airplane networks pt. 1

I have been so unlucky with my flights this year; I haven’t had a trip yet where one of the flights wasn’t either delayed or canceled. The closest I’ve got to a perfect trip was just a few weeks ago where my flight got delayed by 15 mins, but everything else has been by either a couple hours or has been a cancellation. For one of my originally planned trip to Dallas, my flight there got canceled and I never got to catch any other flight to Dallas that weekend because of all the people whose flights got canceled and were then on the stand-by list (there were basically around 100 per flight).

This happens to me now mostly because I’m flying from NYC (as opposed to Pittsburgh where the only time I’ve ever had an issue was once when I was flying to … you guessed it, NYC). Specifically, NYC (and Atlanta for that matter) are such big airports in terms of air traffic and interconnectivity with other airports that a small weather delay on one side of the country has drastic ripple effects in NYC since there are missing planes or crews. Maybe I’ve just been at the brunt of a lot of bad luck and we can’t design these airport systems any better but perhaps there’s an interesting question here about how we can do better. Sure there are some unavoidable situations, such as a city being inherently desirable to travel but there are factors that we can control such as how many resources to dedicate to a specific airport or whether or not to connect two airports by a flight path.

I’ll go more in detail about how we’ll be representing airline traffic networks and the optimization process in a post in the future but to be able to do the optimization we need to make sure we have a well-defined problem. Specifically, we need some framework of characteristics that are good and a way to classify one traffic network as being better than another. This is by no means an exhaustive list but here are some characteristics that I’ve thought of.

• Network A is better than Network B if it costs less.
• Network A is better than Network B if the closing of one or more airports affects fewer flight routes or flight traffic.
• Network A is better than Network B if the average flight path duration is less.

To be able to claim a best network, we have to also come up with some relative weightage for how much we value one of these characteristics over another. I’m not going to make any sort of claim on this here just because that gets into more normative questions about which of the above are more important than the others.

On one hand, the question of optimizing this network is indeed interesting but I’m also curious about what is the worst that we can do. What would the worst case air traffic network look like? In this case to make sure there is a well-defined problem to solve, we have to also craft a unitary definition for the worst network or a class of bad characteristics and find networks that have all of them. We can consider it to just be the opposite of the good characteristics above, but I’m sure there is another classification that might make more sense based on how we mathematically portray these airline traffic networks. At one edge case it could be a network where no node is connected to another but I don’t think that really qualifies as a legitimate air traffic network so we would also have to apply more restrictions such as ensuring that there is at least one path from each node of the network to another. One other design that I initially think of that could be maximally bad is one where there is one mega airport that connects to every other airport and no other airports have any other connections between eachother. This way, a weather event in the central airport would disrupt travel everywhere, but then again I’m not sure if this is the objective worst.

This post is only part one because I did not have the time to fully flesh out the pdf that I wanted to type out. There might be some code in the future there as well although I have no idea how I’m going to have the time generally.