29 Apr 2016
In Part I of this blog, we showed a simple state-
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 -
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 -
Seating Times 0/1/2: 10, 15, 20 seconds -
DT: 0.1 second -
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 -
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:
The simulated boarding time for this strategy was 1266 seconds, and watching the animated simulation it is easy to see why -
What about boarding from the outside-
In the outside-
Although effective, there are two issues with outside-
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-
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-
If we were to modify the back-
Back to front 6-
Over 10 simulation runs, the 6-
Since the outside-
Outside to inside 6-
Over 10 simulation runs, the the average boarding time was only 480 seconds, handily beating both the back-