Uncertainty is what people dislike
Research into queueing consistently finds that an unexplained wait feels longer than a known one. A stated wait that proves accurate is tolerated; one that passes without explanation generates complaints out of proportion to the time.
So the objective is not minimising the predicted wait. It is producing a number people can rely on.
What the prediction needs
- Current queue length and how long those ahead have already waited
- Number of servers currently active, which changes with breaks and shifts
- Service time distribution, ideally by case type rather than an average
- Arrival rate, which varies strongly by time of day and week
- Priority rules, where some cases jump the queue
- Abandonment rate, since people leaving shortens the queue
Abandonment is frequently omitted and matters considerably in phone queues, where a meaningful share hang up. Ignoring it produces predictions that are systematically too long, which then causes more abandonment.
Asymmetric errors
Being wrong in the two directions costs very differently. Predicting ten minutes and taking twenty produces a complaint. Predicting twenty and taking twelve produces a pleasantly surprised customer.
| Prediction | Actual | Reaction |
|---|---|---|
| 10 min | 20 min | Complaint, distrust of future estimates |
| 20 min | 12 min | Positive surprise |
| 20 min | 20 min | Neutral, trust maintained |
| 10 min | 9 min | Neutral |
This argues for predicting a high percentile rather than the middle - the same logic as quantile forecasting for stock. Aim to be right or slightly generous most of the time.
Ranges and updates
Giving a range - 'about 15 to 20 minutes' - is more honest than a single number and better received, because it sets expectations correctly without seeming evasive.
Update it as the situation changes, but not too frequently. A number that visibly fluctuates undermines confidence more than one that updates every few minutes, even if the volatile one is technically more accurate at each instant.
Use the prediction operationally too
The same model that tells customers their wait can trigger operational responses: open another till, call in a break, switch a server from back-office work, or offer a callback.
That is often where the larger value sits. Telling someone they will wait thirty minutes is useful; preventing the thirty-minute wait is better, and the prediction is what gives time to act.
Customers forgive a wait they were told about. They do not forgive one they were promised would be shorter.