## 2 Results
### Simulation Results  
The numerical results for the fixed MRN mobility pattern scenario over a simulation time of 5 h are presented below. The results given are the averages of 10 simulation runs. Figure 2 compares the number of RLFs that occurred in the proposed scheme with the number that occurred in the existing scheme when the Event A3 condition was used. The existing network-controlled hard HO (NCHH) scheme based on Event A3 uses relay nodes. RLF is a key indicator of the HO procedure. The \(X\)-axis represents the simulation run time, while the \(Y\)-axis is the average number of RLFs. When the HO of MRNs occurred, the proposed self-optimization HO scheme proved more useful \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Value** \\ \hline Train speed & up to 350 km/h \\ Carrier frequency & 2.6 GHz \\ Tx power of DeNBs & 25 dBm \\ Threshold of HPI & 4\% \\ Hysteresis of Event A3 & \(-\)72 dB \\ Time-to-trigger (TTT) & 300 ms \\ Path loss model & 128.1 + 37.6 log10\(d\), \\ \multicolumn{3}{c}{\(d\) is distance between mMRN and DeNB} \\ Cell radius & 1 km \\ HO overlap area & 300 m \\ mMRN measurement interva & 50 ms \\ Adjustment value of CIO (\(\Delta\)) & 1 dB \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters. DeNBs, donor Evolved Node Bs; HPI, handover (HO) performance indicator; mMRN, main mobile relay node. Figure 1: Simulation network model: 19 cells, two fixed mobility patterns. than the existing scheme. The average number of RLFs for the existing HO scheme ranged between 8 and 13 throughout the entire simulation, whereas in the proposed scheme, the number of RLFs decreased to four after 100 min, which demonstrates a better wireless communication quality and improvement for high-speed trains with dual MRNs. In summary, the number of RLFs decreased, and slight changes occurred during the HO procedure of the proposed scheme. Figure 3 shows the average number of RLFs that occurred late and early in the proposed HO scheme. Several HOs that were too early were slightly modified because the HOs that are too early are regulated by the HPI threshold. Let us now evaluate the performance of the proposed HO scheme in terms of delay time, HO triggering probability and communication interruption time. We define the HO delay time as the time interval from  
Figure 3: Performance of the proposed optimized HO scheme for late and early HOs, respectively. Figure 2: Performance comparison of the proposed self-optimization handover and network-controlled hard HO (NCHH) scheme, the average number of the radio link failures (RLFs) and the fixed mobility pattern with high speed (300 km/h). the MRN receiving the last packet from the serving donor NB (DeNB) to its receipt of the first packet from the S-GW through the target DeNB. In [16], the time consumption of all messages is defined. Only NCHH is supported in the LTE system. Therefore, the communication interruption is defined by the path switch phase of the HO procedure and the time interval in which cells do not serve MRNs. Figure 4 illustrates the average HO delay time with various MRN velocities up to 350 km/h. The velocity of the vehicle was higher than 120 km/h; accordingly, the HO delay time varied between 102 ms and 108 ms in the proposed HO procedure. Conversely, the existing scheme's HO delay time increased to a maximum of 230 ms. Thus, the proposed scheme demonstrated that it can provide data communication with a relatively low average delay time during the HO procedure. We also compared the existing and proposed HO schemes in terms of communication interruption time. The results are shown in Figure 5. The proposed scheme reduced the communication interruption time by approximately 9.8 ms at 200 km/h, which is sufficient for the provision of good quality of service to passengers. Further, the communication interruption time of the proposed HO scheme with dual MRNs was less than that for the existing scheme in a higher velocity environment. Figure 4: Average HO delay.