<Bob> OK Leslie, I suppose we had better do some actual work, which seems a shame on such a wonderful spring day.
<Leslie> Yes, I suppose so. There is actually something I would like to ask you about because I came across it by accident and it looked very pertinent to flow design … but you have never mentioned it.
<Bob> That sounds interesting. What is it?
<Bob> Ah ha! You have stumbled across the Queue Theorists and the Factory Physicists. So, what was your take on it?
<Leslie> Well it all sounded very impressive. The context is I was having a chat with a colleague who is also getting into the improvement stuff and who had been to a course called “Factory Physics for Managers” – and he came away buzzing about the VUT equation … and claimed that it explained everything!
<Bob> OK. So what did you do next?
<Leslie> I looked it up of course and I have to say the more I read the more confused I got. Maybe I am just a bid dim and not up to understanding this stuff.
<Bob> Well you are certainly not dim so your confusion must be caused by something else. Did your colleague describe how the VUT equation is applied in practice?
<Leslie> Um. No, I do not remember him describing an example – just that it explained why we cannot expect to run resources at 100% utilisation.
<Bob> Well he is correct on that point … though there is a bit more to it than that. A more accurate statement is “We cannot expect our system to be stable if there is variation and we run flow-resources at 100% utilisation”.
<Leslie> Well that sounds just like the sort of thing we have been talking about, what you call “resilient design”, so what is the problem with the VUT equation?
<Bob> The problem is that it gives an estimate of the average waiting time in a very simple system called a G/G/1 system.
<Leslie> Eh? What is a G/G/1 system?
<Bob> Arrgh … this is the can of queue theory worms that I was hoping to avoid … but as you brought it up let us grasp the nettle. This is called Kendall’s Notation and it is a short cut notation for describing the system design. The first letter refers to the arrivals or demand and G means a general distribution of arrival times; the second G refers to the size of the jobs or the cycle time and again the distribution is general; and the last number refers to the number of parallel resources pulling from the queue.
<Leslie> OK, so that is a single queue feeding into a single resource … the simplest possible flow system.
<Bob> Yes. But that isn’t the problem. The problem is that the VUT equation gives an approximation to the average waiting time. It tells us nothing about the variation in the waiting time.
<Leslie> Ah I see. So it tells us nothing about the variation in the size of the queue either … so does not help us plan the required space-capacity to hold the varying queue.
<Bob> Precisely. There is another problem too. The ‘U’ term in the VUT equation refers to utilisation of the resource … denoted by the symbol ? or rho. The actual term is ? / (1-?) … so what happens when rho approaches one … or in practical terms the average utilisation of the resource approaches 100%?
<Leslie> Um … 1 divided by (1-1) is 1 divided by zero which is … infinity! The average waiting time becomes infinitely long!
<Bob> Yes, but only if we wait forever – in reality we cannot and anyway – reality is always changing … we live in a dynamic, ever-changing, unstable system called Reality. The VUT equation may be academically appealing but in practice it is almost useless.
<Leslie> Ah ha! Now I see why you never mentioned it. So how do we design for resilience in practice? How do we get a handle on the behaviour of even the G/G/1 system over time?
<Bob> We use an Excel spreadsheet to simulate our G/G/1 system and we find a fit-for-purpose design using an empirical, experimental approach. It is actually quite straightforward and does not require any Queue Theory or VUT equations … just a bit of basic Excel know-how.
<Leslie> Phew! That sounds more up my street. I would like to see an example.
<Bob> Welcome to the first exercise in ISP-2 (Flow).