To analyse the potential benefits of PANDA, we wanted to estimate the effect of PANDA’s recommendations on the passenger flow. Therefore, we conducted an experiment in which we simulated and analysed several thousands of independent decisions. Here, we assume that all of PANDA’s recommendations are realizable in practice. Thereby, we ignore problems of practical feasibility, for example due to track capacities.
We use the German train schedule of 2015 (with about 66,000 trains and about 280,000 transfers used by passengers per day) and realistic passenger flow information provided by Deutsche Bahn, consisting of about 3.3 million passengers on 320,000 different routes on each day. For our evaluation we used recorded data for actual delays of 10 days in June and October 2015.
For each critical transfer on our test days, we simulated a waiting decision based on the delay situation as known 15 min before the connecting train was scheduled to depart. We measured the effect of each decision on the passenger flow and compare the results with the status quo. For the latter we used the realized event times. It may well happen that the delay situation changes in the last 15 min between the decision and its actual execution so that the decision would have been different with full knowledge of future delays.
Data about 154,000 critical cases were gathered this way. These cases also include transfers, which are not regarded in practice because of train-category priority rules. For instance, a dispatcher does not consider to delay a connecting subway train in order to keep the transfer from a delayed Intercity-Express train. After filtering out all such cases, an overall number of 106,000 critical transfers remained.
On each day, realized departure and arrival event times were available with a resolution of 1 min. However, we did not have explicit information whether a transfer has been maintained by an active dispatching decision or not. Therefore, we tried to infer a posteriori, based on the realized time stamps, for each critical transfer whether it had been dispatched or not. Given the actual departure time dep(ct) of a connecting train ct, the actual arrival time \(arr( ft )\) of a feeding train \( ft \), and the minimum transfer time mintt required to change from the feeding to the connecting train, the buffer time
\( buf \) for a transfer can be calculated as \( buf = dep(ct) - arr( ft ) - mintt\). Since the recorded data available to us does not contain the information which transfers have been actually maintained, but we would like to compare the number of (actively) maintained connection in the status quo and by PANDA, a formal notion is required which can be computed from available data. Therefore, we counted a train as dispatched for a particular transfer if (1) it has departed at least 2 min later than possible (or in other words: if it has gathered a new delay at the departure event of at least 2 min) and the available buffer time satisfies \(-1 \le buf \)
Footnote 1 or (2) if its real departure time was at most 1 min earlier than calculated by PANDA for the waiting scenario.
To reduce potential misclassifications, we considered in our final evaluation only those transfers where—with respect to the time stamps 15 min before the scheduled departure of the connecting train—the departing train had to be delayed by at least 3 min to keep the transfer. After this filtering step, about 64,000 cases remained.
For each case, we asked PANDA about its waiting recommendations 15 min in advance. As PANDA offers several independent decision criteria, we used a simple majority rule to combine the criteria into a binary waiting recommendation: PANDA suggests to wait, whenever the number of criteria that are in favour of the waiting scenario exceeds the number of criteria that are in favour of the non-waiting scenario. To assess the impact on passengers, we consider four different measures, namely the total delay, i.e. the sum of the final delay over all passengers, and the number of passengers with a delay of at least 30, 60, or 120 min at their final destination.
Under our assumptions, 28.2% of all critical connections are kept by dispatching. In comparison, PANDA recommends to wait for 31.8% of these cases. Table 1 gives the average absolute numbers of passengers per day which benefit from PANDA’s recommendations, while Fig. 6 shows the relative benefit of using PANDA’s recommendations in comparison with what has been executed in practice. For all measures, we observe a significant potential to reduce passenger delays by using recommendations given by PANDA. The strongest relative reduction can be obtained for the group of passengers which would suffer from delays by 120 or more minutes. The number of passengers in this group could be reduced by about 50%, if PANDA’s recommendations would be realized (see again Table 1 for the absolute numbers of passengers affected per average day). The total sum of delay minutes could be reduced by about 24%. Recall, however, that not all recommendations are realizable due to other constraints.
In Table 2, we report among all considered transfers the percentages of transfers maintained by PANDA, but not in the status quo, and conversely, by the status quo, but not by PANDA. Likewise, we do this for the non-waiting decisions. We observe that there is a significant fraction of cases where the status quo and PANDA do not agree. In 16.7% of all cases status quo decides WAIT, but PANDA recommends NO-WAIT, and conversely, in 20.3% of all cases PANDA decides WAIT, but status quo opts for NO-WAIT.