There is a very easy and quick-to-cook recipe for chaos.

All we have to do is to ensure that the maximum number of jobs that we can do in a given time is set equal to the average number of jobs that we are required to do in the same period of time.

Eh?

That does not make sense.  Our intuition says that looks like the perfect recipe for a hyper-efficient, zero-waste, zero idle-time design which is what we want.

I know it does, but it isn’t.  Our intuition is tricking us.

It is the recipe for chaos – and to prove it all we will have to do a real world experiment – because to prove it using maths is really difficult. So difficult in fact that the formula was not revealed until 1962 – by a mathematician called John Kingman while a postgraduate student at Pembroke College, Cambridge.

The empirical experiment is very easy to do – all we need is a single step process – and a stream of jobs to do.

And we could do it for real, or we can simulate it using an Excel spreadsheet – which is much quicker.

So we set up our spreadsheet to simulate a new job arriving every X minutes and each job taking X minutes to complete.

Our operator can only do one job at a time so if a job arrives and the operator is busy the job joins the back of a queue of jobs and waits.

When the operator finishes a job it takes the next one from the front of the queue, the one that has been waiting longest.

And if there is no queue the operator will wait until the next job arrives.

Simple.

And when we run simulation the we see that there is indeed no queue, no jobs waiting and the operator is always busy (i.e. 100% utilised). Perfection!

BUT ….

This is not a realistic scenario.  In reality there is always some random variation.  Not all jobs require the same length of time, and jobs do not arrive at precisely the right intervals.

No matter, our confident intuition tells us. It will average out.  Swings-and-roundabouts. Give-and-take.

It doesn’t.

And if you do not believe me just build the simple Excel model outlined above, verify that it works, then add some random variation to the time it takes to do each job … and observe what happens to the average waiting time.

What you will discover is that as soon as we add even a small amount of random variation we get a queue, and waiting and idle resources as well!

But not a steady, stable, predictable queue … Oh No! … We get an unsteady, unstable and unpredictable queue … we get chaos.

Try it.

So what? How does this abstract ‘queue theory’ apply to the real world?

Well, suppose we have a single black box system called ‘a hospital’ – patients arrive and we work hard to diagnose and treat them.  And so long as we have enough resource-time to do all the jobs we are OK. No unstable queues. No unpredictable waiting.

But time-costs-money and we have an annual cost improvement target (CIP) that we are required to meet so we need to ‘trim’ resource-time capacity to push up resource utilisation.  And we will call that an ‘efficiency improvement’ which is good … yes?

It isn’t actually.  I can just as easily push up my ‘utilisation’ by working slower, or doing stuff I do not need to, or by making mistakes that I have to check for and then correct.  I can easily make myself busier and delude myself I am working harder.

And we are also a victim of our own success … the better we do our job … the longer people live and the more workload they put on the health and social care system.

So we have the perfect storm … the perfect recipe for chaos … slowly rising demand … slowly shrinking budgets … and an inefficient ‘business’ design.

And that in a nutshell is the reason the NHS is descending into chaos.

So what is the solution?

Reduce demand? Stop people getting sick? Or make them sicker so they die quicker?

Increase budgets? Where will the money come from? Beg? Borrow? Steal? Economic growth?

Improve the design?  Now there’s a thought. But how? By using the same beliefs and behaviours that have created the current chaos?

Maybe we need to challenge some invalid beliefs and behaviours … and replace those that fail the Reality Test with some more effective ones.