# Delay Management in Regional Railway Transport
## 3 Results
The following disposal measures were used:  
* the exchange of arrival order of even-direction trains on line Sp and even-direction trains on line R11 at the Jihlava station past the odd hours, because this arrival order is more probable in the range of delays corresponding to anticipated waiting times (as the Sp line has a greater ability to shorten the delays in the Jihlava-Trest\({}^{\prime}\) section than does the R11 line in the Jihlava-Krahulov section);
* the exchange of train sequence order on lines Os2 and R11 in the Jihlava-Jihlava mesto section in both directions, as it enables the extension of line Os3 waiting times at the Jihlava station and removes restrictive influences for R11 line trains reversion, because during the process of locomotive change, there is one train that is less restricting with respect to locomotive shunting (i.e., the train of line Os2). The assembled operational/technological processes graph in Supplementary Figure S1 is displayed in cut-out form in Figure 7. The vertices are represented by:  
* brown if it is a vertex of \(a_{t,i}\) type (train arrival); or
* black if it is a vertex of \(d_{t,i}\) type (train departure or passage). The corresponding name of the traffic point \(i\) is introduced in bold type in the grey field in which the vertex is placed. The vertex is divided into 4 to 5 rows:
* in the first row, the sign of train \(t\) is introduced (the line sign, behind which there is an ordinal number of the train in brackets that grows with the period ordinal number; even numbers are used for trains of even direction, odd numbers for trains of odd direction);
* in the second row, the scheduled arrival/departure/passage time \(s\) is introduced;
* in the third row, the earliest possible arrival/departure/passage time \(e\) is introduced;
* in the fourth row, the latest possible arrival/departure/passage time \(l\) is introduced;
* alternatively, in the fifth row, the latest possible departure time \(l_{IN}\) is introduced. In time details in the second, third, fourth, and fifth rows, \"S\" means an even hour, while \"L\" means an odd hour. Oriented edges are represented by:
* blue if it is an edge of \(r\) type (train runs);
* red if it is an edge of \(dw\) type (train dwells);
* green if it is an edge of \(t\) type (transfer bindings between trains);
* orange if it is an edge of \(h\) type (operational interactions between trains); or
* purple if it is an edge of \(c\) type (circulation bindings between trains). The evaluation \(mtt\) is introduced in minutes near the edge by the same color as the edge's. The transfer waiting times for regional transport trains, using the new operational concept in the Vysocina Region for the basic weekend IPT model, are summarized in Table 2.  
Transfer waiting times for the Sp line, determined by the authors' approach, were implemented by the train operating company (Ceske drahy) and by IM SZ for regular  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Line** & **Traffic Point** & **Direction** & **Maximum Waiting Time** \\ \hline \multirow{3}{*}{Sp} & Havlücküx Brod & odd (\(>\)jhllava \(>\) Télc \(>\) Slavonice) & 12 min \\  & Jihlava & odd (\(>\)Trest\({}^{\prime}>\) Télc \(>\) Slavonice) & 11 min \\  & Jihlava & even (\(>\)Havlückoperational control in this area. Other transfer times, as determined, were moderately adjusted to take into account the transportation (passenger time) factor. Reached results of train delays and achieving transfer connections for the first half-year of operation of the new concept showed that qualified steps and projected values of transfer waiting times were calculated correctly. If unplanned and unexpected incidents, operational disruptions, vehicles breakouts, and signaling system breakouts do not occur, the operation functions stably. Transfer connections are functional in the maximum possible volume, and a low delay in operations leads to compliance with the planned timetable.