## 4 Simulation Results and Discussion  
As the OIS in each car of a train operates independently and uses the same toss-and-catch algorithm, the statistical data generated by a single car should be virtually identical to those generated by multiple cars if a long-term observation is performed. To facilitate our simulation, we only considered the case of a train with one car, that is, only one OIS is in operation, and simulated the proposed algorithm's performance using Matlab. In order to produce more realistic simulations, this study also performed simulations of fading in different channel environments by employing Nakagami-\(q\) fading channels in which \(q=3\), 1, and 1/2 [26; 27]. This was done with the aim of developing SBS selection and handover methods that are more practical for mobile terminal equipment in the future. Note that since a channel is influenced by the degree of fading, \(d_{i}\) in (2) changes accordingly as well.  
The performance items that were tested include the following: (1) connection hold rate: the ratio of the communication connection time between the OIS and SBSs to the train's total travel time; (2) handover frequency: frequency of OIS handovers (total number of handovers/total travel time); (3) average RSS: OIS's average RSS in relation to total travel time; and (4) manageable load percentage of the OIS: percentage of OIS's load that the SBSs can handle. Train speed and OIS's load ratio were designated as the variables for testing these four performance items.  
We demonstrated the advantages of the proposed method by conducting a comparison involving two control groups:  
1. Control Group 1: Unlike the proposed method, the method applied to this group did not incorporate SBS categorization and the overload support mechanism and adjusted the mode of each SBS according to the SBS's load ratio. Note that the worst-case time complexity of Control Group 1 is \(O(N(|\Re|+|\text{SBSG1}\,|\log\,|\text{SBSG1}\,|))\).
2. Control Group 2: This group is identical to Control Group 1 in all ways except that it uses a random selection mechanism instead of a score-based one. Note that the worst-case time complexity of Control Group 2 is \(O(N|\Re|)\).  
Although the levels of time complexity of these two control groups are lower than that of the toss-and-catch algorithm, the analysis in Section 3.6 has shown that the toss-and-catch algorithm's complexity level remains acceptable in a typical scenario. The complete  
\begin{table}
\begin{tabular}{p{142.3 pt} p{142.3 pt} p{142.3 pt}} \hline \hline
**Pros** & **Cons** \\ \hline \hline \(\bullet\) Combines designs derived from multiple viewpoints to create an effective algorithm that optimizes handover selection & \(\bullet\) Does not consider different sets of quality-of-service requirements \\ \(\bullet\) When the OIS has multiple SBS options, unnecessary handovers can be avoided, which helps improve overall communication quality. & \(\bullet\) Does not consider interference issues 1 \\ \(\bullet\) Adapts well to changes in channel environments & \(\bullet\) Does not consider interference issues 1 \\ \(\bullet\) Applicable to all types of fixed-rail transportation & \(\bullet\) Does not consider interference issues 1 \\ \(\bullet\) Ensures reliable transmission & \(\bullet\) Does not consider interference issues 1 \\ \(\bullet\) Ensures non-interruptible handovers & \(\bullet\) Does not consider interference issues 1 \\ \(\bullet\) Serves as a good base for developing or integrating various emerging information and communication technology applications & \(\bullet\) Does not and detailed simulation results that are subsequently obtained show that, compared to the two control groups, the toss-and-catch algorithm enables superior performance for the four performance items of interest discussed above and only at the slight expense of time complexity. This superior performance is particularly pronounced with respect to the connection hold rate and manageable load percentage of the OIS.