Uncovering Little’s Law: Exploring Assumptions and Violations (#2 in Series)

Agile Coaches, Scrum Masters, and their ilk (referred to here as Agile Coaches) often enthusiastically invoke Little’s Law for its implications on Work In Progress (WIP) limits. However, when pressed for further explanations, we often stumble in elucidating the Law’s applicability within flow systems.

In this mini-series, I delve into Little’s Law, aiming to propose an application that can enhance our work with teams and organizations. But before we proceed, it’s crucial to lay a strong foundation. In this second article, we will examine the assumptions and how they are typically violated.

Returning to the Assumptions

In my previous article, I outlined the four assumptions that underpin Little’s Law equation:

1. The average departure rate equals the average arrival rate (TH = A).
2. There are no jobs that get lost or never depart from the system.
3. The WIP size remains roughly constant at the beginning and end of the observation period.
4. The average age or latency of the WIP neither grows nor declines.

Let’s scrutinize these assumptions individually, elucidating their meaning and common breaches. Here we go!

Assumption 1: Average Departure Rate Equals Average Arrival Rate

Flow systems share common phases:

1. Introduction of an item into the system for processing.
2. Processing of the item within the system.
3. Departure of the item from the system in a changed state.

For example, consider an airport’s runway:

1. An airplane arrives at the runway (Arrival).
2. It undergoes processing, including passenger disembarkation, refueling, and waiting for the next flight (Processing).
3. The airplane departs from the runway to another destination (Departure).

Now, imagine two scenarios involving hypothetical airports with imbalanced arrival and departure rates.

Scenario 1: An Airport Has An Arrival Rate Higher Than Its Departure Rate

Airport A welcomes 20 airplanes every hour but only has 10 airplanes departing in the same hour.

A 24 hour tally of airplanes in and out of Airport A

On the surface, this pattern might seem stable: 20 in, 10 out, hour after hour. However, behind the scenes, an issue emerges.

Accumulative Counts of Arrivals / Departures in Airport A

By the 12th hour, the airport has 120 planes parked, idle, and occupying valuable space. By the day’s end, this number swells to 240 planes. These planes show no intention of leaving, posing a significant challenge.

For an airport to rectify this situation, it would need to halt arrivals for the next 24 hours, focusing solely on departures. The first assumption requires that arrival and departure rates align over the observation period to follow Little’s Law.

Scenario 2: An Airport Has A Departure Rate Higher Than Its Arrival Rate

This scenario requires reversing the numbers, resulting in a negative number of airplanes, which is impossible. An example is seen during the COVID-19 pandemic when airports experienced dwindling numbers in their charts, causing severe financial repercussions for airports and airlines.

What are the signals of Assumption 1 being broken?

Based on the above, we can list down two signals:

1. Clogging — a system is piling up jobs
2. Starvation — a system is always running out of jobs

Assumption 2: No Jobs Get Lost or Abandoned

Assumption 2 differs from Assumption 1 in that it addresses cases where jobs are introduced to the system but are later abandoned in the process.

For instance, consider an airline that parks its fleet on a runway but then goes bankrupt, leaving all its planes stranded.

What are the signals of Assumption 2 being broken?

These are instances where flow literally stops for those jobs. I can think of two signals that show this assumption being broken:

1. Whenever software development teams have tickets that are marked as “Cancelled”, “Obsolete” or “Rejected”
2. Whenever there are jobs that have aged way beyond the typical processing trends to the point that the team has stopped following up on them, losing hope

Assumption 3: No Significant Growth or Decline in WIP Size

Imagine Airport C, that is having moments in which it is welcoming a huge number of airplanes, others in which it sees a lot of airplanes leaving, and others in which the numbers are not so drastic. Let’s have a look at 24 hours in this airport:

24 hour schedule of Airport C

The number of airplanes in the runway are as follows:

Accumulative Arrival / Departures for Airport C

Now imagine that, for the next 24 hours the pattern is totally different. And again for the 24 hours that follow.

What are the signals of Assumption 3 being broken?

Looking at the above numbers we can understand how what Airport C is experiencing is a constant fluctuation between the symptoms experienced by Airport A (clogging and piling up) and Airport B (starvation).

The signals, therefore, are the same signals we saw in Assumption 1.

Assumption 4: The Average Age of WIP is Neither Growing nor Declining

Assumption 4 introduces a fourth flow metric: work item age. This metric, though not explicitly mentioned in Little’s Law, holds significant influence over flow systems.

Work item age is a leading indicator that empowers team members to impact the system’s flow by addressing aging work items.

What are the signals of Assumption 4 being broken?

1. In systems handling physical objects, aging items occupy real space and can trigger frustration.
2. Virtual work items may be less conspicuous, but monitoring their age is essential to prevent delays in value production.

Summary

The journey to this point in the article was indeed a lengthy one, taking us through multiple airports and planes. To provide a concise reference, here’s a table summarizing the four assumptions and their signals of being broken in a flow system.

In the next article, we will explore how this information can be used to analyze flow data.