Optimal boarding was worked out in 2008 and no airline uses it. Two reasons get given: you can't line 186 strangers up in an exact order, and families won't be split apart. Neither survives a simulation. Order bookings instead of people, paint the numbers on the ground, and both go away.
All of it comes off the seat number that is already on the pass.
Three things multiply out to twelve groups: your class, your side of the aisle, and whether your row number is odd or even.
Class is the most aisle-ward seat you booked. A solo in 27A is window-most. A family in 27A+B+C is aisle-most and boards as one.
One lane, marked in descending row bands toward the door: 31–30, 29–28 … 3–2, 1. Sixteen decals.
Your group gets called, you stand on your row's mark. Your party stands on it with you. That is the whole instruction.
Side and parity are in the formula for exactly this. One class on one side is at most one booking per row, and each mark covers two rows, one odd and one even. So one mark, one booking.
Nobody negotiates position with anybody. The lane comes out in exact back-to-front, every-other-row order.
Window-middle-aisle ordering is only there to stop people climbing over seated strangers. Inside a booking nobody is a stranger.
So a party takes the aisle once instead of three times and generates no seat-shuffle at all. Boarding time stays flat as the party rate goes up.
| Booking | Most aisle-ward seat | Class | Side | Row | Group |
|---|---|---|---|---|---|
| 27A | A, a window seat | window-most | left | odd | 2 |
| 27A+B+C | C, an aisle seat | aisle-most | left | odd | 10 |
| 14D+E | D, an aisle seat | aisle-most | right | even | 11 |
| 8E | E, a middle seat | middle-most | right | even | 7 |
Class sets the block: window-most is groups 1 to 4, middle-most 5 to 8, aisle-most 9 to 12. Inside a block the four slots run left-even, left-odd, right-even, right-odd. The two row-27 bookings are on the same side of the same row and still get different numbers, because a booking is classified by its most aisle-ward seat: the family has someone in C, the solo passenger in 27A does not.
Same physics for every method. One booking at a time per aisle slot, stowing a bag blocks the aisle, climbing over a seated stranger blocks it for longer. Parties walk on together in every method, because they will anyway. The only thing that changes is the order of the queue.
The bottom two are the "people won't actually do this" test.
Run at whatever aircraft size and dials you have set above. Mean boarding time, lower is better.
My first answer was that the group is enough. Everyone in a group sits at least two rows apart, so they can all stow at once, so who cares what order they walk in.
Compare 12 groups, no row marks against 12 groups + row marks at 31 rows. Same twelve groups, same twelve calls, same passengers. The only change is that people stand on a painted number instead of milling into the lane, and it is worth about half the boarding time.
Window-middle-aisle scatters a family of three across groups 1, 5 and 9, and no family accepts that. Correct. You never have to ask.
Window-middle-aisle is only there to stop people climbing over strangers who are already sitting down. Inside a booking that does not apply: they arrive together and sit in whatever order suits them. So the constraint is per booking, not per passenger, and the rule that falls out of it is one line. Your booking's class is its most aisle-ward seat.
Drag travel parties on board from 0% to 75% and watch the boarding time. It does not move. Past about half it gets marginally quicker, because 186 solo passengers is 186 separate stops at the aisle and a party-heavy cabin is about 122, and a family's bags go up while one of them is already sliding into the window seat.
The climb-overs readout is the mechanical reason. Random boarding on a full A320 produces 30 to 70 events where somebody has to stand up and let a stranger past, depending on how many people are travelling together. This produces zero, at every party rate, by construction. Set help from your own party to none, which is a family whose bags go up strictly one at a time with nobody helping, and it still lands at roughly half the random time.
Splitting families up is in the dropdown, and it buys nothing. At 31 rows with three in ten passengers travelling together it lands within a few seconds of keeping them together, which is inside the noise. Push the party rate to 75% and it is about fifteen seconds slower. So the concession that was supposed to be the expensive one is free, and past a point it pays.
| Modelled | Not modelled |
|---|---|
| Single-file aisle, one booking per row slot. Bag stow 5–19s, blocking. Seat shuffle 6s per seated stranger climbed over. A travel party is one unit: one aisle stop, bags at a discount, no internal shuffle. Non-compliance drops bookings back in at random. Sloppy placement swaps neighbours in the lane. | Overhead bin scarcity and backtracking. Wheelchair and pre-boarding. Two-door boarding. Gate-checked bags. Late arrivals. Cabin crew intervention. Aisle width letting people squeeze past. Premium cabin loaded first. Small children who need buckling in. Parties seated across the aisle or across rows rather than side by side. |
What happens when people don't play along. The two bottom dials are the test. Ignore their group drops that fraction of bookings back into the queue at a random point, which is the person who wanders up whenever they feel like it. At 31 rows the scheme runs 6:32 with everybody complying, 9:50 with a fifth ignoring their group, and 11:57 with two fifths ignoring it. Random boarding is 15:01, so it stays ahead throughout — but at two fifths it has given up most of its lead, and buys about what twelve groups with no floor marks buys with full compliance. The scheme is not fragile, but it does need people to actually wait for their number.
Calibration warning. Against the one real-world experiment I know of, Steffen & Hotchkiss's 72-volunteer mock 757, this model exaggerates in both directions. They measured Steffen's method at 0.76× random and I get 0.43×. They measured back-to-front at 1.31× random and I get 1.69×. Good orders come out better than they really are and bad orders come out worse. Treat the ranking as solid and every margin on this page as an upper bound.
The thing I would worry about in the field is not modelled at all. Window passengers board first and fill the bins above rows they only walk past, so late aisle passengers walk back looking for space. That eats into any window-first scheme.