# Determining the Optimal Positions of Infill Balise Groups for ERTMS/ETCS Level 1 Applications
## 3 Results
### Test Case
#### 3.2.2 Results  
As a first test, we evaluated the effects of different initial speeds and the number of infill balise groups on the optimal positions as well as the weighted additional runtime. We chose initial speeds from 40 km/h to 160 km/h in increments of 10 km/h--as typically, permitted speeds are engineered with that increment, although ETCS now allows for increments of as low as 5 km/h--and two or three infill balise groups. The farthest infill balise group was positioned by taking the calculated IP and adding the distance travelled in 4 s at maximum line speed, leading to its position shown in Table 5. In the same table, the compressed results from the 26 calculated scenarios are also presented. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Speed [km/h]** & **Acceleration [m/s\({}^{2}\)]** & **Deceleration [m/s\({}^{2}\)]** \\ \hline \([0;10]\) & 0.926 & \(-0.072\) \\ \((10;20)\) & 0.926 & \(-0.194\) \\ \((20;30)\) & 0.926 & \(-0.295\) \\ \((30;40)\) & 0.926 & \(-0.379\) \\ \((40;50)\) & 0.926 & \(-0.450\) \\ \((50;60)\) & 0.926 & \(-0.512\) \\ \((60;70)\) & 0.926 & \(-0.565\) \\ \((70;80)\) & 0.926 & \(-0.612\) \\ \((80;90)\) & 0.694 & \(-0.653\) \\ \((90;100)\) & 0.556 & \(-0.690\) \\ \((100;110)\) & 0.556 & \(-0.723\) \\ \((110;120)\) & 0.463 & \(-0.753\) \\ \((120;130)\) & 0.463 & \(-0.780\) \\ \((130;140)\) & 0.347 & \(-0.804\) \\ \((140;150)\) & 0.347 & \(-0.826\) \\ \((150;160)\) & 0.309 & \(-0.833\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Step functions approximating the deceleration and acceleration of the train used for testing. Figure 6: Example of the ETCS braking curves for the train modelled with an initial speed of 160 km/h. Screenshot from [44]. The direction of travel is from left to right. The first result that meets the eye are the differences in the additional runtime between the scenarios with two infill balise groups versus three of them. In this setting, the absolute delta is calculated to be between 1.3 s at 40 km/h and 6.3 s at 150 km/h. The relative delta lies between 8.2% and 12.1% in favor of three infill balise groups. It does not surprise us that more infill balise groups lead to lower additional runtimes, as an additional location is introduced where infill information can be transmitted to the train, but the benefit most likely does not outweigh the costs when dealing with only one train type. If the train characteristics become more diverse, the additional infill balise group will be able to significantly improve the overall system performance. For example, two infill balise groups might be placed to optimally serve two different train types with largely different braking capabilities and a third one providing infill near the EOA. Still comparing two infill balise groups to three of them, the optimized location of the infill balise group closest to the EOA in the two-infill-balise-group scenario always lies between the two optimized locations of the two infill balise groups closest to the EOA in the three-infill-balise-group scenario. One can see that the IP increases proportionally more than the optimal positions of the infill balise groups when increasing the initial speed. It seems that positions of infill balise groups closer to the EOA are more favorable than ones farther out. Calculating the ratio between the infill balise groups and the IP at their respective speeds leads to a ratio between 0.52 and 0.27 for the scenario of two infill balise groups, the former for slow speeds, the latter for high speeds. When considering three infill balise groups, the two ratios come out at 0.76 to 0.45 and 0.52 to 0.15, respectively. This can be explained by the relatively small additional runtime at the beginning of the braking, i.e., close after passing the IP. The more the train must slow down, the longer it takes to accelerate to the initial speed and the greater the additional runtime becomes. Therefore, the minimal additional runtime can be found when placing the infill balise groups in the space laid out by the ratios calculated above.