## 5 Discussion
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Track\_Resist [\%]** & \(t\_sum\_65\) **[s]** & \(s\_sum\_65\) **[m]** & \(t\_sum\_75\) **[s]** & \(s\_sum\_75\) **[m]** \\ \hline
0 & 64.48 & 578.57 & 74.40 & 775.05 \\
0.5/\(-\)0.5 & 64.93 & 582.59 & 74.92 & 780.43 \\
1/\(-\)1 & 66.24 & 594.34 & 76.43 & 796.17 \\
1.5/\(-\)1.5 & 68.52 & 614.79 & 79.06 & 823.57 \\
2/\(-\)2 & 71.98 & 645.78 & 83.05 & 865.08 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Time and length of braking distance up to stopping of both train sets. * One or an identical edge;
* Two neighbouring edges when the incidental vertex of the two edges did not dispose of any track branching or vehicle crossing (e.g., stations). For the detection of nonstandard situations, we used a computer simulation that induces rail vehicle operation. A reduced track profile was used to calculate the dynamics of the rolling stock. A reduced track profile was used to calculate the dynamics of the rolling stock, which replaced the complex properties of the railway infrastructure. From the measured values obtained in Section 3, it was concluded that, for the simplified dynamics of rolling stock, it was possible to assume a linear approximation with a reliability of R\({}^{2}\) = 0.99996 negative acceleration for a descending track profile, or of R\({}^{2}\) = 0.99974 negative acceleration for an ascending track. If we subsequently considered the speed of a selected set as 65\(\frac{\mathrm{km}}{\mathrm{h}}\), then by applying relations (3)-(6), the braking distance of a train set _(s)_ corresponded with the values in Table 3. Further monitored parameters were negative acceleration or deceleration (_a_) and time (_t_). Within the experiments, attention was focused on the opposite direction of two track sets of the same type when 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. Table 3 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 by 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 speeds of 65\(\frac{\mathrm{km}}{\mathrm{h}}\) and 75\(\frac{\mathrm{km}}{\mathrm{h}}\) are indicated in Table 4, which shows that, if the speed was increased by 15%, then the overall braking distance of both train sets increased by 34%. It was also demonstrated that, for the identification of nonstandard situations on an identical edge at the train set speed of 65\(\frac{\mathrm{km}}{\mathrm{h}}\), the 30 s period of current position detection was sufficient. However, for a speed of 75\(\frac{\mathrm{km}}{\mathrm{h}}\), this period may not be suitable in certain cases, and the train sets may not stop safely. It is important to note that all the above-mentioned values were theoretical in this experiment, and the real values would have to include the reaction time of the whole system and of the relevant human entities. The proposed concept of support for the dispatcher control of railway transport on single-track lines was in its final stage of development when it was presented to representatives of the Czech state enterprise: the Railway Infrastructure Administration (SZ, s.o.). However, its potential deployment requires a number of technical and administrative changes, which are the subject of further negotiations.