different parts of your process.
Process States and Bottlenecks
Tasks can only enter the next process state once they leave the previous state. This means that the throughput of the entire system cannot be higher than the throughput of the slowest step. In this way, bottlenecks cause the whole Kanban system to suffer. This means that underutilized capacity (team members with nothing to do) should always focus on resolving a bottleneck as their first priority.
Segmentation and Classes of Service
When segmenting WIP into different types with Classes of Service (CoS), Little’s Law can then be applied to each of the different CoS. For example, we might want to use Little’s Law to analyze all work flowing through our system, or we may want to use it to just look at our Standard work items.
We can investigate if our different segments are violating the assumptions of the law, and if so, how severely. Or maybe grouping two diverse segments together (Expedite and Fixed Delivery Date, for example) that is causing the issue. In most cases, this type of segmentation is very useful and could provide a more sophisticated approach to analyzing process performance.
Little’s Law is about examining what has happened in the past and analyzing the predictability of your system. The power of Little’s Law rests on the assumptions behind it. It provides a guide of a set of process policies to adopt in order to maintain a stable system. Instead of making predictions, adopt the Little’s Law assumptions as explicit policies to drive consistency and predictability of your workflow.
Additionally, it can be used to analyze your work by class of service to find where these assumptions break down. Most importantly, it gives a deeper understanding of how the three basic flow metrics are connected – and how changing one inevitably affects the other two.
Has Little’s Law helped you understand how the main flow metrics are connected? How did it help you analyze your own process performance? Tell us about your experience in the comments!
Meet the Author
Sonya Siderova is a passionate product manager and a driving force behind Nave, a Kanban analytics suite that helps teams improve their delivery speed through data-driven decision making. When she's not catering to her two little ones, you might find Sonya absorbed in a good heavyweight boxing match or behind a screen crafting a new blog post.
Take your training and consultancy sessions to a whole new level. With Kanban analytics on their existing tools, yo… https://t.co/4G3X9FehF5Follow
Learn how to make accurate, data-driven predictions to stay on track, meet deadlines and keep a high level of custo… https://t.co/zPBlWxv5X7Follow
The Flow Efficiency Chart shows your average flow efficiency, as well as how trends have been moving over time. Ide… https://t.co/Eff9ITFFnrFollow
Learn more about the difference between thin-tailed and fat-tailed distributions and the approaches to evaluate you… https://t.co/oHCaDCa4WXFollow
Last chance to get 60% off! We list our Sustainable Predictability digital course at the lowest price ever! The off… https://t.co/Af5U0kiBIEFollow
Get straight to the essence of your Azure board data and analyze your processes with our immersive data-visualizati… https://t.co/MpB4kgNiCeFollow
Kanban can help you run your business better, make your processes more efficient and empower your team to accomplis… https://t.co/RwXHnb4UcEFollow
A Cycle Time Histogram with a big hump on the left and a very long tail to the right indicates that your cycle time… https://t.co/mFKXLpx4HhFollow
Service level agreements define the responsibilities of a service provider to their customers. Defining SLAs are im… https://t.co/s7HeXDvfkWFollow
Today, we’ll explore the consequences of moving cards backward has on your performance, as well as the most effecti… https://t.co/IZmafKMe9YFollow
Value stream mapping is a visual technique that depicts the lifecycle of your product and finds and eliminates wast… https://t.co/fyJZvdPVCxFollow
Our digital course Sustainable Predictability is listed for $397 until Nov 30th. Take advantage of the 60% discount… https://t.co/8bBbiaWPa3Follow
Start making reliable decisions and eliminating the bottlenecks caused by unclear priorities with a dynamic priorit… https://t.co/hVpa8sCtR9Follow
Take your team to a whole new level with Nave's Kanban analytics for Trello. Picture what's going on behind your da… https://t.co/BhnrABnsPBFollow
In our latest article, we’ll take you through the key steps to reducing the impact that blockers have on your deliv… https://t.co/10L6MoruB4Follow
30% discount on all annual plans until the 30th November! Subscribe now with a coupon code NAVEBLACK20… https://t.co/dnSM2KzS5cFollow
The dotted horizontal lines on the Cycle Time Scatterplot are called percentiles. We use percentiles to define the… https://t.co/nlUcIGRDm3Follow
High pressure over long time periods leads to your team suffering from burnout and its symptoms. Learn more about w… https://t.co/hcYg29OE3YFollow
Successful project managers are effective leaders whose decisions will drive a business forward. Here are the top 5… https://t.co/gDVZffzmDbFollow