Unlocking Real Impact: An Introduction to Little’s Law (#1 in Series)
While preparing for the PKT license I took a deep dive into the famous Little’s Law. I was surprised by the wealth of ideas and opportunities for discussions that this research has unveiled to me, richness which I had overlooked until now.
From reading blogs and articles I found myself playing around with data (yepp, on a Google Sheet) to experiment with the insights that Little’s Law can provide. I stumbled upon something exciting, which inspired me to write this mini-series on Little’s Law and how it can help flow in teams and organizations.
A Quick Primer on Little’s Law
If you live anywhere close to the world of Agile or Lean you must have, at some point in your existence in that space, heard about Little’s Law. If you haven’t, I have you covered with this summary.
Dr. John D.C. Little recalls an episode when, while teaching an Operations Research (OR) course, he got challenged to prove the relation between the average queue length (L) and average waiting time (W) is represented by the arrival rate for the queue (λ) — which back then was a “reappearing formula” though still unproven used by the likes of Philip M. Morse, considered to be the father of OR.
Guess what, Dr. John Little managed to prove the formula, and that is why it now carries his name: Little’s Law.
The importance of Little’s Law, even when it was still unproven, lies in the fact that it can provide understanding of flow — a quality in queuing systems and operational setups that, when experienced, provides a feeling of efficiency, effectiveness and predictability. Especially powerful is the fact that this understanding can be achieved even for those systems that receive items for processing without a predictable pattern.
So whether it’s a factory building dolls (the example used in one of the original sources), software development jobs, or even (this one comes from personal experience) food items stored in a pantry, flow is sought to be managed in order to enjoy its benefits. Nobody can control the demand for dolls, the influx of software ticket requests and even less the impulsiveness by which I buy snacks, pasta, and rice — but everyone wants to reduce waste, increase the value out of the work and maintain promises with their clients.
The Formulas
Little’s Law is often expressed through one of the following equations:
Equation 1:
which means: The Average Length of a queue (L) is equal to the Average Arrival Rate ( λ) multiplied by the Average Waiting Time (W).
or
Equation 2:
which means: Average Work in Progress (WIP) is equal to the Average Throughput (TH) multiplied by the Average Time it takes an item to be processed, or cycle time (CT).
The Agile world has adopted mostly Equation 2, and it is often presented as:
Little’s Law in the Context of Agile
Writing about how poorly Little’s Law was introduced and applied in infinite number of slide-decks, classrooms and other material by Agile Coaches, Scrum Masters and the like (to which I will simply refer to as Agile Coaches) is akin to rehashing old news.
Instead, I will just contain myself at commenting on the fact that reading primary sources is probably not the best attribute for a many Agile Coaches, particularly when the original writings contain an important element of mathematics.
It all becomes worse if we find some quick and easy explanation from secondary sources, in which case skipping the original sources comes in natural. I have done that myself, and that is the reason I am writing this series.
Before I share what I have learned, however, I will share how Little’s Law is typically presented by Agile Coaches. To avoid this article being misread or misquoted, I will try to mention those points that, despite not complete, are still aligned to the essence of Little’s Law.
- Agile Coaches declare that Little’s Law provides a perspective of how Cycle Time can be improved (shortened) if speed is your goal: A) Either controlling (limiting) WIP or B) Increasing Throughput
- Agile Coaches warn that plugging in the numbers from your work management system will probably not result in the two sides of the formula being equal
- Agile Coaches also warn that Little’s Law is not a forecasting tool, so you can’t manipulate the numbers expecting future projections
Here is where I realize there is a challenge for those who are interested: If Little’s Law can guide me how to speed up the system, but then I cannot plug in the numbers neither to analyze nor to experiment, what is the real use of Little’s Law?
Why is it so important?
Nobody Talks About Assumptions
It’s not really nobody, but surely not enough do.
Beneath the surface of the elegant equation are four assumptions that sustain it. Assumptions are key to understanding the logic behind any formula. They are the reasons the left hand side can ever equate to the right hand side.
However, as you can observe in the preceding section, most explanations of Little’s Law tend to focus solely on the equation, without delving into the underlying logic that supports it. My intention is to present you with the four assumptions, with the hope that, later on in this series, we can even explore their validity in analyzing flow.
The next article will delve deeper in to the assumptions, but for curiosity’s sake, the four assumptions are the following (taken from this source):
- the average output or departure rate (TH) equals the average input or arrival rate (A)
- that all jobs that enter the shop will eventually be completed and will exit the shop; there are no jobs that get lost or never depart from the shop
- we need the size of the WIP to be roughly the same at the beginning and end of the time interval so that there is neither significant growth nor decline in the size of the WIP
- we need some assurance that the average age or latency of the WIP is neither growing nor declining
In the next article I will look at every assumption separately and try to explain deeper what they mean and how they are typically broken.
