# Evaluating Classical Airplane Boarding Methods for Passenger Health during Normal Times
## 5 Simulation Results
### Numerical Results for Individual Boarding Time  
The best (and equally good) individual boarding times result from WilMA and reverse pyramid in each of the considered luggage scenarios--Table 9. The increasement in the quantity and type of hand luggage brings an increasement of this risk of at most 94.59% (S\({}_{7}\) vs. S\({}_{1}\)). The low values of the individual boarding times for these methods is related to the absence of seat interferences.  
The remaining boarding methods, from best to worst, are the following in sequence: open seating, random with assigned seats, back-to-front-by-row, back-to-front-by-5-groups,  
\begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline \multirow{2}{*}{**Boarding Method**} & \multicolumn{8}{c}{**Aisle Standing Risk**} \\ \cline{2-7}  & **S\({}_{1}\)** & **S\({}_{2}\)** & **S\({}_{3}\)** & **S\({}_{4}\)** & **S\({}_{5}\)** & **S\({}_{6}\)** & **S\({}_{7}\)** \\ \hline Open seating method & 6913 & 6523 & 6131 & 5768 & 5443 & 5063 & 4258 \\ \hline Random with assigned seats & 7764 & 7368 & 6970 & 6585 & 6258 & 5879 & 5266 \\ \hline WilMA & **5501** & **5202** & **4908** & **4670** & **4488** & **4207** & **2859** \\ \hline Back-to-front-by-3-groups & 12,493 & 11,604 & 10,839 & 10,039 & 9388 & 8668 & 7756 \\ \hline Back-to-front-by-4-groups & 13,496 & 12,534 & 11,539 & 10,717 & 9966 & 9222 & 8228 \\ \hline Back-to-front-by-5-groups & 14,283 & 13,195 & 12,168 & 11,269 & 10,452 & 9632 & 8629 \\ \hline Back-to-front-by-row & 21,834 & 19,426 & 17,312 & 15,370 & 13,940 & 12,452 & 11,007 \\ \hline Reverse pyramid & 5798 & 5485 & 5189 & 4916 & 4720 & 4390 & 3034 \\ \hline \hline \end{tabular}
\end{table}
Table 8: Aisle standing risk.  
\begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline \multirow{2}{*}{**Boarding Method**} & \multicolumn{8}{c}{**Individual Boarding Time**} \\ \cline{2-7}  & **S\({}_{1}\)** & **S\({}_{2}\)** & **S\({}_{3}\)** & **S\({}_{4}\)** & **S\({}_{5}\)** & **S\({}_{6}\)** & **S\({}_{7}\)** \\ \hline Open seating method & 87 & 82 & 77 & 72 & 67 & 61 & 51 \\ \hline Random with assigned seats & 97 & 92 & 86 & 81 & 77 & 71 & 62 \\ \hline WilMA & **72** & **67** & **63** & **59** & **55** & **50** & **37** \\ \hline Back-to-front-by-3-groups & 131 & 121 & 113 & 105 & 98 & 91 & 80 \\ \hline Back-to-front-by-4-groups & 139 & 129 & 119 & 110 & 103 & 95 & 83 \\ \hline Back-to-front-by-5-groups & 145 & 134 & 124 & 115 & 106 & 98 & 87 \\ \hline Back-to-front-by-row & 212 & 189 & 168 & 150 & 136 & 122 & 106 \\ \hline Reverse pyramid & **72** & **67** & **63** & **59** & **55** & **50** & **37** \\ \hline \hline \end{tabular}
\end{table}
Table 9: Individual boarding time.  
back-to-front-by-4-groups, and back-to-front-by-3-groups, and back-to-front-by-row. This sequence of relative performance is identical to the sequence for aisle standing risk. Consequently, individual boarding time may be used as a proxy for aisle standing risk when comparing boarding methods. We mention this because individual boarding time would be easier to calculate than aisle standing risk and has an added advantage in that it bears a relationship with customer satisfaction due to passengers preferring shorter individual boarding times.