Queuing Theory, Slack and Utilisation.

Wait Time vs Utilisation

In our psychological safety and management workshops, we cover a huge range of topics, but one of the most important things we address is the need for ‘slack’ in teams. Slack, also known as buffer or spare capacity, is non-committed or un-utilised time. It’s the time when team members are not already committed to set tasks. Slack is a useful idea to explore when we need to know how long it will take for someone (or something – this can apply to machines too!) to find time to complete an unexpected or unplanned piece of work – a concept known as ‘wait time’. It turns out that there’s a simple mathematical relationship between these two variables, and the graph below illustrates the relationship between the amount of time someone or something is utilised and the corresponding wait time.

Wait time vs Utilisation

To bring this to life, imagine an emergency room in a hospital. When a patient arrives at a quiet time, they have a good chance of being seen straight away, but when it’s very busy, patients are likely to have to wait longer to be seen. If the ER team is busy and committed to treating patients 50% of the time, then a new patient has a 50% chance of being seen immediately. The time we expect to wait is proportional to the % of time the team is utilised divided by the % of time the team is free. In  this case, it’s 50/50, which is 1, so we can take “1” as our proxy for “Wait Time”.

This is a simplification of Kingman’s Formula, which takes into account task variance, takt time and process time, and is beyond the scope of this article, but worth studying if you’re interested.

Application in practice

Now let’s imagine the team is busier, and we increase the utilisation up to 80%. The medics in the ER are now utilised 80% of the time, and free 20% of the time. Dividing 80 by 20, and we get a proxy for our wait time of 4, a fourfold increase. 

Now, let’s imagine we’re an efficiency-minded manager, and we want to get even more out of the team – we don’t want anyone ‘idle’ for long. We take away a person from the team, which takes utilisation from 80% to 90%. That only seems like a small change in utilisation, so it’s not going to have much effect on wait time, right? Nope. 90 divided by 10 is 9, so our wait time proxy has just increased from 4 to 9 – it’s more than doubled.

And you can probably guess what we’re going to try next – let’s see what happens if we max people out. Let’s commit people to working at 99% capacity. They’re busy 99% of the time, and free 1%, so our wait time proxy becomes 99/1 = 99. With an even smaller increase in utilisation, wait time has increased exponentially. When utilisation gets to 100%, wait time is effectively infinite…

This is why, when teams are working with a high percentage of their time utilised, it seems like work can go from just busy to spiralling out of control without much warning. And you can see from the graph that there’s a sort of tipping point around the 80% mark. If we go above that, then stuff starts to go sideways pretty quickly, because people (and machines, if we’re applying it to machines) may not be able to deal with incoming requests in an acceptable time frame. 

Why does this matter?

As Gareth Lock pointed out in a recent LinkedIn post, spare capacity allows us to deal with the unexpected. Fundamentally, this free time is “slack” or “buffer” time, a core concept in Resilience Engineering and, frankly, should have been in the 12 Agile Principles. We cannot adequately respond to changes, incidents or threats if we’re operating at capacity. And it applies to people, machines, computers, traffic and more – whether you’re running a factory floor, a busy kitchen, a software development team, or a hospital ER, percentage utilisation is impacting how well your team can adapt to a changing environment. 

Why is it so tempting to push the utilisation percentage higher?

There is a persistent, sticky, misconception that unutilised time is waste, and therefore costly:

“The voices crying out for a variety of “improvement” efforts – the measure and manage orthodoxy of Lean, Six Sigma, TQI, etc. – are popular, loud, and increasingly bristling with external power, leaving advocates for slack as lonely voices crying in the wilderness.” (Wears, 2017).

Managers often receive praise for increasing “efficiency”, and it’s an easy thing to put a metric to, whilst managers rarely receive praise for increasing organisational agility and resilience, partly because it’s so much harder to measure.

Ironically, as so often happens in organisations, a desire to maximise efficiency and productivity actually ends up harming the organisation, especially if done without regard for the capacity for resilience and adaptability. And this is particularly true in complex and highly variable environments.

But does unutilised time mean team members are doing nothing?

No, and this is another reason that allowing for slack can be foundational to creating a high-performing organisation. Slack time shouldn’t be wasted – you can use it for innovating, supporting, experimenting and learning – as long as tasks taking place in slack time are ‘interruptible’, you’re retaining the ability to respond quickly to unforeseen demands. 

This is actually the basis behind Google’s infamous “20% time” – the principle that engineers and developers should be spending around 20% of their time on interesting side projects. This is often seen as a ‘nice to have’ bonus, that developers get a bit of pressure free playtime, with the chance to create some cool new innovation, but in fact, the key principle here is that that 20% time is considered interruptible. If an urgent request comes in or an incident occurs then they’re able to react and respond immediately.

What’s more, if your team also has high psychological safety, by creating slack time, you may also be giving more opportunity for them to think a bit more deeply, and highlight threats, address concerns, and suggest ideas to address them. 

Does slack matter in every context?

Not necessarily. If we’re solely concerned with throughput, and we operate in a very steady and reliable environment, we need not concern ourselves too much with managing slack. If we very rarely have to deal with unplanned work, changes, or urgent and out-of-band requests, then we can get closer to that 100% utilisation mark without much impact on the system’s ability to cope. The danger comes when we believe that we operate in a consistent, planned and stable environment when we don’t. And of course, if we’re utilising people at 100%, we probably have other problems to deal with, or we will do soon!

Interested to learn more about Queuing Theory, Slack, Buffer and Wait Times?

What we’ve outlined here is a simplified representation of Queuing Theory, a branch of operations research that has its origins in research by Agner Krarup Erlang, who created models to describe the system of incoming calls at the Copenhagen Telephone Exchange Company. Since its inception in telecoms and call centres, it’s been used and applied in managing road traffic and public transport, computing (the graph above is notoriously the only chart in Gene Kim’s “The Phoenix Project”), industrial engineering (read Goldratt’s “The Goal” for more) and in healthcare. 

Today we’ve just taken a very high-level view of queuing theory – consider it a flying visit! If you’re interested to find out more, Kingman’s Formula, Little’s Theorem, Kendall’s notation, various queue types & disciplines, and different queuing models are all good avenues to explore.

Psychological Safety at Work

This week I hope everyone who celebrated had a Happy Halloween, Ognissanti and Día de los Muertos! In recognition of these holidays, community member, newsletter regular, and friend Roberto Ferraro drew up this Management Horror Bingo card, inspired by our recent “bad management” piece. Roberto also highlights the very important point that “bad” management doesn’t mean “bad” person – we can always do better and we all make mistaks.

Thanks to psychological safety community member Jonathan Cohen for writing and sharing this piece on psychological safety in anaesthesiology. I like this principle approach: “Start with messaging: “The operating room is a dynamic and complex environment, and it’s unlikely that I have all the answers all the time.”“

Thanks so much to Navya Adhikarla, graduate student in the Master of Engineering Management program at Duke University, for submitting a guest post to psychsafety.com. This piece: “(Don’t) Look me in the Eye: The Challenge of Eye Contact”, challenges some of the existing Western paradigms around “good” body language and behaviour, and highlights how difficult it can be for some people to maintain eye contact. She introduces counterpoints both from a neurodivergent perspective as well as a culturally Eastern perspective, and provides some alternative and additional approaches to take. 

Are you in academia? Or do you have experience in working in or with academia? Here’s a collaborative Miro board that was spawned from a discussion with Isabella von Holstein, Jade Garratt and myself. We’re examining the various factors that drive and influence academic culture, from the pressure to publish to adversarial reviews and “defending” papers. Take a look and contribute here. 

I love this from Notes To Strangers on Instagram. Waiting until it’s perfect is waiting forever.

This week’s poem:

Waiting for the Barbarians by C P Cavafy, translated by Edmund Keely and Philip Sherrard.


What are we waiting for, assembled in the forum?

      The barbarians are due here today.


Why isn’t anything going on in the senate?
Why are the senators sitting there without legislating?

      Because the barbarians are coming today.
      What’s the point of senators making laws now?
      Once the barbarians are here, they’ll do the legislating.


Why did our emperor get up so early,
and why is he sitting enthroned at the city’s main gate,
in state, wearing the crown?

      Because the barbarians are coming today
      and the emperor’s waiting to receive their leader.
      He’s even got a scroll to give him,
      loaded with titles, with imposing names.


Why have our two consuls and praetors come out today
wearing their embroidered, their scarlet togas?
Why have they put on bracelets with so many amethysts,
rings sparkling with magnificent emeralds?
Why are they carrying elegant canes
beautifully worked in silver and gold?

      Because the barbarians are coming today
      and things like that dazzle the barbarians.


Why don’t our distinguished orators turn up as usual
to make their speeches, say what they have to say?

      Because the barbarians are coming today
      and they’re bored by rhetoric and public speaking.


Why this sudden bewilderment, this confusion?
(How serious people’s faces have become.)
Why are the streets and squares emptying so rapidly,
everyone going home lost in thought?

      Because night has fallen and the barbarians haven’t come.
      And some of our men just in from the border say
      there are no barbarians any longer.


Now what’s going to happen to us without barbarians?
Those people were a kind of solution.


From C.P. Cavafy: Collected Poems. 


Thanks to my mum for sharing this with me!