The Kingman’s Equation
By: Cristina Marini
We’re going to discuss something a bit different this week – the Kingman’s Equation. Don’t worry, it isn’t as bad as it sounds — maths isn’t completely required for this one!
The Kingman’s Equation is centred around monitoring and understanding queues. When used correctly, it should help us to prevent their lengths from increasing.
Long queues can easily create problems, as well as going against key Lean aims:
- The amount of Muda (waste) will go up;
- The extent of Mura (unevenness) will also increase;
- The volume of Muri (overburden) will, finally, become larger.
The length of a queue can be influenced by three variables:
If the arrival and process variations can be decreased, there will be an opportunity to process more and decrease queue times. The arrival variation can be influenced by, for example, extending opening hours or moving work of a lesser importance to a quieter time. The process variation can similarly be influenced by taking measures to make staff more flexible and take the time to specifically train them in aspects of the process.
Luckily, the Kingman’s Equation can help us to prevent this from happening.
A handy graph has been created by Simon Lewis, the Director at the Lean Competency System:
On the vertical line, we have the average queue time.
On the horizontal line, we have the available capacity for utilisation
There are three different types of variations, all which mpact the length of a queue and utilisation:
— High variation (significant change)
— Moderate variation (neutral change)
— Zero variation (no change)
The formula for the queuing-theory relationship can be achieved by dividing the average arrival rate with the average service rate.
The Kingman’s Equation is a useful way to monitor queues and, more importantly, why queues occur.
The can reveal what exactly causes a queue length to increase or decrease; that if there’s plenty of capacity available, queues will usually remain at 0; how if there’s an increase in busyness, the queue will increase again and, finally, if the arrival rate of customers reaches its capacity, queues will get worse.