Trying to Understand Why Kanban Works

Recently, I came across a book chapter explaining Little's Law; published by Massachusetts Institute of Technology. This chapter is an excellent read which is simple and yet digs into the heart of Little's Law. Reading about queuing theory is provocative and makes me relate many of the already established ideas to Lean software and Kanban.

One of the issues which I found this book chapter explaining very well is the difference between Little's law in its original formulation (which considers the Arrival Rate as one of the formula parameters) and its application in manufacturing systems (which replaces arrival rate with throughput). Here is an explanation:

Little’s Law

Little's Law state that:

L = λ W

where

L = average number of items in the queueing system
λ = arrival rate of new items to the system
W = average wait time for an item in the system

John Little argues that this law is robust and generic and holds exactly to any queuing system given an essential condition; which is "to have a finite window of observation that starts [when the system is empty] and stops when the system is empty" (p.88). Moreover, Little provides a mathematical proof for the law along with many applications in reality.

Little’s Law in Software Systems

Let's jump into software and map these concepts to Kanban. In Kanban, this is how Little's Law is stated:

WIP = Th * CT

where

WIP (average Work In Process) = average amount of unfinished items (bugs, user stories, change requests, etc.) in the development system
Th (Throughput) = Team output in unit of time
CT (Cycle Time) = Average time it takes the team to finish one item

Two basic differences between the two formulas: The first one talks about input or arrival rate, whereas the latter talks about output rate or throughput. The second issue is the condition which Little stated: that the system should start with 0 items and end at 0 items. In software, we rarely witness a system which has no maintenance requests.

To resolve these differences, Little indicated a more subtle condition of the Law to hold, which is no items to go inside the system and get lost or do not get finished, which he calls “conservation of flow” (p. 93). If we apply this condition to the system, we can easily show that the input rate = output rate, and therefore, we can relate Lambda (λ) with throughout (th).

For the second condition (system should start and end in 0 items), Little argues that the law “still applies, at least as an approximation, as long as we select a time interval that is long enough”. (p. 93)

What’s useful about this Law?
Little’s Law is a very powerful tool to use for managers. If we have two parts, and we can instantly calculate the third.

Increase team throughput

If your capabilities are fixed and want to increase throughput, the only solution is to increase WIP, and increase the team size. If this is not doable, and your input rate is high and getting higher, you may decide to decrease the cycle time instead of increasing the WIP and this may involve automating the deployment process.

Stabilize Cycle time

If you are struggling to stabilize the process so that to meet some SLA, Little’s Law gives insight about what to change in the system. You may either increase/decrease with WIP or empower your team to meet a specific SLA.

Study behavior of specific request types
Little’s Law works for a sample of item in the system as well. You may zoom into the items in the system and study the dynamics of a specific segment (like high severity bugs, for instance).