Two maintenance teams cover similar portfolios with similar work. One is scheduled to about 80 percent of its capacity and consistently turns work around quickly. The other is scheduled to 95 percent, looks more efficient on paper, and is drowning: residents wait days, the team feels permanently behind, and every week the backlog is a little worse. The natural explanation is that the second team is understaffed, badly run, or both. The natural fix is to tighten scheduling and push utilisation higher still. Both the explanation and the fix are wrong, and the reason they are wrong is a property of queues that has been understood mathematically since 1961. This article covers why a busier team is a slower team, why maintenance is the worst kind of work for this effect, and what the actual levers are.

The Counterintuitive Part, and Where It Comes From

The instinct in every operation is that a resource should be kept as fully utilised as possible. Idle time is waste. A technician booked to 95 percent of capacity is doing more useful work than one booked to 80, so the first looks like the better-run operation.

For throughput, that instinct is correct. For wait time, it is close to backwards, and the reason is that maintenance requests do not arrive on a tidy schedule. They arrive when things break, which is to say unpredictably, and a queue fed by unpredictable arrivals behaves in a way that ordinary capacity arithmetic does not capture.

The relationship was formalised by the mathematician John Kingman. In queueing theory, Kingman's formula is an approximation for the mean waiting time in a queue, expressed as the product of three terms that depend on utilisation, variability and service time. It was first published in his 1961 paper on the single server queue in heavy traffic, and it is known to be generally very accurate, especially for a system operating close to saturation.

The detail that matters for maintenance is the utilisation term. It takes the form ρ/(1−ρ), where ρ is utilisation. That fraction is not a straight line. As utilisation climbs toward 100 percent, the denominator shrinks toward zero and the whole term climbs toward infinity. The wait does not rise in proportion to how busy the team is. It rises far faster, and near the top it rises almost vertically.

Put numbers to just that term and the shape is obvious.

The jump from 80 to 95 percent utilisation looks, on a capacity chart, like a modest efficiency gain of fifteen points. In the wait a resident actually experiences, it is not modest. The multiplier goes from about four to about nineteen. The team that looks fifteen percent busier is delivering waits several times longer, and it did not do anything wrong to get there. It followed the instinct to stay fully booked.

A necessary caveat on the numbers. Kingman's formula describes a single-server queue and is an approximation; a real maintenance operation has several technicians and more structure than the simplest model. The specific multipliers above illustrate the shape of the utilisation term, not a prediction for any given team. But the shape is the point, and the shape is robust: wait time is flat and forgiving at low utilisation, then turns sharply upward as the operation approaches full capacity. Every queue with unpredictable arrivals has this elbow.

Why Maintenance Is the Worst Case

Kingman's formula has a second term, and for property maintenance it is arguably more important than the first. Alongside utilisation, waiting time depends on variability: specifically, the variability of when work arrives and how long each job takes.

This is where maintenance is unusually exposed. The variability term is driven by the coefficient of variation of arrivals and of service times, and emergency maintenance is high on both.

Arrivals are erratic by definition. A burst pipe, a failed HVAC unit and a lockout do not queue politely at even intervals; they cluster, often in weather, and a cold snap can deliver a week's worth of heating calls in a day. Job durations are erratic too. One call is a five-minute reset and the next is a two-hour repair that needs a part nobody has. Both of those are exactly the conditions that inflate the variability term.

And the two terms multiply. High utilisation alone lengthens waits. High variability alone lengthens waits. A maintenance operation that is both fully booked and fed by emergency-driven, unpredictable demand sits at the product of the two, which is the worst square of the grid. This is why a maintenance team can feel like it is failing while doing everything asked of it. It is not failing. It is operating at the exact point where the mathematics turns against it.

The Staffing Conclusion Runs Backwards

The practical implication overturns the instinct the article started with.

If you plan a maintenance team to 100 percent utilisation, you have not built an efficient operation. You have built one whose wait times, by the formula, tend toward infinity, because you have parked it at the far right of that curve where the denominator approaches zero. Planned full utilisation does not maximise service. It guarantees the queue.

The counterintuitive move is to build in deliberate slack. A team held at around 80 percent utilisation has genuine spare capacity to absorb the bursts, which is precisely what keeps the wait short. That slack is not idleness or waste, even though it looks like both on a utilisation report. It is the capacity that absorbs variability, and it is doing the most important job in the system: keeping the operation off the vertical part of the curve.

This reframes a familiar argument. When a maintenance team says it needs more people while the utilisation report shows it is not yet at 100 percent, the report is not the rebuttal it appears to be. Slack below full utilisation is not evidence of overstaffing. On emergency-driven work it is the mechanism that makes fast response possible, and removing it to look more efficient is how an operation books itself onto the steep part of the curve.

The Second Lever Nobody Reaches For

Because waiting time is the product of a utilisation term and a variability term, there are two ways to shorten it, and operations habitually reach for only one.

The reflex is to add capacity, which lowers utilisation and moves the team leftward down the curve. That works, and sometimes it is the right answer. But the formula says variability is a co-equal lever, and variability is often the cheaper one, because a large share of it is self-inflicted and reducible.

The route to reducing it is preventive maintenance, seen through the queueing lens rather than the reliability one. Every failure caught on a planned inspection is an emergency arrival that never happens. Converting an unpredictable breakdown into a scheduled task does two things at once: it removes a high-variability arrival from the emergency queue, and it replaces it with a low-variability one that can be smoothed across quiet periods. That lowers the variability term directly, which shortens waits for everything else in the queue, not just the item that was serviced.

This is a different case for preventive maintenance than the usual one. The standard argument is that prevention is cheaper than failure, which is about the cost of the individual repair. The queueing argument is about the whole system: planned work lowers the variability of the arrival stream, and lower variability shortens every wait in the operation. It is a case for prevention that a CFO can read straight off the same formula that explains the wait times.

Conclusion

The busier team is the slower team, and it is worth being precise about why, because the wrong diagnosis leads to the wrong cure. The slow team is not slow because it is undisciplined or lazy. It is slow because it has been booked onto the steep part of a curve that turns sharply upward near full capacity, and the harder it is pushed toward 100 percent utilisation, the longer its queue becomes. Tightening the schedule, the instinctive fix, moves it further up the same curve.

The levers that actually work both look, at first glance, like inefficiency. Holding utilisation below full capacity looks like paying for idle time. Investing in preventive maintenance looks like spending on failures that have not happened. The queueing formula says both are doing the same essential job: keeping the operation off the part of the curve where waits explode, one by leaving room for the bursts, the other by making the bursts smaller.

Knowing which lever to pull requires knowing where on the curve a given operation actually sits, and that is a measurement question. Real utilisation and the true variability of the arrival stream are not in anyone's head; they are in the work order history, in the timestamps of when requests arrived and how long jobs took. An operation that can read its own arrival pattern out of that record, RIOO among the systems that hold it, can tell whether its problem is capacity, variability, or both. Most operations argue about it instead, because the number has never been looked at.

A fully-booked maintenance team is not a well-run one. It is a warning sign, and the mathematics has been telling us so since 1961.

FAQs

1. Why does a busier maintenance team have longer wait times?
Because maintenance requests arrive unpredictably, and in a queue with unpredictable arrivals, waiting time rises far faster than utilisation does. Kingman's formula expresses the effect through a term, ρ/(1−ρ), that climbs toward infinity as utilisation approaches 100 percent. A team booked to 95 percent can have several times the wait of one booked to 80, even though it looks only slightly busier.

2. What utilisation should a maintenance team target?
There is no single correct figure, but the important point is that it should be meaningfully below 100 percent. Operations research on queues generally points to keeping utilisation in the region of 80 percent for work with variable demand, because that leaves enough slack to absorb bursts without the wait times climbing the steep part of the curve. The right number for a given operation depends on how variable its demand is.

3. Is spare capacity in a maintenance team just waste?
Not for emergency-driven work. Slack below full utilisation is what absorbs the unpredictable bursts of demand, and it is the main thing keeping wait times short. It looks like idle time on a utilisation report, but it is performing the function of preventing the queue from exploding. Removing it to raise utilisation is what produces long waits.

4. How does preventive maintenance reduce wait times?
Through variability, not just through preventing individual failures. Kingman's formula makes waiting time depend on the variability of arrivals as well as on utilisation. Every failure caught by planned inspection is an unpredictable emergency arrival that never enters the queue, which lowers the variability of the arrival stream and shortens waits across the whole operation.

5. How do we know where our operation sits on this curve?
From the work order history. Actual utilisation and the variability of the arrival stream can be calculated from the record of when requests were received and how long jobs took. Most operations have never computed either number and argue about staffing on the basis of how busy the team feels, when the data to settle it already exists in the dispatch record.