## 4 Results
### Detection of a Train Position  
For the detection of nonstandard situations, we used a computer simulation that induces rail vehicle operation.  
The designed testing tool contained a core discrete simulation cooperating with a standard calendar of the processor messages performed according to the time stamp. The  
Figure 17: Train deceleration.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Track\_Resist [\%]** & \(a\) [m \(\cdot\) s\({}^{-2}\)]** & \(t\) [s]** & \(s\) [m]** \\ \hline \(-2\) & 0.7374 & 24.49 & 219.69 \\ \(-1.5\) & 0.6931 & 26.05 & 233.75 \\ \(-1\) & 0.6487 & 27.83 & 249.73 \\ \(-0.5\) & 0.6044 & 29.88 & 268.06 \\ \(0\) & 0.5600 & 32.24 & 289.29 \\ \(0.5\) & 0.5151 & 35.06 & 314.53 \\ \(1\) & 0.4701 & 38.41 & 344.64 \\ \(1.5\) & 0.4252 & 42.47 & 381.04 \\ \(2\) & 0.3802 & 47.49 & 426.09 \\ \hline \end{tabular}
\end{table}
Table 3: Time and length of the braking distance.  
simulator used data resulting from a real situation based on the processing of historical data of passing trains and generated data. These data were obtained based on cooperation with the Czech state enterprise: Railway Infrastructure Administration (SZ, s.o.). Our attention in the next experiment was focused on the opposite direction of two rail sets of the same type, while evaluating the following parameters:  
* Mutual position (distance) of the two vehicles at the time of detection of a nonstandard situation;
* Braking distance and mutual position (distance) after the two vehicles stopped.  
The experiments were processed for the selected time periods when the vehicle sent its current position:  
* 5 s;
* 10 s;
* 30 s;
* 60 s.  
If we focused on the opposite drive detection on an identical rail or edge (according to the procedure displayed in Figure 14), then their mutual positions (distance) at the time of the detection could be statistically expressed, as shown in Table 4.  
Table 4 shows that the average and median decreased with the growing time frequency, while the standard deviation increased. The frequency of 60 s was clearly unsuitable: in two cases, there was a collision.  
In the second case, opposite drive detections were evaluated at two adjacent rails or edges, according to the procedure shown in Figure 14. The results are presented in Table 5.  
Table 5 demonstrates that, compared to the first experiment results (Table 2) where the median and standard deviation values were roughly double the value, we saw significantly smaller differences in the distances of all the monitored parameters.  
For simplification, in the opposite train drive, we assumed identical speeds of both train sets and equal track value resistance in which a nonstandard situation was detected. The overall braking distance was, thus, obtained with the sum of the partial braking distances for the monitored track resistance, for the upward gradient, or for the downward gradient. The braking-time values (_t_sum_) and distances (s_sum_) of both train sets for the speeds of \(65\frac{\mathrm{km}}{\mathrm{h}}\) and \(75\frac{\mathrm{km}}{\mathrm{h}}\) are indicated in Table 6.  
\begin{table}
\begin{tabular}{l c c c c} \hline \hline  & **Period 5 [s]** & **Period 10 [s]** & **Period 30 [s]** & **Period 60 [s]** \\ \hline Min & 1000 & 1000 & 600 & 0 \\ Max & 2500 & 2500 & 2400 & 2400 \\ Average & 2016 & 1968 & 1628 & 1140 \\ Median & 2100 & 2100 & 1800 & 900 \\ Standard & 396.67 & 413.49 & 519.63 & 726.64 \\ deviation & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 4: Resulting distances [m] at the time of detection of two trains on an identical edge.  
\begin{table}
\begin{tabular}{l c c c c} \hline \hline  & **Period 5 [s]** & **Period 10 [s]** & **Period 30 [s]** & **Period 60 [s]** \\ \hline Min & 2500 & 2500 & 2000 & 1400 \\ Max & 3900 & 3900 & 3600 & 3600 \\ Average & 3084 & 3064 & 2776 & 2624 \\ Median & 3000 & 3000 & 2700 & 2700 \\ Standard deviation & 402.67 & 418.45 & 443.87 & 612.32 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Resulting distances [m] at the time of detection of two trains on two neighbouring edges.