## 3 Results
### Case Study in Slovakia
#### 3.1.8 Calculation of the Practical Throughput by the ZSR Methodology  
Using the ZSR calculation method with given input data, we obtained the values presented in Figure 10.  
Figure 10 provides useful results, as explained below. According to the ZSR methodology, we obtained the total occupancy time of Tobs as the sum of multiples of the product of the number of trains in the corresponding sequence and the resulting headway time of the particular train sequence (from Figure 8). Whereas there is a double track section, the method used above calculates in either an even-even or odd-odd direction. The even direction (Sladkovicovo-Senec) was chosen as the representative direction. The calculated practical throughput indicators are given in Table 3[36].  
Figure 8: Resulting headway times (in minutes) for Sládkovicovo railway station—direction from Senec station, ETCS L3.  
Figure 9: Resulting headway times (in minutes) for Senec railway station—direction from Sládkovicovo station, ETCS L3.  
As shown in Table 3, the condition of a minimum buffer time given by regulation D 24 is met:  
\[t_{mcdz}^{sk}\geq\ t_{mcdz}^{po} \tag{5}\]  
This condition guarantees that the train schedule in which we consider the expected amount of regular transport of 98 trains per day is feasible. Finally, it is necessary to calculate the practical throughput and two qualitative indicators of the train schedule. Calculation of the practical throughput [35]:  
\[n=\frac{T-(T_{vl}+T_{stl})}{t_{obs}+t_{mcdz}^{po}}=\frac{1440-(60+0)}{2.35+1.75 }=336\ \text{train.day}^{-1} \tag{6}\]  
Figure 10: Resulting table with occupancy times of individual train sequences, ETCS L3 is shown for the even direction (ZSR methodology).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Indicator** & \multicolumn{3}{c}{**Final Value**} \\ \hline Occupancy time (average time) of the specific facility or & \(\mathbf{t_{obs}}\) & 2.35 & min \\ element by one train & \(\mathbf{T_{medz}}\) & 1149.42 & min \\ Occupation per one train path/consumption time & \(\mathbf{T_{obs}}\) & 230.58 & min \\ Average buffer time per one train & \(\mathbf{t_{medz}^{sk}}\) & 11.73 & min \\ Required buffer time per one train & \(\mathbf{t_{medz}^{po}}\) & 1.75 & min \\ Total time for maintenance/supplement for maintenance & \(\mathbf{T_{vyl}}\) & 60 & min \\ Total time of permanent handling operation & \(\mathbf{T_{stl}}\) & 0 & min \\ Number of trains & \(\mathbf{N}\) & 98 & train.day\({}^{-1}\) \\ Practical throughput permeability (capacity) & \(\mathbf{n}\) & 336 & train.day\({}^{-1}\) \\ Infrastructure occupation rate & \(\mathbf{S_{o}}\) & 0.17 & [-] \\ Practical throughput efficiency utilization index & \(\mathbf{K_{P}}\) & 29.17 & \% \\ \hline \hline \end{tabular}
\end{table}
Table 3: Identified indicators of the practical throughput in the analyzed section, ETCS L3 for even direction.  
Infrastructure occupation rate per one train path [37]:  
\[S_{O}=\frac{T_{obs}}{T-(T_{vt}+T_{stl})}=\frac{230.58}{1440-(60+0)}=0.17 \tag{7}\]  
Calculation of practical throughput utilization index [37]:  
\[K_{P}=\frac{N}{n}*100\%=\frac{98}{336}*100\%=29.17\% \tag{8}\]  
These calculations show that the practical throughput on a given railway section is 336 trains per day in the odd direction, which is more than the daily scheduled range of 98 trains on a given railway section. The required buffer time is lower than the calculated buffer time, so an additional train path insertion is possible. The use of the train schedule is 29.17%, so it still provides enough space for the traffic expansion on the given track section. The complex results for the even direction are the same as for the odd direction.