# Delay Management in Regional Railway Transport
## 2 Materials and Methods
### Waiting Time Issue
#### 2.2.3 Introduction to the Czech Praxis  
In Czech railway transport, the basic terms related to transfer waiting times are defined in the timetable manual, \"Transfer connections between passenger trains\" [30], which is published by Czech Infrastructure Manager Sprava zeleznic (\"IM SZ\"). According to this timetable manual, transfer connection applies to a pair of trains, where there are at least 2 min and at most 60 min between the scheduled arrival time of the first (connecting) train and the scheduled departure time of the second (continuing) train. Different transfer times are mentioned in the manual for every station. Non-connection refers to pairs of trains for which the transfer connection will not be ensured, despite the in-time ride of the trains, for example:  
* when trains are traveling in opposite directions on the same railway line without regard to stopping patterns (e.g., when a connecting train arrives from the same neighboring station that a continuing train departs from, regardless of whether the trains stop there); exceptions are cases when the neighboring station is a turning station without a stop;
* when trains are traveling in the same direction on the same railway line and both trains have the same scheduled stop;
* when there is a longer transfer time at a station that is not reached, between the connecting train's arrival time and the continuing train's departure time (this scenario is mentioned for every station in the manual \"Transfer connections between passenger trains,\" and in the timetable for passengers);  
Figure 4: The course of the delay sum of trains caused by delayed train A with input delay \(t_{\text{input,A}}\) in the case of the stable timetable. In the delay spread phase, the increase of delay caused by mutual interactions between trains is at a higher level than the gradual elimination of those delays. At the stagnation stage, both of these factors are at approximately the same level. In the delay elimination phase, the level of delay elimination is higher than the ongoing delay spread. After expiring \(c_{\text{stab}}\)-multiple of the timetable period from the time of the input delay origin (T\({}_{0}\)), there comes a total elimination of that delay and all delays caused by it. It is clear from the chart that local anomalies are possible. Source: the authors. when the manual \"Transfer connections between passenger trains,\" as well as the timetable for passengers, mention that there is no transfer connection between particular trains;
* when trains are from different operating companies, subject to exceptions mentioned in the manual. The transfer waiting time means the maximum possible departure delay (compared to the regular or exclusion timetable) of the continuing train from the transfer station/junction, influenced by waiting for a delayed connecting train. Transfer time is also included in transfer waiting time. Waiting time cannot be exceeded without special instruction from the train's operating company (i.e., via the dispatcher). Basic transfer waiting times in the network of IM SZ are determined uniformly for all stations: 5 min for express trains (category \"Ex\") and 10 min for fast trains (category \"R\"), fast regional trains (category \"Sp\"), and regional trains (category \"Os\"). Basic transfer waiting times are valid for all continuing trains if there is no exception for an individual station and/or for pairs of trains. Continuing trains do not have to wait for a connecting train to set the transfer waiting time if there is no transferring frequency of passengers for the continuing train, if this is announced by train staff to operation employees. In the contemporary Czech praxis, the train's operating company evaluates transfer waiting times. For PSO-services, the carrier does this after a discussion with the public purchasers of the service. Unfortunately, in most cases, the values of transfer waiting times are only estimations, arrived at without deep traffic analysis or any supporting tools (e.g., mathematics or simulations).