Week 10: Queues in Networks

1Why an aisle is not an ordinary queue

The server and the queue occupy the same space.

Everything in Act I assumed a separation that does not hold here. A bank has a counter and a lobby; the tellers work while the lobby waits, and the lobby’s length does not slow the tellers down. An aisle has no such division. The person being served is standing in the queue, and the queue cannot flow around them.

So boarding time is not governed by average passenger speed. It is governed by how often a stow blocks the aisle and for how long — which is week 2’s lesson, variance rather than load, in its purest available form. An aircraft where every passenger had identical bags and identical seats would board in a fraction of the time with no change whatever to the mean.

There are exactly two blocking events, and it is worth naming them separately because the four strategies attack them differently.

The stow. Somebody stops at their row, lifts a bag, and everybody behind them stops. Duration: highly variable, and the variance is what costs you.

The seat shuffle. Somebody in an aisle seat has to stand up and step out so that the window passenger behind them can get in. This one is pure self-inflicted damage: it happens only because of the order people were let on, and there is a strategy below that eliminates it entirely.

2Four strategies

Back to front is what many airlines use and what intuition endorses.

Random scatters passengers along the aisle.

Outside-in (windows, then middles, then aisles — often called WILMA) eliminates the seat shuffle, which is the other blocking event.

Steffen interleaves both: alternating rows, outside-in, so consecutive boarders are two rows apart and never in each other’s way.

The Steffen result is not only a simulation finding. It was proposed in 2008 and then tested with real people — a mock cabin, volunteers, luggage, timed runs — and the field experiment broadly confirmed the ordering, with the interleaved method coming in at around half the time of back-to-front. So the effect survives contact with actual humans who do not read instructions carefully, which is more than most operational research manages.

3So why does nobody use the fast one?

This is the actually interesting question, and it is not a technical one.

It fights the revenue model. Priority boarding is a product. Week 8 applies exactly: an operator earning money from congestion has acquired a reason to preserve it. Steffen ordering is incompatible with “zone 1 boards first” because zone 1 is something the airline sells.

It separates people travelling together. Families ignore the sequence, and Steffen degrades sharply under non-compliance in a way random boarding does not.

It is hard to explain at a gate, in a second language, over a poor PA, to tired people.

The constraint that binds is almost never the one in the model.

A strategy that is optimal only when everyone obeys is not optimal in an airport — which is week 6’s warning about self-reported job lengths arriving again, in a different building, with luggage.

Notice the shape of the comparison, because you will need it in your brief. Steffen is the best strategy under compliance and degrades fast without it. Random is mediocre under compliance and degrades not at all, because it has nothing to degrade from. Outside-in sits between the two and is what most airlines that have improved anything have actually adopted, precisely because it survives families, late arrivals and people who did not hear the announcement.

That is a general design principle and it is worth more than the boarding result: rank your options by how they perform when half-followed, not by how they perform when obeyed.

4The gate is not one queue, it is a network

Boarding is the visible queue. It is one node in a small network that has to complete before the aircraft can move, and the reason the airline cares about boarding at all is what that network does.

Deplane. Clean. Cater. Fuel. Load the hold. Board. Some of those can run at the same time; several cannot. Cleaning cannot start until deplaning finishes. Boarding cannot start until cleaning finishes. Fuelling may or may not overlap with boarding depending on the operator’s rules.

Which produces the first result of network thinking, and it is brutal: the turnaround takes as long as the longest chain of things that must happen in order. Everything not on that chain has slack, and improving anything with slack changes nothing at all.

5Bottlenecks move, they do not disappear

Now the result that makes networks genuinely dangerous rather than merely complicated.

Once queues are connected, improving one of them can make the whole system worse.

The mild version first, because it is the one you will actually meet. Speed up check-in and you deliver a denser stream to security, which is now the bottleneck. Total journey time is unchanged and you have moved the crowd into a smaller room with fewer seats and worse air. Somebody will report this as a success, because check-in’s numbers improved and security’s numbers belong to a different manager.

The strong version is Braess’s paradox, from 1968, and it is worth seeing once because it is genuinely counter-intuitive: in a road network where drivers each choose their own fastest route, adding a new road can make everybody’s journey longer. Not “can fail to help” — can actively worsen, at equilibrium, for every single driver. The new road is individually attractive and collectively destructive, and each driver taking it is behaving perfectly rationally.

The reverse has been observed too. Closing a major road has, in several widely cited cases, left city-centre traffic no worse and sometimes better, which is the same mathematics run backwards and is much harder to get funded.

The same structure, in three more buildings:

Emergency departments. A department can be working perfectly and still have a twelve-hour queue, because the wards upstairs are full and patients cannot leave. The ED is not the bottleneck; discharge is. Every intervention aimed at the visible queue — more triage nurses, a faster front door — pushes harder against a closed exit. This is well documented and it is the clearest real-world lesson in the lecture: the queue you can see is often the symptom of a constraint somewhere you cannot.

Networks. Adding buffer memory to routers to stop packets being dropped produced bufferbloat: enormous queues, enormous latency, and no more throughput, because the signal that told senders to slow down was the dropped packet. The fix for congestion turned out to require keeping the queue short on purpose.

Any pipeline of teams. A development team that doubles its output delivers twice as much work to a review queue that did not change, and the lead time gets worse. Week 3’s arithmetic predicts it exactly.

6The general result

Look at the pink bars in the cabin again rather than the clock. Every strategy loads the same bags into the same lockers, so the total stowing is identical — and yet the worst row goes from causing eleven and a half minutes of other people’s waiting to causing one. Back-to-front does not create interference. It arranges for the interference to happen where the queue is standing.

That sentence is the whole of Act III’s first half, and it generalises past aircraft: in a connected system, where a delay lands matters as much as how big it is, because a delay that lands on a bottleneck propagates and a delay that lands on slack evaporates.

Next week: what happens when the people in the queue can see it too.