The surprising thing about queues is that they build up even when you think you’ve got enough capacity. This is because of the inevitable fluctuations in arrival rate and service rate.
The good news is that you CAN predict the size of queues, and you can therefore work out how much extra capacity you need (and the cost of this) if you want to keep queues down to a certain level.
If you want to keep your queues down to an average of 4 (so if it takes 3 minutes to serve each person then they are waiting 12 minutes on average – is that acceptable, you must ask yourself) then you will need 20% spare capacity. This means that your people will be working 80% of the time, it’s called 80% utilisation. The formula is Q = U/(100-U) so for 80% utilisation you get Q = 80/(100-80) = 80/20 = 4 people in the queue.
So you can see that if you have 90% utilisation the queue goes up to 90/10 = 9 people. It approximately doubles if you reduce your resources by 10%. Interesting!
I’ve made a video on this subject, here: https://youtu.be/m74zWJaYaFA
I hope you enjoy it – don’t be put off my the maths, it’s easy when you get used to it!
sayeed says
Thank you very much to simplify the concept for the rest.