# End-to-End Delay Model for Train Messaging over Public Land Mobile Networks
## 1 Introduction
The RobustRail project [10] has studied the possibility of replacing the GSM-R with LTE in the railway scenario. The Railenium project [11] is concerned with the intelligent interaction between the infrastructure and vehicles to optimize both the performance of signalling systems and railway transport capacity. The Satloc project has addressed the adoption of the European Geostationary Navigation Overlay Service (EGNOS) for train positioning and speed determination [12]. Several papers have investigated the introduction of LTE for railway communications. In [13], authors investigate the use of LTE micro-cell deployment in high-density railway areas to support bandwidth hungry applications. Other papers have focused on transmission performance for high-speed trains, tackling problems due to Doppler shift [14], problems caused by too frequent base-station handovers [15] and retransmissions protection to provide data integrity as in [16]. To evaluate the performance of train control procedures based on public radio networks, channel characterization is important, as also highlighted in [17]. Authors in [17] report the main results of a measurement campaign in China for high-speed railway communications. As shown in [17], due to high channel dispersion and variability, authors propose the adoption of solutions to be considered in the design phase of the LTE system, such as Coordinated Multi Point and the cell combination for improving performance. In the 3 InSat project [18] within the framework of the European Space Agency (ESA) Advanced Research in Telecommunications Systems (ARTES) 20 programme, by means of an experimental campaign, we have investigated on the possibility of achieving acceptable QoS on public terrestrial networks integrated with satellite [8; 19] as the economical feasibility of this approach. Considering that in the short/medium-term radio bearers provided by public networks will offer best-effort services, in [18], we also made evidenced that the satellite is an important component to achieve the required QoS levels. Performance results in [8] suggest that the usage of a public radio network including satellite for supporting train control communications is a viable choice for actual and future railway communications on local/regional lines. Typical propagation models used to assess communication performance on the railway focus on transmission aspects at the physical (PHY) layer [17; 20]. In this paper, we model the behavior of the radio transmission channel as seen by the railway control applications, which run on the on-board European Vital Computer (EVC) and at the Radio Block Centre (RBC). In this case, the channel behavior can be completely characterized by the end-to-end (E2E) delay and by the loss probability of the control messages exchanged by the applications. The E2E delay channel model presented in this paper allows the railway operator to evaluate performances of train control procedures, whose messages exchanged between the railway control applications (i.e., EVC and RBC) are sent on a public radio network managed by a telecommunication operator. In this case, for the railway operator, it is not possible to know exactly the behavior of the public radio network as well as to influence it in any way. The railway operator can only infer/measure the E2E delay for the messages sent by applications. The proposed E2E delay model aims at reproducing the main behavioral characteristics of the process describing the E2E delay as observed from experimental data [18] obtained over a regional line. It is shown that the proposed model can be applied to generate the E2E delay for a generic railway line when the positions of handover areas have been identified along the line and the received power levels and information on the radio serving technologies are available. The model can be used for preliminary performance analysis of railway control procedures for trains moving over local/regional lines.