# Railway Lines across the Alps: Analysis of Their Usage through a New Railway Link Cost Function
## 6 Discussion and Conclusions  
In this paper, the usage of Alpine passes is analyzed, before: 'current scenario', and after: 'project scenario', the construction of the new base tunnels and the new railway lines under construction or planned. The rail network of a large part of Europe has been modelled through a graph and a new cost function for rail links has been developed. Only a few rail link cost functions exist in the literature and, generally, they are not very detailed: only the cost functions proposed by [PERSON] (2018), [PERSON] (2018) and [PERSON] (2018) take into account in detail the monetary cost components. However, the cost function proposed by [PERSON] does not always provide precise values. For example, the number of locomotives is not taken into account explicitly, while for the traction cost only a maximum, a minimum and an average value are provided, which do not depend explicitly on the geometrical characteristics of rail lines. The cost function proposed by [PERSON] provides more precise values, especially as far as locomotive and wagon costs are concerned. However, some cost components are not taken into account: the staff cost, and the rail track cost. Moreover, as regards the traction cost, only some reference values have been provided for some different line slopes. The cost function proposed by [PERSON] (2018) is more complete, but it does not consider explicitly the influence of the geometrical characteristics of railway lines on the traction cost and on the number of locomotives necessary to operate a train. Moreover, it does not report reference values for all cost components taken into account, but only for some of them. The new proposed cost function takes into account: staff cost; amortization, maintenance and insurance costs of locomotives and wagons; rail track usage cost; traction cost. The number of locomotives is taken into account explicitly, and the traction cost has been determined precisely given all the resistances to motion. Detailed information on the geometry of each rail line has been collected, with special concern for the lines crossing the Alps. For each Alpine line, the number of locomotives necessary to operate a train, and the maximum towed weight have been collected. The proposed cost function will be improved as follows. Firstly, times and monetary costs of shunting operations, related to adding and removing locomotives in case of double and triple traction, were not considered in the proposed cost function, and will be taken into account in a future step of this research. Secondly, the same locomotive is taken into account in the whole network, but in some lines, this results in a greater number of shunting operations. Therefore, in a future step of the research, a different locomotive will be considered on each line. From the analysis carried out, as far as the 'current scenario' is concerned, the following observations can be done. The most important rail line is the Gotthard one: because of its geometrical characteristics, as the Gotthard base tunnel has been recently opened, and because of its geographical position, as it is connected to all important destinations, not only in Switzerland, but also in Germany, France, Belgium, and The Netherlands. Moreover, the three branches of the Gotthard line, on the south of the base tunnel, across Luino, Varese, and Chiasso, connect the Gotthard to all destinations of the Italian Padan Plain. The Brenner line is currently in competition with the Gotthard and Tarvisio-Tauern lines for origins in north Italy and destinations in Central-Eastern (for example Berlin) and Southern Germany (for example Munich). The current Brenner line is disadvantaged by its geometrical characteristics: indeed, double traction on the Italian side and triple traction on the Austrian side are necessary. Other important railway lines, for Central-Eastern European destinations, are: Tarvisio, Tauri, Semmering and Karavanke.