2006 Graduate Workshop in Computational Social Science Modeling and Complexity

All Aboard

by Stephen Haptonstahl and Rimma Yusim

Problem:

Consider the following situation:

Around one hundred travelers are waiting in the passenger lounge of the airport. The airline agent at the gate picks up the microphone and begins to board the aircraft. What happens?

· Model, using whatever techniques you wish, the above scenario.

• Explicitly state your model and key assumptions.
• Summarize key results.
• Suggest some potentially interesting future directions and questions for the model

Model:

The objective of our model is to maximize the satisfaction of the passengers as well as minimize the boarding time. We used simulation bottom-up approach to this model. That is there is no social planner optimizing the behavior of passengers. We allow for the composition of passengers’ preferences to change and analyze the effect on the level of satisfaction and boarding time.

Assumptions:

· 100 passengers; full flight; 25 rows, 4 seats each.

· Heterogeneous preferences: each passenger has preferences over the seating –window, aisle, any.

· Satisfaction of 1 is achieved when passenger’s preferences are met, satisfaction of 0 –otherwise.

· No prior assigned seating. The passenger gets a specific seat once he boards the plane.

· The boarding queue number is distributed randomly.

· The time it takes to move one row is measured in one unit of boarding time.

· Finally, we assumed perfect foresight in our model. That is passengers are able to predict what are the seating intentions of those standing in front of them and adjust their own decisions accordingly. This assumption allows us to ignore the two-way traffic in the plane for now. We realize that this is rather restrictive assumption and will try to relax it in the future.

The Dynamics:

The queue before boarding is distributed randomly; there are no assigned seats. Once the passenger starts to board, he has a specific goal in mind –window, aisle or no preference. The satisfaction is reached if the preferences are met. If the seat is unavailable, the passenger gets another random seat. If more than one passenger is interested in one seat, the first one in line wins and the rest settle for any available seat close by.

Theoretical prediction:

We predict the overall satisfaction to increase with the rise in the number of ‘indifferent’ passengers and decrease otherwise. Thus, it is preferable to board the passengers possessing particular preferences first and the ‘indifferent’ ones later. We observe the implication of this principle in the boarding policy of some airline companies. Those passengers who have strong preferences over their seating are encouraged to choose their seats online, while those who agree to seat anywhere are assigned in the last minute.

The results:

1)

We were interested in analyzing the change in overall satisfaction associated with changes in distribution of initial preferences. The simulation yielded the following results after 10 runs: holding the number of “any” preferences constant and equal to 20, the increase in the window preferences leads to decrease in overall satisfaction.

Thus, we observe that the symmetric distribution of preferences: 40-window , 40-aisle and 20-any yields the maximum satisfaction of 100.

2) The second result of the simulation refers to boarding time. The average boarding time decreases with less symmetric distribution of preferences.

This seemingly counterintuitive result can be explained largely by the Perfect Foresight assumption. If the passenger wants a seat (window or aisle) that is in the back but cannot have it because someone ahead has claimed it, they choose another seat at random, and this random seat will tend to be closer. If they want one toward the front, the random seat they choose will be, on average, farther away. However, this latter scenario may be less likely because the person ahead taking the desired seat can have more people behind him when closer to the back of the aircraft than when in the front of the aircraft, and he would only be in the back when heading toward a seat in the back.

Possible extensions and future work:

· Introduce a new type of passengers-pairs. They want to be seated next to each other. Maximum satisfaction is achieved if this requirement is fulfilled; the next best choice is to answer the seating preferences of each individual.

· Refine the satisfaction measure: the satisfaction decreases the further the passenger has to move from the desired seat.

· Introduce the problem of bags allocation on the aircraft.

· Allow for variability in walking speed of the passengers.

· Compare the satisfaction and boarding time with assigned-seating policy.

· Allow for imperfect information and simulate taking into an account the possibility of two-way traffic in the aisle.