# Determining the Optimal Positions of Infill Balise Groups for ERTMS/ETCS Level 1 Applications
###### Abstract  
This paper presents a method to determine the optimal positions of infill balise groups for applications of European Train Control System (ETCS) level 1. ETCS will be the only train protection system in the European Union of the future. Level 1 specifically enables a less complex system while retaining full compatibility to and interoperability of ETCS level 2. In level 1, the Movement Authority (MA), which contains information on how far and at what speed the train is authorized to run, is transmitted at fixed locations where switchable radio beacons--infill balise groups--are placed. Due to technical and economical constraints, their locations need to be optimized so that they provide the maximum operational benefit. Such a method with universal adaptability has not been available to date, so we developed an algorithm that determines the optimal locations of infill balise groups. The algorithm uses the basic laws of motion combined with domain knowledge about railways in general and specifically ETCS. All important parameters are considered while retaining simplicity in the application, making it convenient to use for planning new ETCS deployments and as a foundation for future research on ETCS level 1. The algorithm was implemented using Python and tested with real-world train characteristics. a 2024 14 8165 11  
groundwork for interoperability in the railway sector in 1996 by introducing the concept of Technical Specifications for Interoperability (TSI), starting with high-speed lines. In 2001, this was extended to include conventional rail lines with Directive 2001/16/EC focusing on trans-European transport [4]. Three years later, both directives were amended and concretized by Directive 2004/50/EC [5] and then recast in 2008 by Directive 2008/57/EC [6]. More recently, Directive 2012/34/EU [7] laid the groundwork for and established the term \"single European railway area\", stressing the importance of overall interoperability in the railway sector. The aim is to have a unified railway network where national borders are not relevant for or hinder the trans-European railway transport of passengers and freight. In 2016, a major revision and recast of the interoperability of the railways in the European Union was adopted by the new, still-in-force Directive (EU) 2016/797 [8]. In itself, ETCS is a positive train control system as it uses a Movement Authority (MA) to authorize a train to move until a specified location within a specified speed envelope [9; 10]. Additional information may be provided by ETCS as well. In contrast, a negative train control system allows for unhindered movement as long as no restriction--approaching a stop signal, for example--is imposed on the train. All necessary information of ETCS for the train driver is presented on the harmonized Driver Machine Interface (DMI) [11] in the driver's cab, making ETCS a cab signaling system. This information includes the actual speed, the currently permitted speed, the target speed, and the target distance. The need for a MA results in the need to update the currently valid MA to further authorize the movement. This process is carried out by providing \"infill information\" from the trackside to the train, which updates the MA. Under normal circumstances, infill extends the current MA. The information required on the train can either be transmitted by means of balises (electronic beacons at fixed locations in the track) or by means of radio. Transmitting by means of balises is defined as ETCS (application) level 1, whereas transmitting via radio is defined as ETCS (application) level 2. Level 2, per the latest specifications [10], includes the former ETCS level 3, where information is transmitted via radio and the train integrity is checked on-board, so no trackside train detection system is needed and moving block operations are possible.