5.1 Connecting time
For all departure dates and data collection rounds, a statistically significant difference in connecting time is observed (Asymptotic Sig. (2-sided test) < 0.001), with most traditional itineraries rendering shorter connecting times. During the first week of August 2019, for example, the traditional itineraries have shorter connecting times in 88.8–95.1% of all markets (i.e., the minimum and maximum negative iTR-VI differences across all 21 departure dates and data collection rounds, see also Fig. 3A. However, the opposite situation is also sometimes found: for 4.8–11% of the airport pairs (i.e., the minimum and maximum positive iTR-VI difference across all 21 departure dates and data collection rounds), the virtually interlined flight renders a shorter connecting time. Only in a minority of cases (0.1–0.2%), both types of flight exhibit an identical connecting time. Similar results are obtained with respect to the departure dates in the first week of October 2019: for 93.3–95.7% of the airport pairs, the traditional flight itinerary has a longer connecting time. In only 4.2–6.6% of cases, the opposite situation is observed. With respect to the departure dates in the first week of December 2019, these two categories respectively encompass 91.5–95.3% and 4.6–8.3% of the airport pairs.
Figure 3B, in turn, shows the relative frequency of the magnitude of the connecting time differences for all markets where the virtually interlined flight renders a longer connecting time (i.e., VI connecting time > iTR connecting time). Cumulatively, for 67–83.7% of the airport pairs, the connecting time difference exceeds 6 h. For 39.8–62.2% of the airport pairs, the virtual interlined passengers spend more than an additional 12 h at the transfer airport(s) relative to those travelling on the traditional schedule. While 6.1–24.6% of the connecting time differences even exceeds 24 h, travellers rarely (0–0.5%) lose more than 48 h at the transfer airport(s) by choosing the virtually interlined flight option.
In order to reflect in more detail upon the connecting times as well as the spatial configuration of the transfer airports in the virtually interlined flight network, Fig. 4 visualises (1) the number of times an airport acts as transfer airport within the virtually interlined schedules, and (2) the median connecting time for each transfer airport (departure date: 02 October 2019; data collection round: b).
The top-10 transfer airports are Barcelona, London Stansted, Milan Bergamo, London Luton, Athens, Palma de Mallorca, Brussels South Charleroi, Gdansk, Vienna, and Dublin Airport. Overall, it can be observed that virtual interlined transfers predominantly take place at major LCC airport bases. This is in line with the findings by [33], who showed that virtually interlined flights rendering a price advantage are mostly operated by Europe’s leading LCCs. Barcelona Airport, for example, ranks first in the top-10 transfer airports and is the primary airport base of Vueling Airlines [8]. London Stansted, in turn, ranks second and constitutes Ryanair’s largest airport base [40]. Finally, Milan-Bergamo completes the top-3 and forms the third largest airport base of Ryanair. It can furthermore be observed that multiple secondary airports stand out, presumably due to (ultra-)LCCs which mostly operate on low-density routes between secondary airports (see, for example, [14]). An example hereof is Brussels South Charleroi Airport, which constitutes the sixth largest base of Ryanair [40]. With respect to connecting times, the top-10 transfer airports exhibit median connecting times ranging from circa 10 h (Dublin Airport) to circa 12 h (Gdansk Airport).
In parallel to Figs. 4, 5 visualises (1) the number of times an airport acts as transfer airport within the traditional schedules, and (2) the median connecting time for each transfer airport (departure date: 02 October 2019; data collection round: b).
In the traditional flight network, Europe’s leading full service network carriers’ (FSNC) hub airports are dominant. In this case, the top-10 transfer airports are Amsterdam Schiphol, Athens, Madrid, Rome Fiumicino, Oslo, Paris Charles de Gaulle, Munich, Frankfurt, Düsseldorf, and Warsaw Airport. Many of these airports constitute a primary base of a FSNC. Amsterdam Schiphol, for example, ranks first in the top-10 and forms the home base of KLM [26]. Frankfurt Airport, in turn, ranks eighth and is the largest Lufthansa hub [30]. Median connecting times associated with these top-10 transfer airports are between approximately one (Munich Airport) and two hours (Düsseldorf Airport), which yet again illustrates the large connecting time differences between both types of networks.
Finally, in order to assess whether there exists a correlation between the (magnitude of) the positive fare differences (iTR-VI fare > 0) and the negative connecting time differences (iTR-VI travel time < 0), a Kendall’s Tau-b correlation was computed. The Kolmogorov–Smirnov test results and the Kendall’s Tau-b test results are provided in Additional file 1: Appendix D and Additional file 1: Appendix E, respectively. For all departure dates and data collection rounds a weak to very weak negative correlation was found between the positive fare differences and the negative connecting time differences (N = between 8089 and 22,615, τb = between − 0.161 and − 0.047, p < 0.01). Hence, although the correlation is weak at best, there is some evidence that the greater the price advantage of a virtually interlined flight, the greater the connecting time cost relative to its traditional alternative. This in turn informs research on passengers’ value of time, which will be elaborated on in Sect. 7.
5.2 Geographical detour factor
For all departure dates and data collection rounds, a statistically significant difference in geographical detour factor is observed (p < 0.001), with most traditional itineraries characterised by shorter detours. More specifically, in the first week of August 2019, the traditional itineraries have smaller geographical detour factors in 63.2–72.0% of the markets (see also Fig. 6A). The opposite is observed for 21.1–28.6% of the airport pairs. Similarly, for the first week of October and December 2019, the indirect traditional flight itineraries have smaller geographical detour factors in 62.8–72.3% and 65.3–73.5% of cases, respectively. In contrast, for 20.5–26.9% and 20.5–25.8% of the airport pairs, the virtually interlined flight covers less distance in the first week of October and December 2019, respectively. This shows that the larger number of possible connection points within the virtually interlined flight network does generally not translates into a reduced geographical detour factor when the cheapest flight itineraries are considered. Nonetheless, the relative frequency of the positive/negative differences seem somewhat less pronounced compared to the connecting time differences displayed in Fig. 3A.
Figure 6B, in turn, shows the relative frequency of the magnitude of the negative differences in geographical detour factor (i.e., VI geographical detour factor > iTR geographical detour factor). Cumulatively, for 41.5–62.5% of the respective airport pairs, the difference in geographical detour factor is greater than 0.5. This means that the extra distance covered by the virtually interlined flight equals more than half the GCD of the hypothetical non-stop flight between the origin and destination airports. For 21.3–43.1% of airport pairs, the difference in geographical detour factor is even greater than 1, implying that the extra distance covered by the virtually interlined flight is more than the entire GCD of a hypothetical non-stop flight between the origin and destination airports. For 4.1–11.8% of cases, the difference in geographical detour factor is larger than three.
Similar to the previous section, we furthermore test whether a correlation exists between the (magnitude of) the positive fare differences (iTR-VI fare > 0) and the negative geographical detour factor differences (iTR-VI geographical detour factor < 0). To this end, a Kendall’s Tau-b correlation is again calculated (see Additional file 1: Appendix E). For the majority of departure dates and data collection rounds, a weak to very weak positive correlation was found between the positive fare differences and the negative detour differences (N = between 5960 and 16,888, τb = between 0.023 and 0.130, p < 0.01). Although the correlation is weak at best, this implies that the greater the price advantage of a virtually interlined flight, the smaller the difference in geographical detour factor. In contrast, for a single configuration (i.e., 07 August 2019 data collection round c), a very weak, negative correlation was found. In three configurations (i.e., 04 August 2019 data collection round c, 05 August 2019 data collection round c, and 06 August 2019 data collection round c), no statistically significant correlation was found. Given these contradictory results, we cannot speak of a clear/unambiguous correlation between the fare profits and the detour costs associated with virtual interlining.