 ## A Little Pyramid

### Sunday, February 2, 2020

A short while back, I was at a customer site delivering a course for Agil8. At one point we were discussing Kanban and the subject quickly got round to queuing theory and Little's law, as Kanban conversations often do.

As most of you already know, Little's law is the heuristic that tells us the average number of items in a system (W) is equal to the average rate of flow (R) multiplied by the average time (T) that an item spends in the system. You might express this equation as W = R * T.

For example, if there are an average of 5 items arriving per week (R) and it takes an average of 2 weeks to process each item (T) then the system needs to be able to cope with an average of 10 items (W) in process at any one time to enable a steady flow of output at the same rate of input.

If we increase the arrival rate, we need to either increase the number of items we can have in process, or decrease the processing time to maintain stability. Ignoring this leads to work building up in a queue at the entrance to the system.

Conversely, if we find a queue building up in front of our system, we can use Little's law to solve the problem by altering either the processing time or WIP to increase the throughput. As with all equations, you can phrase W = R * T in different ways to calculate whichever bit of the formula you are missing and it was when we looked at dividing the work in process (W) by the cycle time (T) to find the rate of flow (R) that it dawned on me how similar Little's law was to Ohm's Law governing the behaviour of electrical circuits.

Way back in 1827, a German scientist, Georg Ohm, measured the effect of applying electricity to electrical circuits consisting of varying lengths of wire. He used the results of his measurements to formulate a quite complex calculation that has now been reduced to the much simpler form that we now know as Ohm's Law. Ohm's Law is commonly stated as I = V/R where I is the rate of flow in Amps, V is the voltage and R is the resistance of the circuit. Many others have noticed the similarity between the behaviour of electron flows and the behaviour of work flows and have expounded on the analogy, for example here.

However, for me the usefulness of the analogy is that electricians are taught to view the equation as a pyramid: like this: Viewing any similar equation or formula as a pyramid like this makes it easy to visualise the different ways the equation can be stated:

I = V/R

R = V/I

V= I x R

When it comes to Little's law, I think an easy way to remember it is, Rate = WIP over Time (R=W/T)

We can do the same with Little's law as the electricians do with Ohm's law by drawing it as a pyramid like so: This makes it easy to  visualise that:

R = W/T

T = W/R

W = R x T

Hope this helps and I'd be happy to hear of any other ways people have of remembering key equations/formulae