# Determining the Optimal Positions of Infill Balise Groups for ERTMS/ETCS Level 1 Applications
## 3 Results
### Test Case
#### 3.2.2 Results
Notably, the ratios seem to stabilize at the upper end of the speed spectrum. Figure 7 depicts the optimal positions when assuming an initial speed of 160 km/h and using three infill balise groups at 243 m, 705 m, and 1759 m ahead of the EOA. This leads to a weighted additional runtime of 52.0 s compared to an unhindered journey, as depicted in the green trajectory. \begin{table}
\begin{tabular}{c c c c c c} \hline  & & \multicolumn{2}{c}{**Two Infill Balise Groups**} & \multicolumn{2}{c}{**Three Infill Balise Groups**} \\
**Speed [km/h]** & **Indication Point [m]** & **Positions [m]** & **Weighted Additional Runtime [s]** & **Positions [m]** & **Weighted Additional Runtime [s]** \\ \hline
40 & 283 & 146 – 327 & 15.1 & 146 – 216 – 327 & 13.8 \\
50 & 359 & 183 – 415 & 20.2 & 145 – 244 – 415 & 17.9 \\
60 & 441 & 198 – 508 &  
Comparing the results to the scenario with only two infill balise groups at 420 m and 1759 m ahead of the EOA, the weighted additional runtime increases by 4.7 s or 9.0% to 56.7 s, as shown in Figure 8.  
To gain further insights, we evaluated the weighted additional runtime from manually placing the infill balise groups according to five different strategies and comparing the results to the optimal positions. The first two use the fixed locations akin to the positions of the distant signal and the trackside magnets of the German legacy intermittent train  
Figure 8: Plot of the trajectories with two optimally placed infill balise groups for the test train. The direction of travel is from left to right. The colors correspond to receiving infill information at IF_2 (green), IF_1 (yellow), or at the EOA (purple). Figure 7: Plot of the trajectories with three optimally placed infill balise groups for the test train. The direction of travel is from left to right. The colors correspond to receiving infill information at IF_3 (green), IF_2 (yellow), IF_1 (red), or at the EOA (purple). protection system Punktformige Zugbeeinflussung (PZB) 90 for braking distances of 1000 m and 700 m, respectively. The next two strategies divide the distance between the IP and the EOA into equally long segments delimited by the infill balise groups at half or one-third and two-thirds, depending on whether one or two additional infill balise groups are to be positioned. The last one is based on [34] and uses one additional infill balise group at a fixed distance ahead of the EOA. In summary, the five strategies are:  
* two additional infill balise groups at 1000 m and 250 m ahead of the EOA;
* two additional infill balise groups at 700 m and 250 m ahead of the EOA;
* two additional infill balise groups at one-third and two-thirds of the IP;
* one additional infill balise group at one-half of the IP;
* one additional infill balise group at 400 m ahead of the EOA like the setting of [34]. We calculated the weighted additional runtime of these five strategies for both 120 km/h and 160 km/h as the train's initial speed. The other parameters and constraints match the first part of the test case. The results are shown in Table 6 for three infill balise groups and Table 7 for two infill balise groups alongside the delta of the weighted additional runtime compared to the optimal positions with the minimum weighted additional runtime from our algorithm, as presented in Table 5.  
One can clearly see that all five strategies for both initial speeds are close to the optimum in terms of the absolute weighted additional runtime. One case (strategy 4 at 160 km/h) yields a delta of more than 5 s to the weighted additional runtime of the optimal locations. These results support the definition of a good-natured system behavior, as the additional time losses are relatively small compared to other factors influencing the train's driving behavior. However, in heavily utilized sections of a railway network and especially in disturbed conditions, these few seconds or up to 10% reduction in time lost can be important to increase capacity and to restore operational quality more quickly.