## 3 Demand-Related Drivers of Vertiport Operations
### Drivers of Delay  
Instead of using the accumulated daily demand, the peak-hour demand will now serve as indicator. In Figure 6, it can be seen that the overall residual error improved from \(R^{2}=0.51\) to \(R^{2}=0.76\), showing that the peak-hour demand predicts delay better than the accumulated daily demand. Using 4 min as the threshold for the practical hourly capacity, the baseline vertiport layout shows \(PHCAP=264\). While the exponential fit is more accurate, there are still many outliers for peak-hour demands lower than the threshold. In a next step, all scenarios with peaks higher than 264 will be removed in order to investigate the source of the outliers.  
It has been proposed that imbalance between arrivals and departures, filling up or draining the vertiport of vehicles, is the second strongest driver of delay after peak-hour demand. In Figure 7, the average passenger delay is plotted over the maximum imbalance reached during the day for the remaining scenarios. Vehicle stock means the current number of vehicles present in the simulation environment minus the current number passengers present in the simulation environment is larger than the initial number of vehicles (16 for the baseline scenario). Passenger stock means this number is smaller than the initial number of vehicles. How vehicle and passenger stock evolve over the course of a day of operations is shown exemplary in Figure 8. For each scenario the higher value between vehicle stock and passenger stock is selected and visualized in Figure 7 including individual linear regressions and a combined linear regression. With a residual error of \(R^{2}=0.77\), the quality of the regression is similar to the exponential fit for peak-hour demand. The imbalance of arrivals and departures has a lower impact on delay than peak-hour demand, but it is unclear how much lower the impact is. Therefore, a threshold of 2 min is chosen, which is half the threshold of 4 min that was applied earlier to the peak-hour demand. The threshold of 2 min is applied as an analogue to the practical capacity concept. This results in a \"practical imbalance capacity\" (PICAP) of \(PICAP=33\).  
Figure 6: Analyzing the effect of peak-hour demand on the average passenger delay and identification of the practical hourly capacity PHCAP.  
To better decouple the two effects of peak-hour demand and maximum stock, the scenarios are split into four groups corresponding to the two thresholds. In Figure 9, the variation of average passenger delay for the four groups can be seen, including the size \(n\) of each group. As expected, when looking at scenarios which stay below both thresholds, the average passenger delays are low: 36 s median delay and below 3 min maximum delay, to be precise. This not only confirms that peak-hour demand and maximum stock are the two main design drivers, but also that the delay can accurately be predicted by abstracting the demand-profile to these two factors. It is further confirmed that peak-hour demand has the larger impact, as the group above the PHCAP threshold and below the PICAP threshold results in greater delays than the group below the PHCAP threshold and above the PICAP threshold. Furthermore, when excluding the effect of imbalance, the residual error of the exponential fit improves from \(R^{2}=0.76\) to \(R^{2}=0.87\) (see Appendix B). This affirms the accuracy of the PHCAP to predict delay.  
Figure 8: Illustration of vehicle and passenger stock resulting from imbalances in arrivals and departures.  
Figure 7: Analyzing the effect of vehicle/passenger stock on the average passenger delay and identification of the practical imbalance capacity PICAP.