# End-to-End Delay Model for Train Messaging over Public Land Mobile Networks
## 5 Usage of the Proposed E2E Delay Model  
The proposed E2E delay model could be used in association with an ERTMS/ETCS traffic simulator (not discussed in this paper) to assess values for the Key Performance Indicators (KPIs) envisaged for the train control procedures on local/regional lines. Railway applications in the EVC and RBC exchange position report (PR) (from EVC to RBC) and movement authorization (MA) messages (from RBC to EVC), while the train is moving on the railway line. Eurorado protocol [21] is commonly adopted to guarantee the required safety level over the radio link. The E2E delay of each PR/MA message is evaluated in accordance with the proposed E2E model. We further assume that the message can be lost with probability \(p_{Loss}\), obtained from experimental data, and that loss events are assumed to be statistically independent.  
The scheme in Figure 8 shows one possible utilization of the proposed model inside a simulator.  
The considered channel model can be implemented as a (software) process running independently by the generation of the messages of the railway applications. Every time a message is generated from the railway application the channel process is interrogated to return the E2E delay associated to the generated message. The E2E delay is added to the transmission time \(T_{i}\) to obtain the receive time \(R_{i}\) in accordance with Equation (2). The channel state is updated at regular time interval \(\Delta T\). In our case, we assume \(\Delta T=200\) ms, which is the time interval between two consecutive messages used in the measurement campaign. As outlined in the previous section, model parameters have been related to the radio coverage characteristics over the railway line (e.g., locations of roaming/handover areas and positions of the tunnels, if any), to the received power level and to the serving radio technology. It should be observed that, in realistic simulation setting, PR and MA messages are continuously  
Figure 8: Principle scheme for the usage of the proposed model for performance assessment.  
exchanged between the EVC and RBC for controlling the train speed. Thus, the time instants the train passes over the handover areas or enter/exit the tunnel should be updated step by step accounting for the train speed variations. The main effect of train speed in the simulation can be related to the variation in the received power, which in turn influences the statistics of the random variables \(X_{0}\) (\(X_{H}\)) and \(X_{1}\) as detailed in the next section. As shown in Figure 8, the E2E model can use information from the topology database of the (selected) railway line; it can use measurements/estimates of the received power at the train/BS and information on the radio technology at a specific location. The topology database should contain information on the presence of tunnels. Furthermore, preliminary radio coverage analysis of the line (possibly accounting for the presence of one or more MNOs over the area) is necessary to assess the positions and extensions of the handover/roaming areas and possible coverage holes. In the absence of radio coverage, connection is lost so that the process generating the E2E delays is suspended and re-activated when the train exits from the coverage hole.  
In an even more realistic simulation setting, train mobility pattern is influenced by the content of the MA message issued by the RBC in accordance with the current traffic on the railway network. For this reason, in Figure 8, we have assumed that the contents of MA messages could be used to modify train mobility. Finally, KPIs can be recorded at the application level to assess performance.