The rule you have believed#
since you were four#
SLOP2710 · Week 5 · Act II begins
Around 1970#
Banks replaced one queue per teller with one queue for all tellers.
Customers hated it.
It looked longer. It was longer.
Four tellers. Same customers.#
What does merging the lines buy?#
Nineteen minutes → six#
And the unluckiest tenth: 43 minutes → 13
Nobody is working faster. There are still four tellers.
- W one line
- —
- W four lines
- —
- W₉₀ one line
- —
- W₉₀ four lines
- —
- stranded teller-min an hour
- —
If anyone is waiting,
no window is free.
That is the entire mechanism.
But the gain shrinks with size#
Staffing ≈ work + √work
- 4 tellers’ work → ~2 of safety → 50% overhead
- 100 tellers’ work → ~10 of safety → 10% overhead
Four reasons not to pool#
- generalists may be slower than specialists
- pooling costs travel
- it couples things that were independent
- some partitions are deliberate (the express lane, the resus bay)
And the real reason people hated four lines#
With four lanes, yours is fastest one time in four.
So three-quarters of the time, somebody who arrived after you leaves before you.
And you watch them do it.
The fairness claim, properly#
- needs no information about you
- verifiable from inside the queue
- strategy-proof, except by arriving earlier
- needs no justification at the counter
FCFS is not what four queues implement.#
It is what one queue implements.#
What it costs#
Ignores job length → week 6
Ignores urgency → week 7
Tests free time → who could be here at 9am?
Arrival order is not a fact the queue discovers.
It is an allocation that already happened, somewhere else,
before anybody reached the door.