## 5 Discussion and Conclusions  
The study we present here focuses on the relationship between the volume of passengers and the frequency of different delay sizes. Several previous studies have highlighted that as passenger volumes increase, the passenger exchange time increases as well. Most of those studies indicated a linear relationship where an additional passenger leads to an additional unit of time needed to complete the passenger exchange. However, using multiple years of automatic passenger count data, our analysis shows that although the frequency of dwell time delays increases as passenger volumes increase, the size does not necessarily increase along with it. We also find differences in this trend for the frequencies of delays that are dependent on the scheduled dwell time. Chi-squared goodness of fit tests revealed statistically significant differences in the frequency distribution of dwell time delay sizes under different volumes of passengers and the unconditional frequency for dwell time delays for both types of stations. Visually analysing the frequencies shows that if passenger volumes are not accounted for, dwell time delays will be routinely underestimated in most cases when passengers are present. Post hoc pairwise comparisons show that the difference between the unconditional and conditional frequencies is statistically significant across the board when dwell times are set at 42 s. Looking at the effect sizes, we find that statistically significant effects exist when passenger volumes start to exceed 10 boarding and alighting passengers. Although pairwise comparisons show statistically significant differences in the tail of the frequency distribution, these effect sizes are found to be negligible. These larger delays are influenced less by the volume of boarding and alighting passengers. When stations have longer scheduled dwell times of 120 s, pairwise comparisons show that significant differences occur only for delays of less than 15 s. The visual graphical analysis shows that when the volume of boarding passengers is low, less than 10 in our case, there are fewer delayed stops. Once passenger volumes start to increase, the frequency of delays starts to increase. Figure 5: [PERSON]’s W effect sizes for Chi-square goodness of fit test results for stations with a scheduled dwell time of 42 s (**a**) and 120 s (**b**). The visual analysis also revealed that the frequency distributions start to converge once delays exceed 15 s, which is in line with the results from the pairwise comparisons. Several things can be mentioned in terms of what this means for dwell times. First, the initial increase in passengers leads to an increase in the frequency of small delays in both types of stations considered. It is, however, not until passenger volumes increase further that the size of the dwell time delays increases as well. Based on our data, this threshold seems to be around 20 boarding and alighting passengers. This value is, however, case specific. For stations that have longer scheduled dwell times, this being 120 s in our case, we only find an increase in the frequency (not size) of smaller delays. Small extensions to dwell time can thus go a long way in terms of reducing the frequencies of delays. Even at stations with longer scheduled dwell times, delays of 15 s or less are still common, and the frequency of such delays increases with larger passenger volumes. Extending dwell times alone seems insufficient for reducing dwell time delays, as these smaller delays still occur. This leads us to the second observation: speeding up the boarding and alighting process, such as through measures on platforms, can be beneficial for overall punctuality. Although one cannot expect measures aimed at speeding up this process to yield large improvements in boarding and alighting times, our findings here suggest that even small improvements can go a long way. The findings presented here point in several directions in terms of future studies.