# Determining the Optimal Positions of Infill Balise Groups for ERTMS/ETCS Level 1 Applications
## 2 Materials and Methods
### Algorithm
This is carried out by finding the position or positions of infill balise groups where the weighted additional runtime of a specified scenario is minimal, and therefore, the lowest operational impact of the track section ahead not being free on time is to be expected. The additional runtime is calculated for each possible trajectory corresponding to a position or a combination of positions of infill balise groups. The trajectories are constructed from the ETCS braking curves--in general, the Indication Curve--as the deceleration curve and the acceleration a specific train can archive. How the ETCS braking curves can be optimized for best usage has been worked on by [PERSON] [41], for example. This is outside this paper's scope. The individual train trajectories modelled can be segmented into the running regimes cruising, deceleration, and acceleration. Trains are not able to transition from deceleration to acceleration and vice versa in an instant. This is due to the nature of the braking systems and the time needed to build up or release the braking force. Train length, brake position, and the type of the braking system are the most important factors influencing the build-up and release times. The same is true for the traction effort; however, modern electric locomotives have significantly better longitudinal agility and dynamics than their predecessors or types with an internal combustion engine. Both effects combined accumulate to roughly less than 10 s for a typical passenger train. This minimum time during the transition between these two regimes is modelled as cruising. To be physically correct, it should be classified as coasting, as neither braking nor traction effort is applied and the forces in play all reduce the train's speed. For practical reasons, this simplification has been made. The ratio of mass to resistance is large enough that for the short time spans in question here, cruising instead of coasting can be used. The typical trajectory of a train needing to apply its brakes and receiving infill consists of the following phases:  
* approaching the IP at the maximum allowed speed (cruising);
* slowing down according to the braking curve starting at the IP until passing an infill balise group providing a new MA (deceleration);
* processing the information (deceleration or cruising);
* transitioning from deceleration to acceleration (cruising);
* accelerating to the maximum allowed speed (acceleration);
* clearing the investigation area at the maximum allowed speed (cruising). Figure 2: Schematic of the infrastructure modelled. Whether processing the information takes place while decelerating or cruising is determined by the train's speed. When the train has already reached the Release Speed (RS) before passing the infill balise group or reaches the RS while processing, it does not slow down further but transitions to cruising. Receiving infill information at any speed higher than that, the train will have processed the information before reaching the RS and a transition to cruising takes place immediately. With these prerequisites, we need to consider running with constant speed and running with constant acceleration or deceleration.