## 4 Model Considerations
### Study Area Determination  
As highlighted before, one of the practical limitations of applying most of the currently available activity-based models is their computation time, especially when detailed geographical unit level is taken into account. In general, the more detailed the geographical unit level considered, the longer computation time is needed. Specifically, to apply the FEATHERS framework based on the BB zoning system, more than two days are needed to complete the model execution if 50% of the full population of Flanders is under consideration, which is three times more than the situation of using the Subzone zoning system.  
To reduce the computation time of FEATHERS, several tradeoffs can be made in actual applications, one of which is to restrain the size of the study area and conduct the computation only for the selected region [16]. In this study, given the fact that the city of Leuven is the target territory, it is possible to apply FEATHERS to a relatively small study area surrounding this target territory rather than to take the whole of Flanders into account. In this way, the computation time of the model is reduced. The question then becomes: what should the minimum size of the study area surrounding the target territory be, and how do we determine it?  
In this study, by defining the accuracy level of the model, we propose an iteration approach to determine the minimum size of study area required for the city of Leuven when performing travel demand forecasting. Different transport modes are taken into account. More specifically, for the target territory of Leuven, one more zone with the shortest centroid distance to this target territory is added, constituting a new study area (\(SA\)). Then, the travel demand (e.g., number of trips) of both departing mode and arriving mode with respect to this new study area to and from Leuven is computed. The difference (\(D\)) between the occurrence of both the departing trips (\(DT\)s) and the arriving trips (\(AT\)s) derived based on this study area and that based on the whole of Flanders can be calculated by Equation (1), which can be further used to estimate the accuracy rate (\(A\)) of this study area using Equation (2):  
\[D=\frac{\sqrt{\left(\text{\# $DT$s in $SA-\text{\# $DT$s in $Flanders$}}\right)^{2}+\left(\text{\# $AT$s in $SA-\text{\# $AT$s in $Flanders$}}\right)^{2}}}{\sqrt{\left(\text{\# $DT$s in $Flanders$}\right)^{2}+\left(\text{\# $AT$s in $Flanders$}\right)^{2}}} \tag{1}\]  
\[A=\left(1-D\right)\times 100\%. \tag{2}\]Such a procedure is repeated, i.e., more zones are added, from close to distant, until the predefined accuracy requirement is reached. The obtained study area is thus the minimum size needed for the travel demand prediction of the target municipality.  
Now, by defining an accuracy level of 90%, the study area for the public transport of Leuven is identified. In fact, it is the largest study area among the different transport modes. In total, 135 municipalities (or Superzones) are included, as illustrated in Figure 4. It should be mentioned here that this restrained study area covers the whole light rail network proposed in Section 3.  
By applying FEATHERS on such a study area, it turns out that the computation time can be reduced considerably. For a single model run, fewer than 29 h are needed (using 50% of the full population), which is only 45% of the computation time if the whole of Flanders is under consideration (see Table 1).  
It should be noted that to determine the required study area for the city of Leuven, we have to first run FEATHERS for the whole of Flanders in order to apply Equations (1) and (2). However, the total computation time will be reduced when multiple model runs are needed (see Section 4.3).