## 3 Materials and Methods
### Design and Implementation of a Multilayer Railway Network Model
#### 3.2.1 Methodology of Data-Micro Model Layer Construction  
The first data layer (data-micro) reflected the physical rail network infrastructure with the minimum degree of abstraction, while individual model and graph vertices corresponded to stationing. Substitute Rails and Hectometer Posts  
Data imported from the input sets unfortunately do not fully reflect the real form of the rail network infrastructure, especially at multiple-line stations. In the case that a station has ten rails (standard and dead-end rails), the input datasets may contain, for example, only three rails. In most cases, the station rails do not converge in any way and continue to the next station. Generally, the TUDU markings of a rail line section change, among others, before and after a station (as a part of the deviated tracks). This means that each station has (with certain exceptions) a unified TUDU marking along the whole length. The same refers to stations with more rails, that is, at each through-running station, the TUDU markings change at the deviated tracks before and after the station. It is important that each of the rails has an identical marking to the TUDU of the neighbouring rails that run through the station and that hectometer posts in the same TUDU have the same kilometric value at each rail (Figure 5). Regarding the above-indicated facts, we decided that, for the model design, the rails in multiple-line stations would be unified into a so-called substitute rail. This ensured, among other things, the convergence of all the rails before the station into one rail and, consequently, optional division of the substitute rail into more rails after the station. The model, thus, made it possible to return to any other departure direction from any arrival direction in the same way as real operation. For this purpose, it was necessary to calculate the new substitute hectometer posts (the calculation is shown below within \begin{table}
\begin{tabular}{l c} \hline \hline
**Subprograms and** & **Specification** \\ \hline \(\bullet\) & The values of the GPS coordinates of the new substitution hectometer posts \\  & correspond to the arithmetic means of the values of the respective coordinates \\  & of all of the hectometer posts from set \(H_{j}^{origin}\). \\ _setData_ ( \(\downarrow\uparrow h_{j}^{\prime}\downarrow H_{j}^{origin}\) ) & If at least one of the hectometer posts out of the set \(H_{j}^{origin}\) bears the sign of a \\  & point, then the new continuous hectometer post also bears the sign of a \\  & \(\bullet\) We adopt further information about the hectometer post from a random \\  & hectometer posts from the set \(H_{j}^{origin}\) in which the hectometer post is located. \\ \hline _findShortestRoute_\(\left(\downarrow h^{start}\), \(\downarrow h^{end},\uparrow\Sigma^{temp}\) ) & Between its outer _super-vertices_, \(h^{start}\) and \(h^{end}\), we find, using the shortest route \\  & search algorithm (in the data-micro layer), a set of part edges \(E^{temp}\). \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Functions. Figure 5: Demonstration of TUDU change on the track. Author’s resource. In the process of making substitute rails, we needed to consider a situation when one substitute rail was not permissible. This can mainly happen at smaller stations on multiline tracks that have no switch along the whole length; therefore, it is impossible to travel from one line to another. The collected data also contained information about the positions of individual switch-points on the line; that is, we could detect a switch-point's presence in the given station or vertex and decide whether a substitute line must be constructed. Another specific requirement of a multiline track was keeping the structure of individual lines crossing outside stations (by switch-points enabling passing from one line to another. The performed examinations demonstrated that rail line sections enabling such crossing had their own TUDU marking, which mostly contained only one or two hectometer posts.