# Determining the Optimal Positions of Infill Balise Groups for ERTMS/ETCS Level 1 Applications
## 2 Materials and Methods
### Algorithm
#### 2.1.2 Track Parameters  
Trackside information needed to perform the optimization includes the line speed and the gradient as fixed parameters of the track alignment. Both parameters are considered to be constant over the whole section of track examined.  
As we consider ETCS level 1 without continuous infill by means of Euroloop or RIU, a RS higher than 0 km/h must be permitted. This enables trains to obtain a new MA or update their existing MA at the EOA after receiving clearance via optical (lineside signal) or digital (using a private or public wireless network directly to the train or to a personal mobile device) means. Typical values for the RS range from 5 km/h to 40 km/h.  
The algorithm needs to have knowledge of some boundary conditions regarding the balise groups used to transmit infill information. First, the number of infill balise groups must be set. Currently, the algorithm is designed to handle two or three infill balise groups besides the necessary main signal balise group at the target (EOA). Fewer balise groups (meaning zero or one) most often do not have practical relevance and no optimization is possible. The installation of four or more infill balise groups yields ever diminishing  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Category** & **Parameter** & **Unit** \\ \hline \multirow{7}{*}{Track} & Line Speed & [km \(\cdot\) h\({}^{-1}\)] \\  & Release Speed & [km \(\cdot\) h\({}^{-1}\)] \\  & Gradient & [9\%] \\  & Balises & [-] \\  & Balise Group Distance & [m] \\  & Balise Positions & [m] \\ \hline \multirow{7}{*}{Train} & Speed & [km \(\cdot\) h\({}^{-1}\)] \\  & Acceleration & [m \(\cdot\) s\({}^{-2}\)] \\  & Deceleration & [m \(\cdot\) s\({}^{-2}\)] \\ \cline{1-1}  & Rotating Masses & [\%] \\ \cline{1-1}  & Indication Point & [m] \\ \cline{1-1}  & Minimum Cruising Time & [s] \\ \cline{1-1}  & Processing Time & [s] \\ \hline \hline \end{tabular}
\end{table}
Table 1: Necessary input parameters for the algorithm to perform the optimization.  
marginal returns. The algorithm presented in this paper could, however, be adapted and applied to those scenarios as well. Balise groups need to be a certain distance apart to allow the train passing over them to read and process all information transmitted before receiving further information. The exact minimum distances vary depending on the speed and the number of single balises inside each of the balise groups and can be obtained from [42] in conjunction with [14]. Typical values for speeds up to 160 km/h range between 3 m and 15 m. A global, constant value can be specified and will limit the freedom on where the flexible balise groups can be placed. The algorithm ensures that this lower boundary is respected for all balise groups. Finally, positions of infill balise groups to be placed at fixed locations are the last input parameter of the category \"track\". At least one balise group--the one farthest away from the target and in rear of the Indication Point of the reference train--must be set. Depending on the total number of infill balise groups (two or three), the remaining balise groups can either be fixed as well with a position in rear of the target or left flexible for the algorithm to optimize their locations.