Why the ticket number skips yours and then comes back

The display is not a single list

Take a ticket, sit down, and watch numbers appear on the screen in an order that has no obvious relationship to arithmetic. Yours is skipped. Three higher numbers are called. Yours arrives eventually, apparently at random. The natural conclusion is that the machine is faulty.

It almost never is. What is usually happening is that the display is a shared window onto several separate queues, and the numbers being called are being drawn from all of them in an order determined by rules that are not shown anywhere in the room.

Prefixes are the tell

The first thing to look at is whether the numbers carry a letter or a colour. A prefix nearly always indicates a queue class — a transaction type, an appointment stream, a position qualified to handle something specific. Each class runs its own sequence, and the display interleaves them.

Once you know your prefix, the apparent chaos resolves. Numbers with other prefixes are irrelevant to your wait entirely, however close to yours they look, and the only meaningful comparison is with the last number called in your own class. Rooms that show a single undifferentiated list are the ones where this is hardest to work out, and they generate most of the frustration, because there is nothing on the screen to explain why the sequence is broken.

Skipping is a real feature, and it is usually about no-shows

Numbers get skipped for the ordinary reason that people leave. A ticket is called, nobody responds, and the position moves on rather than waiting. Most systems then requeue the skipped ticket a short way back so that somebody returning from the corridor is not simply lost, which is why your number can reappear later having been passed over once.

This is also why the announcement matters as much as the display, and why a room with a screen but no chime is worse than it looks. If the only signal is visual, anybody reading, watching a child or facing the wrong way will miss it, get skipped, and then experience a wait that has silently doubled through no fault of their own.

Appointments and walk-ins are different populations

Where a service takes both appointments and walk-ins, the two are almost always separate streams, and appointments are usually served against their slot rather than their arrival. A person who arrived after you can therefore be seen before you with no unfairness involved at all, because they were allocated a specific time and you were allocated a place in a line.

The perception problem is that both groups sit in the same room and neither can tell which the other is. Some places solve it by separating the waiting areas or by stating the arrangement on the ticket. Many do not, and the result is a room full of people constructing theories about queue-jumping from evidence that supports several explanations equally well.

Why the wait per position varies so much

The second source of apparent randomness is that positions are not interchangeable. One may be handling only quick enquiries, another only long applications, a third temporarily restricted while somebody covers a break. A queue class attached to long transactions moves slowly even when the room is nearly empty.

This produces the specific irritation of watching several positions call numbers rapidly while yours does not move. Nothing is wrong. You are attached to a stream with fewer servers or slower work, and the visible activity elsewhere is genuinely nothing to do with you. It would be trivially easy to display this and it is almost never displayed.

Reading a ticket room properly

Three questions get you most of what you need. Which class am I in, which positions serve that class, and what number in my class was called most recently. With those three, a display that looked arbitrary becomes a rough but usable estimate of the wait.

And it is always worth confirming the ticket type at the moment you take it, because tickets are chosen by the person arriving and choosing wrongly is easy. A ticket in the wrong class does not fail loudly. It simply waits in a queue that will eventually call it to a position that cannot help, which is the longest possible route to being told you need a different ticket.

It is worth adding that almost none of this is concealed deliberately. The routing rules exist in a configuration screen somewhere, they were set by somebody solving a real staffing problem, and displaying them would take a paragraph on a wall. That paragraph is missing from most waiting rooms not because anybody decided to withhold it, but because the person who understood the configuration and the person who orders the signage have never met.