Where did the queue go?#
SLOP2710 · Week 9 · Priya Raghunathan
A restaurant with no reservations#
has a queue on the pavement.
The same restaurant with a booking system#
has no queue at all.
- W at the door
- —
- W from wanting a table
- —
- turned away a night
- —
- seats filled
- —
- W at the door, walk-in
- —
The wait did not disappear.
It moved somewhere nobody measures.
Three ways to move a wait#
Appointments — line into calendar
Virtual queues — keep the order, delete the standing
Deposits — week 8 wearing a different coat
All three keep arrival order. All three change where you stand.
The diary has its own mathematics#
Two costs you are trading:
patients waiting ⟷ the doctor idle
No schedule eliminates both, and the size of the trade is set by week 2’s coefficient of variation.
Why your 2:30 is at 3:10#
Delay accumulates through a session and nothing pushes it back.
So 9am runs on time and 4:30 does not. Always. Everywhere.
A clinic runs 40 minutes late every afternoon.#
Cheapest fix?#
Virtual queues: nearly a free win#
Ordering preserved. Hours returned. Best benefit-to-cost ratio in the course.
And it has an eligibility criterion nobody wrote down: a phone, charge, data, a number, somewhere to wait, confidence with the interface.
A physical queue excludes nobody who can stand in it.
The measurement trap#
Walk-in: published wait 90 minutes
Booked: published wait 8 minutes
The four weeks before the appointment are outside the definition.
An 18-week maximum, published.#
What shape does the distribution take?#
A published metric
becomes an ordering rule.
The partial defence#
Report the distribution, or at minimum the tail as well as the rate.
“Share seen within 18 weeks” and “longest anyone waited”.
The second gets worse exactly when the first is being protected.
End of Act II#
| Rule | Charges |
|---|---|
| Arrival order | tests free time |
| Job length | starves the longest |
| Need | rests on a 90-second classifier |
| Price | sorts by ability to pay |
| Appointment | demands commitment in advance |