Simulation - Airplane Boarding, Part II - EdsCave

29 Apr 2016

In Part I of this blog, we showed a simple state-machine-based model to simulate the aircraft boarding process.  The value of such a model, simplified as it is, is that it allows us to quantitatively compare different boarding strategies.

In our model, the two main behaviors that influence boarding time are blocking and seat interference.  Blocking is the condition when a passenger is stopped in the aisle, either because someone is in front of him, or becuase he is preparing to seat himself. Our model assumes that in both of these cases, he will prevent someone immediately behind him from progressing as well, and that lines of people can end up waiting behind a single stopped passeneger.  While in a real airplane it is often possible to squeeze past someone, in many cases it isn't - so assuming this feature in a model is not unjustified.

Seat interference is when a passenger needs to get into a middle or window seat, and needs extra time, either because they need to crawl over someone, or more typically becuase the people who are already seated need to get up to let them in, and reseat themselves. Again, this a readily observable behavior in a real airplane.  Our model simplifies this as a seating time penalty based on the number of occupied seats that must be traversed by a passenger.

All of the simulations run in this blog will assume a common set of parameter values. Keeping these values constant from run to run allows the direct comparison between different boarding strategies.

• Advance Rate: 1 second - passengers advance at one second per aisle cell. In an unimpeded aisle it will take 1 minute for a passenger to make it to the rear of the cabin
  

• Seating Times 0/1/2:  10, 15, 20 seconds - The time required to seat depending on whether there are 0,1, or 2 passengers already seated bateween the aisle and the target seat.
  

• DT: 0.1 second - The simulation timestep.
  

Please note that neither the model or the parameters used have been validated or measured against actual aircraft boarding behavior.  Model calibration would make a huge difference in both the absolute and relative model performance. even without such calibration and validation, the model can still be useful for conducting rough better/worse comparisons of stragies, and also to achive some insight as to how different strategies perform, or fail to do so. Also, as interesting as obtaining 'ground truth' data might be, getting caught making these kinds of 'measurements' while a passenger might very well get you 'diverted' to Guantanamo Bay with no return ticket.  That being said, let's proceed to some boarding strategies.

Strategy #1 - Back-to-Front Boarding

In this strategy, passengers with seats in the rear are boarded first. for each row, the window seats are boarded first, and the aisle seats boarded last. The boarding order can be seen below:

Back-to-front boarding order (Cabin front on left, rear on right)

The simulated boarding time for this strategy was 1266 seconds, and watching the animated simulation it is easy to see why - only one or two people can seat themselves at any given instant, with everyone else queued up behind them - a major blocking problem.  Contrary to what one may think at first glance, back-to-front boarding is not a particularly time-efficient strategy.

What about boarding from the outside-in, first boarding the window seats, then the middle seats, then finally the aisle seats ? If you line up the passengers within each of these waves so that the ones seated at the rear enter first, this is much more efficient than back-to-front, only requiring 234 simulated seconds - about five times faster.

Outside-In boarding order

In the outside-In scheme,  first, everyone getting a window seat marches down the aisle.  When the head of this cohort makes it to the end, the tail has just made it to row #1, at which point everyone can seat themselves nearly simultaneously.  and this process repeats for the cohorts located in middle and aisle seats.  This scheme works so well because it nearly elimiates both aisle blocking, and allows the maxium number of people to seat at the same time.

Although effective, there are two issues with outside-in boarding. First is the model assumption that the aisle holds enough people to fill the seats on both sides. If this is not the case, then the strategy will become less effective. The second issue is that this strategy as presented (as well as the back-to-front strategy) requires people to enter the plane in an exact order, and to behave in a coordinated manner.  As anyone who has ever been on an aiplane knows, passenger boarding behavior more closely resembles that of a European soccer mob than that of the Fred Hill Briefcase Drill Team.  

One strategy that doesn't require much coordination is that of random boarding order. Just have passengers line up at the cabing  door in an order completely independent of seat assignment and get on the plane, something that used to be done by Southwest.  How effective is this?  The average simulation time (over 10 runs)  needed to board the plane using a random strategy was 645 seconds,   which is not as good as the out-side in method, but considerably better than back-to-front.  While it may seem counterintuitive why random boarding should be even moderately effect, consider that it scatters people over the plane, reducing blocking and allowing mutiple passengers to seat at the same time.

While the simulation model itself is deterministic, meaning that a given boarding order results in the same seating time, a stochastic boarding stratagy where the passenger boarding order can vary  (such as random boarding) will result in different boarding times from run to run. For this reason one needs to consider the average of several simulation runs to be able to characterize a particular stochastic strategy.

Over the last few years, airlines seem to have taken an approach where they assign people to multiple boarding zones, then call up all the people within a given zone to get on the plane in whatever order they can elbow their way into at the gate. I suspect that one reason for taking this approach has nothing to do with optimizing boarding order, but is intended rather to keep all 150-200 passengers from converging on the gate simultaneously as an unruly mob.

If we were to modify the back-to-front strategy to use boarding zones, how does it then fare?  Let's assume 6 zones of equal size, spread along the length of the plane, as shown below. The boarding order within each zone is assumed to be random.

Back to front 6-Zone Boarding

Over 10 simulation runs, the 6-zone back-to-front requires an average of 810 seconds, which was a significant improvement over the determinstic back-to-front scheme, but surprisingly, was not as good as the basic random boarding scheme.  Can we do better than random boarding?

Since the outside-to-inside boarding scheme seemed to work well, a zoned variant of this is a likely candidate to try. In this scheme, zones are set up as shown below.

Outside to inside 6-zone boarding

Over 10 simulation runs, the the average boarding time was only 480 seconds, handily beating both the back-to-front and random boarding strategies.  Is this as good as it gets, or can we do even better?  In the final installment of this blog we will examine a technique for developing effective zoning strategies.