study cited: An Investigation into the Determinants of Flight Cancellations

Having just spent the day trying to fly from Boston to Ithaca via LaGuardia and encountering one flight cancellation and two hours of flight delays leading to a missed connection that set me back another two and a half hours, this seemed like an appropriate topic to write about.

When you look at it in a vacuum, each time a flight is canceled, the airline provides some legitimate and seemingly unavoidable reason for why the cancellation was necessary and the passengers just assume they have bad luck. In the real world, however, every frequent flier knows that certain airports have a much worse on-time rating than others and others have high numbers of cancellations. Of course weather often plays a role in these numbers, but the study I looked at took weather out of the equation. The on-time rating of an airport is often affected, like LaGuardia’s today, simply by the airport having too many incoming and outgoing flights (read: network connections) scheduled for the runways to be able to handle. The network effects of flight delays as they cascade across an airline’s network of flights is a very interesting topic and raises questions of dominant strategies for, among others,  how best to dustribute the aircraft. For example, is it better to have one aircraft go back and forth along the same route all the time, or should one plane go globe or continent hopping along a more sophisticated network path? I will not address the questions related to flight delays here, but rather, focus specifically on flight cancellations.

Once weather factors are excluded, conventional wisdom does not dictate which airports are more likely than others to cancel a flight. The statistics that the FAA publishes, however, reveal a different story. As it turns out, flights that go to and from major hubs are canceled approximately 25% less often than other flights. The more major the hub, the less its flights are canceled. Another factor is the number of airlines that fly any given route. Routes where one airline has a monopoly, like US Airways essentially has on the Ithaca-LaGuardia and Ithaca-Philadelphia routes, have a much higher cancelation rate than those with significant competition. The study cites other factors, but these are the two I would like to focus on. Clearly, though, when an airline decides to cancel your flight, the decision is not quite as innevidable and benign as initially thought.

How do these results relate to network theory? The hub factor is obvious. The airlines have an interest in maintaining their network. The flights into the major hubs supply both the passengers and the aircraft needed to keep an extremely valuable node in their network operating at its peak efficiency. Passengers flying ot hubs are often connecting to other flights and the aircraft itself can be slated to fly to a large number of other airports. Canceling one of these flights will cause much more widespread effects throughou tthe network than, say, a flight to Ithaca, where there are only a few places for the plane to go and almost nobody flies there for a connection. This can be expressed in graph form by assigning a weight to each edge that is derived from some formula that takes into account the number of other routes that would be affected by canceling this route, the number of connections that would need to be rebooked, the number of hotel rooms that would need to be paid for, and all the other costs that canceling this flight would add that would not be present if the flight took off. In explaining why flights out of hubs tend to have fewer cancelations, the paper suggests that it is not a matter of an airline’s self-interest, but simply a practical consequence of being a hub, which is that their are more equipment, staff, and repair facilities available than at other airports, which usually leaves the airline with little excuse to cancel a flight rather than delay it.

The monopoly factor can also be expressed in network terms. On a very basic level, an airline knows that a passenger who is flying between two cities now is likely to fly that same route again some time in the future. They need to make sure that that passenger flies on their airline next time too. When their is no competition, the airline needs to do nothing above the bare minimum, which here means getting the passenger to his destination eventually, in order to bring that customer back. Once there is competition however, the airline needs to do better than the competitors and a low cancelation rate is an integral part of that competition. This can be viewed as a graph with each edge given the value of the number of airlines who fly that route. Considering this factor alone, the airline has a much higher incentive to make sure a high valued route takes off than an Ithaca route.

By combining the hub and monopoly factors into a graph of an airlines routes with weights on each edge, it is easy to see why the airline works much harder to get some routes off the ground than others. If we could get ahold of that graph when booking flights, it might change the way we decide which route to take. For example, I might choose to pay a little more to stop only in airports that are hubs for multiple airlines.  Unfortunately, at this point there are so many contributing factors and such complex flight networks that most likely this graph only exists in some computer and it is probably being constantly recalculated. And then we have to factor weather back in.