# Evaluating Classical Airplane Boarding Methods for Passenger Health during Normal Times
## 5 Simulation Results
### Discussion  
The relative performance of the boarding methods obtained for the considered health risk metrics differs depending on the metric. None of the methods is best for all of the health indicators. Before discussing the health performance, we show the total boarding times (average time to complete boarding of the airplane) for the methods and luggage scenarios in Table 10.  
Reverse pyramid provides the fastest boarding time, followed by WilMA. The open seating method, random with assigned seats, and all three of the back-to-front-by-group methods provide similar boarding times with their results ranging between 454 and 885 s, depending on the quantity of hand luggage. The longest boarding process results from back-to-front-by-row, which provides a boarding time up to 148.58% higher than reverse pyramid. Table 11 provides an ordinal ranking of the considered boarding methods for all the metrics based on the results obtained in the S\({}_{1}\) luggage scenario. Based on the ranking in Table 11, the reverse pyramid method performs best in five of the eight metrics, namely: aisle seat risk, type-1 seat interferences, type-2-3-4 seat interferences, individual boarding time, and time to complete the boarding process for all passengers. Furthermore, reverse pyramid performs nearly as well for aisle standing risk as that metric's best method, WilMA. Moreover, we note that the two metrics for which reverse pyramid performs poorly, namely middle seat risk and window seat risk, may not be as important for health as aisle seat risk and the seat interferences given that the middle seat risk and window seat risk refer to risks of the passengers being further from other passengers than with the other health risks. As such, the reverse pyramid method should be seriously considered by airlines who prefer short times to complete the boarding of their airplanes while reducing health risks to their passengers. Meanwhile, WilMA also performs well. It performs best for four of the metrics, namely, aisle standing risk, type-1 seat interferences, type-2-3-4 seat interferences, and individual boarding time. It performs second best for boarding time and third best for aisle seat risk. Its performance for middle seat risk and window seat risk is worse than reverse pyramid. Overall, WilMA performs well but not as well as reverse pyramid. WilMA may be the second-best method for most airlines. \begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline \multirow{2}{*}{**Boarding Method**} & \multicolumn{8}{c}{**Boarding Time**} \\ \cline{2-7}  & \(\mathbf{S_{1}}\) & \(\mathbf{S_{2}}\) & \(\mathbf{S_{3}}\) & \(\mathbf{S_{4}}\) & \(\mathbf{S_{5}}\) & \(\mathbf{S_{6}}\) & \(\mathbf{S_{7}}\) \\ \hline Open seating method & 802 & 747 & 694 & 643 & 598 & 548 & 454 \\ \hline Random with assigned seats & 864 & 813 & 764 & 716 & 675 & 629 & 547 \\ \hline WilMA & 605 & 559 & 514 & 473 & 437 & 391 & 279 \\ \hline Back-to-front-by-3-groups & 842 & 782 & 729 & 679 & 638 & 594 & 516 \\ \hline Back-to-front-by-4-groups & 862 & 801 & 740 & 688 & 645 & 599 & 524 \\ \hline Back-to-front-by-5-groups & 885 & 820 & 757 & 704 & 657 & 608 & 532 \\ \hline Back-to-front-by-row & 1227 & 1095 & 976 & 869 & 794 & 714 & 614 \\ \hline Reverse pyramid & **530** & **491** & **454** & **420** & **390** & **353** & **247** \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Boarding time. Moderate results stem from the back-to-front-by-group methods. The back-to-front-by-5-groups airplane boarding method provides slightly better results than back-to-front-by-4-groups and back-to-front-by-3-groups for three risk indicators: aisle seat risk, middle seat risk, and window seat risk; meanwhile, they achieve the same results for type-1 seat interferences and type-2-3-4 seat interferences and worse results for the aisle standing risk, individual boarding time, and time to complete boarding of the airplane.