Imagine two operations that served 100 people on the same day.
At first, everyone waited 10 minutes.
On Monday, 80 people waited 5 minutes and 20 waited 30 minutes.
Both operations ended the day with the same average waiting time: 10 minutes. But the experience offered was completely different.
At first, the result was uniform. On Monday, a fifth of customers waited six times longer in line than the majority.
This is why tracking just the average wait time can give a misleading impression that the queue is healthy. To understand what really happens, the mean needs to be read together with measures that show the center and slowest part of the distribution, such as the median and P90.
The problem is not in the average, but in what it fails to show
The average waiting time is calculated by adding up all recorded times and dividing the result by the number of appointments. It continues to be useful for monitoring the general behavior of the operation.
The problem arises when the number is treated as a complete description of the experience.
Very high times push the average upwards. Likewise, a large number of very fast services can mathematically compensate for a smaller group of customers who waited too long.
Therefore, two rows with the same mean can have very different distributions.
This behavior is not exclusive to queues. Performance monitoring systems also use percentiles to see the latency distribution and distinguish the typical behavior of the so-called “tail”, where the slowest cases are. The AWS documentation, for example, presents P50 as a measure of typical behavior and higher percentiles as a way to look at slow occurrences that the average doesn't describe on its own.
Mean, median and P90 answer different questions
The three metrics do not compete with each other. Each helps answer an operational question.
Average: how long did customers wait on average?
The average summarizes all times into a single number.
If five people waited 4, 5, 6, 7 and 8 minutes, the average was 6 minutes.
It works well for tracking trends: knowing, for example, if the overall time increased from one week to the next or if an operational change reduced the aggregate wait.
Alone, however, it does not show how these times are distributed.
Median: what was the wait for the typical customer?
The median corresponds to the 50th percentile, or P50. After ordering the times from shortest to longest, it represents the point that separates approximately half of the records below and half above. NIST defines the 50th percentile as the median.
Let's go back to the two operations at the beginning.
In the operation where everyone waited 10 minutes:
- average: 10 minutes;
- median: 10 minutes.
In the operation where 80% waited 5 minutes and 20% waited 30:
- average: 10 minutes;
- median: 5 minutes.
The second operation looks even better when we just look at the typical customer. The median shows that most people were served quickly.
But we still have to see the group that has been waiting a long time.
Q90: how long did 90% of customers wait?
The P90 is the 90th percentile of the distribution.
In operational terms, a P90 of 20 minutes indicates that around 90% of the times observed were within this level, while the remaining portion was above it. This is the same logic used by monitoring tools that report latency percentiles.
In our example:
| Metric | Operation A | Operation B |
|---|---|---|
| Average | 10 min | 10 min |
| Median | 10 min | 5 min |
| P90 | 10 min | 30 min |
| Reading | Uniform wait | Quick majority, but relevant group waits a long time |
The table shows why the three measures together are more informative.
The average says the operations look the same.
The median reveals that the typical service for operation B is faster.
The P90 shows the hidden problem: there is a part of the queue facing a much longer wait.
When mean and median move apart, investigate the distribution
A relevant difference between mean and median is a sign that times are not evenly distributed.
Suppose a unit records:
- average 14 minutes;
- median of 7 minutes;
- P90 for 35 minutes.
The typical customer is being served in approximately half the time indicated by the average. At the same time, the longest services take P90 to 35 minutes.
This suggests that the problem may not be with the entire operation. There may be a specific group of times, services or service points resulting in much longer waits.
This reading is more useful than simply setting the goal of “reducing the average.”
A drop in the average from 14 to 11 minutes may seem like a big improvement. But if the P90 continues at 35 minutes, customers in the slowest part of the line will barely notice the change.
P90 is not a “maximum time”
This is a common error when interpreting percentiles.
If the P90 of the queue is 30 minutes, this does not mean that no one waited more than 30 minutes.
This means that the 90th percentile is at this point in the distribution. There may still be a tail above it, with waits of 35, 50 or 80 minutes.
Therefore, P90 should be used as a service indicator for most customers, not as an absolute upper limit.
Depending on the criticality of the operation, it may also make sense to track P95 or P99. The higher the percentile, the closer the indicator approaches extreme cases, but also the more sensitive it tends to be to small volumes and rare occurrences.
Do not calculate the indicator just for the entire day
Even a panel with mean, median and P90 can hide problems if all services are grouped into a single view.
A queue can present a reasonable P90 in the daily consolidated and still perform poorly during two specific hours.
Diagnosis improves when the same indicators are segmented by operational dimensions that can really explain the difference.
By time
Compare ranges such as 8am–9am, 9am–10am, and 10am–11am.
If the daily average is 8 minutes, but the P90 between 11 am and 12 pm reaches 28 minutes, the bottleneck is probably concentrated in that period.
This can guide decisions about scheduling, staff breaks, opening windows or distribution of demand.
By type of service
Mixing quick and slow services in the same statistic can distort the interpretation.
A document withdrawal that takes just a few minutes and a technical service that requires detailed analysis should not necessarily share the same operational reference.
Separating metrics by service allows you to discover whether a given queue is pushing times up or concentrating the slowest tail.
By counter or service point
Ticket segmentation can also reveal important differences, as long as the indicator is interpreted with context.
A window may present a higher P90 because it receives more complex cases. Another may be poorly configured or experiencing frequent outages.
The metric points out where to investigate; it alone does not explain the cause.
At Biomi Pass, the operation can work with different types of service and specialized counters, which makes these dimensions particularly relevant for queue analysis. The current service page informs that the counters can be specialized by type of service and that passwords can be transferred between queues.
A practical reading to find out if the queue is really healthy
There is no universal average value or P90 that is good for any business.
Waiting 15 minutes may be acceptable for one service and unfeasible for another. The parameter depends on the context, customer expectations, the complexity of the service and the objectives defined by the operation itself.
The most important thing is to interpret the design formed by the indicators.
| Observed symptom | Metric that deserves attention | What to investigate |
| High average and high median | Mean + median | General capacity or flow problem |
| High average and low median | P90 and higher percentiles | Group of very slow services increasing the average |
| Average stable and P90 rising | P90 | Tail getting worse despite apparently normal overall result |
| Median fell, but P90 did not | Median + P90 | Improvement benefited most but not slow cases |
| Good indicators on the day, bad in some periods | Metrics by time | Peaks in demand or insufficient capacity in certain ranges |
| A service has a much higher P90 | Metrics by type of service | Complexity, triage, routing or specific capacity |
| One window stands out from the rest | Metrics per window | Profile of cases, process, availability or configuration |
This matrix avoids a frequent mistake: trying to correct any queuing problem by indiscriminately increasing the speed of all services.
Sometimes the biggest opportunity is concentrated in just one time or service.
Always use the same calculation method
There are different statistical methods for calculating percentiles, especially when the sample is small and the value sought lies between two observations.
NIST itself documents methods based on ordering and interpolation of values.
In practice, this means that two systems can show small differences in P90 using the same data.
For operational management, the most important thing is to define a method and keep it consistent. Changing the formula in the middle of a historical series can create a false impression of improvement or worsening.
It is also advisable to avoid strong conclusions about percentiles when there are very few services in the period. A P90 calculated over hundreds of records is often more stable for comparison than a P90 based on just a few cases.
A healthy queue also needs to be good for those at the tail
Average waiting time remains a useful indicator. He just shouldn't work alone.
The average shows the aggregated result. The median helps you understand what happens to the typical customer. The P90 exposes the experience of those at the slowest part of the line.
When these three numbers are accompanied by hours, service and point of service, management stops asking just “how long do we wait on average?” and goes on to ask a more useful question:
who is waiting too long, when does it happen and where is the problem concentrated?
This change in reading is what transforms a panel number into operational information.
