# An Evaluation Framework and Algorithms for Train Rescheduling
## 5 Framework Part II: Key Aspects for a Systematic Evaluation of Algorithm Performance
Total accumulated delay (TAD) is the total tardiness of all trains at their intermediary, scheduled commercial stations (a commercial station is a station where the train stops for aligning passengers). Total final delay (TFD) is the total tardiness of all trains at their final destinations. The tardiness metrics TAD\({}_{3}\) and TFD\({}_{3}\) capture the delays for a threshold of 3 min. The delays incurred in the solutions output by an algorithm are expected to be as close as possible to the optimal. Total accumulated delay is an important delay metric often used in railway operations analysis [31]. Total final delay is a frequently used metric in the objective functions of existing train rescheduling algorithms proposed by the research community. The reason for selecting a threshold of 3 min is due to its use by the Swedish railway authority to continuously monitor and log arrival and departure train delays in the associated traffic management system. Furthermore, delays larger than 3 min are more likely to cause the passengers to miss train connections, compared to smaller delays. 3. _Delay propagation:_ Trains that are delayed as a direct result of a disturbance experience primary delays. When on-time trains instead become delayed as a result of delay propagation, they are said to experience secondary delays. We compute the number of trains experiencing small secondary delays (\(\leq\)3 min) and large secondary delays (\(>\)3 min) anywhere in their itinerary, in the obtained rescheduled timetables. This indicator is used to reflect the extent to which delays are propagated to other trains (i.e., knock-on effects). It is important to consider this indicator as even a simple infrastructure failure can at times create knock-on effects in the railway network that may continue for many hours. 4. _Freight train performance:_ The timetable deviation [16] evaluates the difference between the originally planned timetable and the new timetable. The latter should ideally limit the deviation from the originally planned times. We compute the timetable deviation for freight trains at their departure yards. Since freight train operators prefer not to increase their travel times, we consider it to be a relevant metric to use when measuring freight train performance. Another important metric for freight trains is the number of unplanned stops [20]. Multiple unplanned stops further increase the travel time, since slowing down and speeding up heavy freight trains is time consuming. In addition, these trains may block critical station tracks during their unplanned stops. In addition, unplanned stops impact operating costs and energy consumption. Hence, we record the number of new stations at which freight trains stopped during their journey. When a freight train arrives very early, problems may arise in the arrival yard where shunting and (un)loading takes place as per its separate schedule. For this reason, we use the percentage of freight trains that are earlier than 15 min as a metric for this indicator. Late arrivals of freight trains are also problematic. The percentage of late freight trains, e.g., with an arrival delay \(\geq\) 30 min, are already accounted for in the general train punctuality indicator, and hence we do not explicitly record them. Note that, if the rescheduling time window does not include the freight train's complete journey, the first and last stations in the problem instance are considered to be the departure and arrival yards, respectively. 5. _Passenger delays:_ Total passenger delay (TPD) captures the total delays experienced by all passengers while alighting at their destinations. This metric is frequently used in the rail literature to estimate passenger inconvenience [23]. We multiply the number of alighting passengers with the associated train delay at that particular train stop, where only a delay larger than a threshold of 3 min is counted. This metric, called TPD\({}_{3}\), is used to estimate the inconvenience that the passengers would experience due to the rescheduled timetable. 6.