# Evaluating Classical Airplane Boarding Methods for Passenger Health during Normal Times
## 5 Simulation Results
### Numerical Results for Aisle Seat Risk  
The overall risk experienced by the passengers with aisle seats who have already taken their seats while other passengers are still moving down the aisle to their assigned seats is measured through the aisle seat risk indicator. Table 3 presents the average aisle seat risk for each of the boarding methods as a function of the luggage scenario. These results are based on agent-based simulations (rounded to the nearest integer and expressed in seconds). For all the boarding methods, this risk decreases as the quantity of luggage brought in the airplane by the passengers decreases from the high-luggage scenario \(\mathsf{S_{1}}\) to the no-luggage scenario \(\mathsf{S_{7}}\). For each of the seven luggage scenarios, the best and third best-performing methods according to this criterion are the reverse pyramid and WilMA boarding methods, respectively. (We highlight the best value of each luggage scenario in bold font within the table.) These two methods share a common attribute of boarding all aisle seat passengers after all window and middle seat passengers have boarded. This means that their aisle seat passengers have aisle seat only from other aisle seat passengers. Observe that with WilMA, all 60 aisle seat passengers board in one group whereas with reverse pyramid, there are 30 aisle seat passengers in group 3 and the other 30 aisle seat passengers in group 4. With reverse pyramid, the passengers in group 3 have aisle seat risk only from other group 3 passengers, and similarly, its group 4 passengers have aisle seat risk only from other group 4 passengers. The division of aisle seat passengers into two groups essentially halves the number of passengers potentially causing aisle seat risk. For each luggage scenario, the aisle seat risk of reverse pyramid is approximately half that of WilMA. The relationship is not exact because aisle seat risk is a time-based metric and thus influenced by the passengers' boarding dynamics over time and not solely by the number of potential interactions. The implication of boarding dynamics is illustrated by the fact that for each of these two boarding methods, the high-luggage scenario S1 results in about twice as much aisle seat risk as the no-luggage scenario S7. While those two methods have an advantage with aisle seat risk from their aisle seat passengers boarding last, the second-best performing method, back-to-front-by-row, has an \begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline \multirow{2}{*}{**Boarding Method**} & \multicolumn{6}{c}{**Aisle Seat Risk**} \\ \cline{2-7}  & \(\mathsf{S_{1}}\) & \(\mathsf{S_{2}}\) & \(\mathsf{S_{3}}\) & \(\mathsf{S_{4}}\) & \(\mathsf{S_{5}}\) & \(\mathsf{S_{6}}\) & \(\mathsf{S_{7}}\) \\ \hline Open seating method & 15,636 & 14,544 & 13,552 & 12,565 & 11,692 & 10,715 & 9318 \\ \hline Random with assigned seats & 18,323 & 17,413 & 16,357 & 15,358 & 14,518 & 13,473 & 12,252 \\ \hline WilMA & 4312 & 3991 & 3681 & 3385 & 3114 & 2769 & 2126 \\ \hline Back-to-front-by-3-groups & 9068 & 8380 & 7772 & 7208 & 6750 & 6319 & 6019 \\ \hline Back-to-front-by-4-groups & 7675 & 7034 & 6467 & 6031 & 5599 & 5276 & 5046 \\ \hline Back-to-front-by-5-groups & 6748 & 6207 & 5734 & 5289 & 4953 & 4639 & 4446 \\ \hline Back-to-front-by-row & 2786 & 2538 & 2316 & 2135 & 2016 & 1937 & 1885 \\ \hline Reverse pyramid & **2244** & **2021** & **1825** & **1652** & **1481** & **1304** & **1045** \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Aisle seat risk. advantage in that its aisle seat risks result only from passengers assigned seats in the same row. Due to the boarding dynamics, those passengers in the same row may be standing in that row's aisle a long time due to seat interferences. Overall, the back-to-front-by row method provides an increased aisle seat risk compared to reverse pyramid by up to 80.38%. The back-to-front-by-5-groups, back-to-front-by-4-groups, and back-to-front-by-3-groups are the 4 th, 5 th, and 6 th best-performing methods for aisle seat risk, respectively.