# Delay Management in Regional Railway Transport
## 5 Conclusions  
This article dealt with the topic of delay management in the timetable planning process, especially in determining transfer waiting times. First, state-of-the-art train scheduling, traffic control, dispatching, and delay management were examined. The authors found that the critical path method is commonly used in some of the tasks carried out for operational traffic control and/or by dispatchers (e.g., for proper time margin positioning), but CPM has not been used for determining transfer waiting times, which was the authors' primary challenge in this research. Next, the article described the basic relationship between line periods/intervals and length of transfer waiting times. With increasing intervals between connections, transfer waiting times grows, because when is lost to a continuing train, real waiting time corresponds with waiting for the following service (and the travel time for passengers is, accordingly, a line-interval longer). The article then described the relationship between transfer waiting times and timetable stability. Timetable stability must also be considered when determining transfer waiting times. The more interactions there are between trains and the more heterogeneous a timetable is, the more potential conflicts between trains arise, with potential sources of delay transmission or formation. Delays tend to spread due to mutual interactions between trains; the number of affected trains increases disproportionately with the number of bindings in the timetable and the delay elimination time. The delay elimination time alone, which can occur in the case of a periodic timetable described by the so-called stability coefficient, is one of the possible indicators of timetable stability. Thus, in the case of marginal connections (e.g., during evening or night), transfer waiting times are generally longer during other times of the day, due to the lower number of interactions. The transmission of delays does not usually take place at the same rate during evenings or night as it does during the day. To determine transfer waiting times, it is necessary to correctly identify the critical section of a railway line, which is decisive with respect to time supplements, reserves, spaces, synchronization times, and the length of interstation sections in cases of crossing or overtaking relocation. The possibility of train crossing and overtaking relocation, or utilization of other disposition measures, also affects the length of transfer waiting times. Therefore, it is common Czech practice to determine transfer waiting times at the same time as compiling instructions (i.e., dispositional measures) for resolving operational disruptions (which are included in the \"D7-Regulation for operational traffic control\" of IM SZ). The researched then described an approach for determining transfer waiting times. This approach, called the maximum transfer waiting times principle, consists of determining transfer waiting times to their maximum value so that none of the crucial transfer connections are disrupted. Using this approach, an algorithm was determined to convert this task into an oriented graph (called the technological-operational processes graph) and use modified CPM (the critical path method) to determine transfer waiting times. This method takes into account operational/technological interactions between trains, but does not consider the transportation (passenger time) aspect. The method was applied as a new operational concept in the Vysocina Region, where it has been implemented since the beginning of the timetable for 2019/20. Based on the waiting times for the long-distance trains Praha-Havlickav Brod-Brno and Plzen-Ceske Budejovice-Jihlava-Brno and the regional trains Kolin-Havlickav Brod-Zd'ar nad Sazavou, transfer waiting times were proposed for relevant regional trains lines at the Havlickav Brod and Jihlava junctions.