# Additional Taxi-Out Time Prediction for Flights at Busy Airports by Fusing Flow Control Information
## 3 Prediction of Additional Taxi-Out Time
### Calculation of UTT
#### 3.2.1 Selection of Arrival and Departure Flow Indicators  
Pudong International Airport is a busy airport with complex aircraft movements during peak times. It is necessary to select appropriate arrival and departure indicators for fitting the taxi time. For a departing flight \(i\), the other arriving and departing flights that have a temporal interaction with it can be classified into eight types. This forms a set of eight candidate arrival and departure indicators, as shown in Figure 3, for departure flow selection and arrival flow selection, as detailed in Table 2.  
Taking ODP SG15-35R as an example, we can apply the Pearson correlation coefficient method to create a correlation heatmap between different arrival and departure flow indicators and taxi-out time, as shown in Figures 4 and 5. The redder the color, the higher the correlation between the indicators and taxi time.  
From Figures 4 and 5, it can be seen that D2 has the highest correlation of 0.81 with departure taxi-out time and A2 has the highest correlation of 0.74 with arrival taxi-out time. In contrast, D3 and A3 have the weakest correlation with the departure and arrival taxi-out time. The figures also show the correlations between different indicators. As the number of indicators increase, the correlations with other indicators are also strengthened. For example, the indicator group D1+D2+D3+D4 has a correlation of over 0.6 with 13 other indicators. In the FAA method, departure flow and arrival flow are defined as D1+D3 and A1+A3, respectively. Figures 4 and 5 reveal that both D1+D3 and A1+A3 show low correlations with taxi-out time, at 0.17 and 0.05, respectively. Therefore, we select the indicators D2 and A2 with the highest correlations as the departure flow and arrival flow indicators for linear regression.  
\begin{table}
\begin{tabular}{c c c} \hline
**Indicator Type** & **Indicator** & **Definition** \\ \hline \multirow{4}{*}{Departure} & \multirow{2}{*}{D1} & For a departing flight \(i\), the number of other departure flights \(j\) that satisfy \(AOBT(j)<AOBT(i)\) \\  & & \(AOBT(i)<ATOT(j)<ATOT(i)\) \\ \cline{2-3}  & \multirow{2}{*}{D2} & For a departing flight \(i\), the number of other departure flights \(j\) that satisfy \(AOBT(j)>AOBT(i)\) \\  & & \(AOT(j)>ATOT(i)\) \\ \cline{2-3}  & \multirow{2}{*}{D4} & For a departing flight \(i\), the number of other departure flights \(j\) that satisfy \(AOT(j)<AOBT(i)\) \\  & & \(AOBT(i)<AOBT(j)<ATOT(i)\) \\ \hline \multirow{4}{*}{Arrival} & \multirow{2}{*}{A1} & For a departing flight \(i\), the number of other arrival flights \(j\) that satisfy \(ALDT(j)<AOBT(i)\) \& \\  & & \(AOBT(i)<AIBT(j)<ATOT(i)\) \\ \cline{2-3}  & \multirow{2}{*}{A2} & For a departing flight \(i\), the number of other arrival flights \(j\) that satisfy \(ALDT(j)>AOBT(i)\) \& \\  & & \(AOBT(i)<AIDT(j)<ATOT(i)\) \\ \hline \multirow{4}{*}{Arrival} & \multirow{2}{*}{A3} & For a departing flight \(i\), the number of other arrival flights \(j\) that satisfy \(ALDT(j)<AOBT(i)\) \& \\  & & \(AOBT(i)<AIDT(j)<ATOT(i)\) \\ \hline \end{tabular}
\end{table}
Table 2: Candidate set of arrival and departure flow indicators.