Hub-and-spoke routing

Why does an airline fly you away from your destination in order to get you there?

You want to go from a modest city to another modest city three hundred miles away. The airline sends you six hundred miles in the wrong direction, makes you change aircraft, and delivers you five hours later. Fuel was burned, time was lost, and an aircraft flew further than the geometry required.

The obvious reading is that this is the airline's convenience purchased at your expense. That is not quite wrong, but it is not the mechanism, and taking it as the answer hides the more interesting fact: for most city pairs, the alternative to the detour is not a nonstop flight. It is no flight.

Begin with demand, because everything follows from its shape. How many people actually want to travel between two particular medium-sized cities on a given day? For a handful of famous pairs, thousands. For the overwhelming majority, a few dozen at most, spread unevenly across the week. Demand between arbitrary places is thin.

Now try to serve that directly. Both levers are unattractive. Fly a large aircraft and it departs nearly empty, so cost per passenger is ruinous. Fly it once or twice a week and it fills, but a service leaving on Tuesday is useless to someone who must be there on Thursday. Thin demand forces a choice between an empty aeroplane and a useless timetable.

So ask what could rescue it. The passengers wanting any one journey are too few — but the passengers leaving that city on a given morning, taken together, are not few at all. They are simply going to many different places. If they could share an aircraft for the first part of their journeys, the thin flows would add into one thick one.

That is what a hub is: a place to add flows together. The morning departure from the small city carries people bound for forty destinations, so it fills a properly sized aircraft, several times a day. At the hub everyone is re-sorted, and each onward flight is filled the same way by arrivals from dozens of other spokes. Every leg is thick, because every leg is shared by many journeys that have nothing else in common.

Notice what was bought. Not distance — that got worse. What was bought is frequency and existence: three or four departures a day instead of two a week, and a usable connection to hundreds of destinations that could never justify a service of their own.

There is a combinatorial fact underneath, worth seeing plainly. Connecting fifty cities to each other directly takes fifty times forty-nine, halved — one thousand two hundred and twenty-five routes. Through one hub it takes forty-nine. But be careful what that proves. Airlines are not short of lines on a map; they are short of aircraft, crews, and passengers per route. The real content of the ratio is that direct connection divides a fixed pool of travellers across a number of routes growing with the square of the network, so the average route thins as the network grows. Consolidation answers that thinning, and the detour is its price.

Which tells us where the arrangement should fail. Where demand is genuinely thick — London to New York, Tokyo to Seoul — there is nothing to consolidate and nonstop wins outright. And once aircraft become efficient enough at smaller sizes to fill on long thin routes, some of those pairs go direct, which is what happened as smaller long-range twin-engine aircraft arrived. The hub is not a law of aviation; it is what you do when a market is too thin to stand alone, and the boundary moves whenever the economics of small aircraft improve.

The costs are real and not only yours. Circuity burns fuel, and connections require a bank of arrivals on the ground together, meaning expensive peaks of gates and staff. Because the design depends on aircraft meeting each other on time, delay propagates: a late inbound spoils not one journey but every onward connection it was feeding. Carriers dominating a hub have also historically charged more for journeys starting there, though that premium's size is argued over.

Two refinements.

First, the hub is not chosen to minimise routes. It is chosen to maximise how many markets a fixed fleet can serve at a useful frequency. Route count is a symptom of the real constraint, which is passengers per departure. Nor is the network you experience quite the one your airline operates: alliances and code-shares mean a single-ticket journey may be assembled from several carriers' hubs, so the reason for your detour can lie in a network you never chose.

Second, it is worth distinguishing this from the hubs that turn up in social and technological networks. In a small-world network a few highly connected nodes emerge and shorten everyone's path — the hub is a consequence of how links happened to form, and it makes journeys shorter. Here the hub is deliberately built, and it makes each individual journey longer. The two share a word and little else: one is an emergent shortcut, the other a designed detour whose payment buys frequency. The same distinction separates this from a packet crossing the internet, where routers forward each packet onward and no consolidation into scheduled, capacity-limited vehicles is involved at all.

• Why a fifteen-minute delay at a hub can cost some passengers an entire day.
• How low-cost carriers built profitable networks by refusing to sell connections at all.

Every term the collection defines is gathered in the glossary.