Every supermarket runs the experiment: a "10 items or fewer" lane, and a queue of full trolleys eyeing it. Queueing theory prices the perk exactly โ a priority lane is zero-sum, every minute the express class skips is paid by the regular class, to the second. But there's a twist: reserve the lane for the short work and the average wait across everyone falls too; bless the big slow work instead and it rises. Which class you wave through changes the whole system โ it's the queueing-theory face of the WSJF and cost-of-delay rule that urgent, small work goes first.
| Policy | Express wait | Regular wait | Everyone |
|---|---|---|---|
| FIFO | 19m | 19m | 19m |
| Express firstchosen | 4m 45s | 23m 45s | 11m 5s |
| Regular first | 47m 30s | 9m 30s | 34m 50s |
Priority here is non-preemptiveStarted work finishes: an express arrival never bumps the job already on the server, it only jumps the waiting line. That in-progress remainder is the Wโ every class โ even the most blessed โ waits out, which is why it appears in every formula above., and it conserves waiting: across all three policies the load-weighted sum of the waits is identical, so the express class's win is paid by the regular class, precisely โ with equal service times a priority lane is pure favouritism. With unequal service times the job-weighted average is up for grabs, and shortest-first provably minimizes it โ Smith's rule, the same rule WSJF applies to a backlog. Bless the big slow work instead and you buy the worst of both: the long jobs gain little while everything short rots behind them.