# Railway Lines across the Alps: Analysis of Their Usage through a New Railway Link Cost Function

^{*}

## Abstract

**:**

## 1. Introduction

- Development of a new monetary cost function for freight railway links;
- Analysis of the geometry and operation characteristics of each line crossing the Alps;
- Construction of the railway network model of a large part of Europe;
- Calculation of the minimum cost paths, based on travel times, as well as monetary and generalized costs, between pairs of Italian and European railway terminals, which require crossing the Alps.

## 2. The Proposed Cost Function

#### 2.1. Monetary Cost

- -
- cost for the production of the service,
- -
- cost for purchasing the service.

#### 2.1.1. State of the Art on Cost Functions of Rail Links

- it does not take into account the different energy consumption for different values of slope, and in particular it does not take into account explicitly the resistances to motion;
- cost values of the cost function components are not in line with those proposed in the literature, and in particular with those proposed in the Baumgartner cost function, which will be described in the following section;
- the number of locomotives considered for each train, for each network link, is not clearly stated.

- electric locomotive purchase, amortization and maintenance costs [€/(km∙locomotive)].
- flat wagon (for containers) purchase and maintenance costs [€/(km∙wagon)].
- electric traction power consumption costs [€/km].

#### 2.1.2. The Proposed Monetary Cost Function

_{d}∙P) + l [km]∙{n

_{L}∙(A

_{L}+ M

_{L}+ I

_{L}) + n

_{W}∙(A

_{W}+ M

_{W}+ I

_{W}) + R + T(V

_{A},i,R

_{c})} + 2∙H∙n

_{ITU}

- C = in € per train service, is the monetary cost on each rail link, having length l and travel time t;
- P = staff cost [€/(h∙driver)]: cost of the train drivers. The staff cost is not the same in the whole Europe: in Italy an average cost per hour, for each train driver, of 35 € was detected (this cost comprises not only the net salary but also pension contributions and healthcare) (Source: Trenitalia, relazione annuale [9]), while in Germany, it resulted in a cost of 42 € per hour per driver [8]. Therefore, for the whole Europe an average staff cost of 38.5 €/h per European driver has been considered.
- n
_{d}is the number of drivers of each freight train (independently of the number of locomotives). Two train drivers per freight train are necessary in Italy, while only one driver is sufficient in the rest of Europe (sources: interviews to Rete Ferroviaria Italiana and [10]); - A
_{L}= amortization cost of one locomotive. In [8] it is reported that a reference amortization cost for a locomotive used for freight transport is 330,670 € per year. Mercitalia Rail (the main Italian rail freight company) has provided a reference value for the number of km travelled each year by a locomotive: 200,000 km. Therefore, the average amortization cost of a locomotive, expressed in €/(locomotive·km), has been estimated: 1.653 €/(locomotive·km); - M
_{L}= maintenance cost of one locomotive: in [8] it is suggested to take it as 5.5% of the amortization cost, that is: 0.091 €/(locomotive∙km); - I
_{L}= insurance cost of one locomotive. In [8], it is suggested to take it as 1.5% of the amortization cost: that is, 0.025 €/(locomotive∙km); - n
_{L}= number of locomotives. The number of locomotives depends on the gradient of the railway link, and it ranges from 1 to 3. The calculation of the number of locomotives is described in detail in the following; - A
_{W}= amortization cost of one wagon; Sgns flat wagons for containers have been considered. In [8] it is reported that the amortization cost for a Sgns is 4898 €/year. Mercitalia Rail has provided a reference value for the number of km travelled each year by a wagon of 50,000 km. Therefore, the average amortization cost of a wagon, is 0.098 €/(wagon∙km); - M
_{W}= maintenance cost of one wagon: in [8] it is suggested to take it as 10% of the amortization cost: that is, 0.0098 €/(wagon∙km); - I
_{W}= insurance cost of one wagon: in [8] it is suggested to take it as 1.3% of the amortization cost: that is, 0.0013 €/(wagon∙km); - R = railway track cost [€/km], i.e., cost for the usage of the railway infrastructure, paid by the railway transport company to the infrastructure manager. This cost has been determined, for all countries involved in this research, according to the values provided in [11] for Italy and in [12] for the other European countries. The rail track cost is different from one country to another, from a line to another, and it depends also on the weight of the train;
- H = cost of handling at rail terminals [€/ITU]. It is available on the Terminali Italia website (source: Terminali Italia [13]), and it is equal to 32.5 € per Intermodal Transport Unit (ITU) for all terminals in Italy. As far as non-Italian terminals are concerned, some terminal operators in Belgium, The Netherlands and Germany have been interviewed: they have provided similar values, equal to around 35 € per ITU;
- n
_{ITU}= number of intermodal transport units (ITUs) transported on each train; - the cost of handling a train at railway terminals is multiplied by 2 because two transshipment movements have been considered: at the two intermodal centres of origin and destination of the railway path;
- T (V
_{A},i,R_{c}) = electric traction cost [€/km]: it has been determined from the power consumption, in kWh/km, multiplied by the cost of electricity, in €/kWh. The power consumption has been calculated considering all resistances to motion. Details on the calculation of the power consumption are provided in the following. Only electrified lines have been considered. In Europe, usually, non-electrified lines show bad geometrical characteristics, particularly high gradients and sharp horizontal curves. Therefore, the diesel traction cost has not been taken into account in our research. The traction cost is a function of: the speed in rank A of freight trains on the link (V_{A}); the link grade (i); the curvature resistance (R_{c}). The resistances to motion have been calculated from the speed in rank A. The speed in rank A, in Italy, is the maximum speed for freight trains as reported in Mayer [14] (p. 49). The inertial resistance has been neglected, the traction is calculated at regime: acceleration and deceleration transitories have been neglected. Freight trains do not make scheduled intermediate stops from the origin to the destination, but, sometimes, they make some stops to let faster trains pass. We have taken into account of all these issues by taking the resistances to motion dependent on the speed in rank A, V_{A}, instead of the average speed, V_{M}.

Component | Grosso | Baumgartner | The Proposed Cost Function |
---|---|---|---|

Staff cost | Maximum, average, minimum values provided | Not taken into account in the cost function | Two reference values for the driver cost per hour were found in literature: in Italy [9] and Germany [8]. An average of these two values (38.5 €/h) has been assumed. Two drivers are necessary to operate a freight train in Italy, while only one in the rest of Europe. |

Number of locomotives | Not explicitly calculated | Not explicitly calculated | Calculated in detail. The number of locomotives depends on the grade and curve resistances of each line section and has been determined, for each rail line, from the ‘Operating Rules’ (‘Norme di Esercizio’) [15]. The operating rules used by the rail transport companies, which effectively operate the services, have been assumed. |

Amortization/rental/leasing cost of a locomotive | Maximum, average, minimum values provided | Calculated from an average purchase cost of a locomotive | In [8], an amortization cost in €/year, valid for locomotives specifically used for freight transport, is provided. In order to calculate the amortization cost in €/km, the number of km/year travelled by a locomotive for freight transport has been provided by Mercitalia Rail. |

Maintenance cost of a locomotive | Maximum, average, minimum values provided | Calculated as a percentage of the amortization cost | Calculated as a percentage of the amortization cost as suggested by [8]. |

Insurance cost of a locomotive | Maximum, average and minimum insurance costs are provided for the entire train and not for simply a locomotive | Not taken into account in the cost function | Calculated as a percentage of the amortization cost as suggested by [8]. |

Amortization cost of a flat wagon | Maximum, average, minimum values provided | Calculated from an average purchase cost of a flat wagon | In [8] an amortization cost in €/year for a flat wagon is provided. In order to calculate the amortization cost in €/km, the km/year travelled by a flat wagon have been provided by Mercitalia Rail. |

Maintenance cost of a flat wagon | Maximum, average, minimum values provided | Calculated as a percentage of the amortization cost | Calculated as a percentage of the amortization cost as suggested by [8]. |

Insurance cost of a flat wagon | Maximum, average, minimum values provided | Not taken into account in the cost function | Calculated as a percentage of the amortization cost as suggested by [8]. |

Handling cost at terminals | Maximum, average, minimum values provided | Not taken into account in the cost function | Calculated according to the costs provided by Terminali Italia [13] and by northern European terminals, as €/load unit. The handling cost at an Italian terminal is 32.5 €/load unit and between 30 and 35 €/ITU in the rest of Europe. The total number of ITUs (Intermodal Transport Units) to be considered for each train has been collected from interviews to the main MTOs operating between Italian and northern European terminals. |

Rail track cost | Maximum, average, minimum values provided | Not taken into account in the cost function | Rail track costs, in €/km, have been collected for each rail line. Rail track costs are not only different from a country to another, but often also from a line to another in the same country. |

Traction cost | Maximum, average, minimum values provided | Reference values have been provided for different values of line slope | It has been determined from the power consumption, in kWh/km, multiplied by the cost of electricity, in €/KWh. The power consumption has been calculated considering all resistances to motion on each line section. |

#### 2.1.3. Calculation of the Traction Cost

_{A},i,R

_{c}) [€/km], has been determined from the power consumption, in kWh/km, multiplied by the cost of electricity, in €/kWh.

_{A}, has been used. As stated before, we have taken into account the acceleration and deceleration transitories, by considering the resistances to motion dependent on the speed in rank A, V

_{A}, instead of the average speed, V

_{M.}The resistances were determined according to the methodology proposed in Vicuna [17], but the formulas for resistances, which were old, have been updated.

#### 2.1.4. Maximum Towable Weight on a Railway Line Section and ‘Lines with Special Operation Characteristics’

- (1)
- The maximum towable weight due to the resistance of train couplers.

- (2)
- The maximum towable weight due to the maximum tractive effort of the chosen locomotive.

- if the sum of the grade and curve resistances is less than or equal to 12 N/kN, only one locomotive has been used;
- if the sum of the grade and curve resistances is more than 12 and less than 20 N/kN, two locomotives (E189) have been used;
- if the limit of 20 N/kN is overcome on a secondary line (for example the Savona–Altare or the Parma–La Spezia lines), this line has not been included in the modelled rail network;
- if the limit of 20 N/kN is overcome on a main line (for example, the main lines crossing the Alps, such as the Brennero, the Frejus and the Semmering lines), information has been collected, from freight railway companies which operate along the given Alpine line, about how the trains are practically operated: in the following such lines will be called ‘line with special operation characteristics’. In our model, on ‘line with special operation characteristics’, we consider the same number of locomotives as used by the MTOs in the real operations to tow a weight of 1234 tons.

#### 2.2. The Calculation of Travel Times

_{m}:

_{A}is the speed in rank A: the maximum speed for freight trains.

_{A}= 0.8636∙V

_{C}+ 2.8732 [km/h]

#### 2.3. Generalized Cost of Rail Links

_{g}= C

_{m}+ VOT·t

- -
- C
_{g}= generalized cost (€), - -
- C
_{m}= monetary cost (€), - -
- VOT = value of time (€/h),
- -
- t = time (h).

## 3. Construction of the European Rail Network Model and Data Collection

- Current scenario

- Project scenario

#### 3.1. Detailed Characteristics of the Alpine Railway Lines Taken into Account in This Study

#### 3.1.1. Gotthard Line and Its Branches

#### 3.1.2. Brenner Line

#### 3.1.3. Turin—Lyon ‘Frejus’ Line

- The new Frejus base tunnel (sometimes called also Moncenisio base tunnel), between Bussoleno and St. Jean De Maurienne, 57.5 km long, of which 45 in France and 12.5 in Italy, with a maximum sum of grade and curve resistances of 13 N/kN (which does not take place in the tunnel itself but in the two, short, adduction ramps on both side of the tunnel). This tunnel will be operated in single traction by the majority of MTOs, but given the locomotive taken into account in this paper, double traction has been considered.
- A new line connecting the freight village of Turin/Orbassano with Bussoleno: this line will be constructed in order to shorten the path between these two places;
- A new line connecting S. Jean de Maurienne with Avressieux, and the duplication of the existing line between Avressieux and Saint Andrè Le Gaz: this line will also shorten considerably the current path, which follows the valley floors therefore it is quite long.

#### 3.1.4. Sempione and Lötschberg Lines

#### 3.1.5. The Tarvisio, Semmering and Tauern Lines

- new Koralmbahn, between Klagenfurt and Graz;
- upgrading of the old line between Graz and Bruck an der Mur
- upgrading of the old line between Bruck an der Mur and Murzzuschlag
- Semmering base tunnel between Murzzuschlag and Gloggnitz.

#### 3.1.6. The Lines Trieste–Divaca, Koper–Divaca, Rijeka–Pivka, and Rijeka–Zagreb

- Line Trieste–Divaca: The railway line from Trieste Campo Marzio to Villa Opicina (border Italy—Slovenia), 15 km, is a part of the line Trieste–Divaca; it shows a sum of grade and curve resistances of 25 N/kN. This railway is part of the Trieste—Ljubljana path and it is operated with triple traction from Trieste Campo Marzio to Villa Opicina (Source: interviews to Alpe Adria, the main MTO operating railway connections to/from the Trieste Campo Marzio rail terminal) and in single traction in the opposite direction. Between Villa Opicina and Ljubljana, instead, the sum of grade and curve resistances is below 20 N/kN and the line is operated with double traction in both directions.
- Line Koper–Divaca: A portion, of about 18 km, of the line from Koper to Divaca, shows a maximum sum of grade and curve resistances of 23 N/kN. This line is operated in double traction (source: interviews to Metrans, the main MTO operating on this line) from Koper to Divaca and single traction in the opposite direction. But, the second locomotive is not added at the beginning of the train but at the end of the train, in order to reduce the stress on train couplers. This line is part of the Koper—Ljubljana path.
- Line Rijeka–Pivka: A portion of 15 km, close to Rijeka port (from Rijeka to Jurdani), of the line Rijeka–Pivka, shows a sum of grade and curve resistances of 27 N/kN. This line is operated with triple traction in this line portion of 15 km, and with double traction in the rest of the line. In the opposite direction, i.e., from Pivka ro Rijeka, the entire line is operated in double traction (source: interviews to Metrans). This line is a part of the Rijeka—Ljubljana path.
- Line Rijeka–Zagreb: A portion of about 25 km, between Rijeka and Moravice, of the line from Rijeka to Zagreb, shows a maximum sum of grade and curve resistances of 28 N/kN. Considering the entire line from Rijeka to Zagreb: the line is operated with triple traction from Rijeka to Moravice and the rest of the line is operated with double traction; while in the opposite direction the entire line is operated with double traction (source: interviews to Metrans).

- New line Trieste–Divaca (Figure 3): several projects have been proposed, but none is approved yet. The new line will have a maximum slope of 17‰, and a maximum sum of grade and curve resistances of 18 N/kN. This line will be operated in double traction from Trieste to Divaca and single traction in the opposite direction. It is not possible to design a line with lower slopes because of geographical constraints due to the high degree of urbanization of the Trieste area.
- New line Koper–Divaca (Figure 3): a new line is under construction (since March 2019), which will be long 27 km, against the 39 km of the line currently in operation, and its sum of grade and curve resistances will be 10 N/kN. This line is strongly supported by the Slovenian government because it will improve the competitiveness of the port of Koper against that of Trieste.
- New line Rijeka–Zagreb: A new railway line between Rijeka and Moravice (Figure 3), which is part of the Rijeka–Zagreb line, is planned. The new line will have a maximum slope of 12.5‰ and a maximum sum of grade and curve resistances of 13 N/kN. It will be operated in double traction because the rail Moravice—Karlovac, which is also part of the Rijeka–Zagreb line, requires double traction. However, an improvement of the entire line Rijeka–Zagreb, that is, also between Moravice and Zagreb, is planned, also because the great majority of this line has only one track. However, as this improvement is planned for a distant future, it was not taken into account in the ‘project scenario’.

#### 3.1.7. The Arlberg Line

#### 3.1.8. The Karavanke Line

## 4. Calculation of Minimum Cost Paths between Pairs of Italian and European Terminals

- Italy: Turin (Orbassano freight village), Novara, Rivalta Scrivia, Busto Arsizio–Gallarate, Milan Smistamento, Parma, Verona, Bologna, Padua, Venice, Trieste, Genoa, La Spezia, Leghorn, Prato (Prato freight village is close to Florence).
- Germany: Munich, Stuttgart, Duisburg, Berlin, Hamburg, Bremerhaven.
- France: Le Havre, Paris, Lyon, Marseilles, Avignon rail junction (beginning of the rail corridor to Barcelona, Avignon rail junction is shown in Figure 1).
- Belgium and The Netherlands: Antwerp, Rotterdam.
- Austria and Switzerland: Vienna, Zurich and Basel.
- Central-Eastern Europe: Koper, Rijeka, Ljubljana, Zagreb, Belgrade, Budapest, Bratislava, Prague.

## 5. Results

#### 5.1. Usage of Alpine Passes

#### 5.2. Travel Times, Monetary Costs and Generalized Costs in the Current and in the Project Scenarios

## 6. Discussion and Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

**Table A1.**Alpine Passes crossed by minimum travel time and by minimum cost routes, in the ‘current scenario’ and in the ‘project scenario’.

O–D Pair | Current Scenario | Project Scenario | |
---|---|---|---|

Turin—Paris | Travel time | Frejus old tunnel | New Frejus base tunnel |

Monetary cost | Frejus old tunnel | New Frejus base tunnel | |

Generalized cost | Frejus old tunnel | New Frejus base tunnel | |

Paris—Turin | Travel time | Frejus old tunnel | New Frejus base tunnel |

Monetary cost | Frejus old tunnel | New Frejus base tunnel | |

Generalized cost | Frejus old tunnel | New Frejus base tunnel | |

Genoa—Paris | Travel time | Giovi Pass, Frejus old tunnel | Third Pass of Giovi, New Frejus base tunnel |

Monetary cost | Giovi Pass, Frejus old tunnel | Third Pass of Giovi, New Frejus base tunnel | |

Generalized cost | Giovi Pass, Frejus old tunnel | Third Pass of Giovi, New Frejus base tunnel | |

Paris—Genoa | Travel time | Frejus old tunnel, Giovi Pass | New Frejus base tunnel, Third Pass of Giovi |

Monetary cost | Frejus old tunnel, Giovi Pass | New Frejus base tunnel, Third Pass of Giovi | |

Generalized cost | Frejus old tunnel, Giovi Pass | New Frejus base tunnel, Third Pass of Giovi | |

Leghorn—Paris | Travel time | Giovi Pass, Frejus old tunnel | Third Pass of Giovi, New Frejus base tunnel |

Monetary cost | Giovi Pass, Frejus old tunnel | Third Pass of Giovi, New Frejus base tunnel | |

Generalized cost | Giovi Pass, Frejus old tunnel | Third Pass of Giovi, New Frejus base tunnel | |

Paris—Leghorn | Travel time | Frejus old tunnel, Giovi Pass | New Frejus base tunnel, Third Pass of Giovi |

Monetary cost | Frejus old tunnel, Giovi Pass | New Frejus base tunnel, Third Pass of Giovi | |

Generalized cost | Frejus old tunnel, Giovi Pass | New Frejus base tunnel, Third Pass of Giovi | |

Milan—Avignon Junction | Travel time | Giovi Pass, Ventimiglia | New Frejus base tunnel |

Monetary cost | Giovi Pass, Ventimiglia | New Frejus base tunnel | |

Generalized cost | Giovi Pass, Ventimiglia | New Frejus base tunnel | |

Avignon junction—Milan | Travel time | Ventimiglia, Giovi Pass | New Frejus base tunnel |

Monetary cost | Ventimiglia, Giovi Pass | New Frejus base tunnel | |

Generalized cost | Ventimiglia, Giovi Pass | New Frejus base tunnel | |

Turin—Rotterdam | Travel time | Sempione, Lötschberg | New Frejus base tunnel |

Monetary cost | Frejus old tunnel | New Frejus base tunnel | |

Generalized cost | Frejus old tunnel | New Frejus base tunnel | |

Rotterdam—Turin | Travel time | Lötschberg, Sempione | New Frejus base tunnel |

Monetary cost | Frejus old tunnel | New Frejus base tunnel | |

Generalized cost | Frejus old tunnel | New Frejus base tunnel | |

Novara—Paris | Travel time | Luino, Gotthard base tunnel | New Frejus base tunnel |

Monetary cost | Luino, Gotthard base tunnel | New Frejus base tunnel | |

Generalized cost | Luino, Gotthard base tunnel | New Frejus base tunnel | |

Paris—Novara | Travel time | Gotthard base tunnel, Luino | New Frejus base tunnel |

Monetary cost | Gotthard base tunnel, Luino | New Frejus base tunnel | |

Generalized cost | Gotthard base tunnel, Luino | New Frejus base tunnel | |

Novara—Antwerp/Rotterdam | Travel time | Luino, Gotthard base tunnel | Luino, Gotthard base tunnel |

Monetary cost | Luino, Gotthard base tunnel | Luino, Gotthard base tunnel | |

Generalized cost | Luino, Gotthard base tunnel | Luino, Gotthard base tunnel | |

Antwerp/Rotterdam—Novara | Travel time | Gotthard base tunnel, Luino | Gotthard base tunnel, Luino |

Monetary cost | Gotthard base tunnel, Luino | Gotthard base tunnel, Luino | |

Generalized cost | Gotthard base tunnel, Luino | Gotthard base tunnel, Luino | |

Turin—Hamburg | Travel time | Sempione, Lötschberg | Sempione, Lötschberg |

Monetary cost | Sempione, Lötschberg | Sempione, Lötschberg | |

Generalized cost | Sempione, Lötschberg | Sempione, Lötschberg | |

Hamburg—Turin | Travel time | Lötschberg, Sempione | Lötschberg, Sempione |

Monetary cost | Lötschberg, Sempione | Lötschberg, Sempione | |

Generalized cost | Lötschberg, Sempione | Lötschberg, Sempione | |

Milan—Paris | Travel time | Chiasso, Ceneri Pass, Gotthard Base tunnel | Chiasso, New Ceneri base tunnel, Gotthard base tunnel |

Monetary cost | Chiasso, Ceneri Pass, Gotthard Base tunnel | Chiasso, New Ceneri base tunnel, Gotthard base tunnel | |

Generalized cost | Chiasso, Ceneri Pass, Gotthard Base tunnel | Chiasso, New Ceneri base tunnel, Gotthard base tunnel | |

Paris—Milan | Travel time | Gotthard Base Tunnel, Ceneri Pass, Chiasso | Gotthard Base Tunnel, New Ceneri base tunnel, Chiasso |

Monetary cost | Gotthard Base Tunnel, Ceneri Pass, Chiasso | Gotthard Base Tunnel, New Ceneri base tunnel, Chiasso | |

Generalized cost | Gotthard Base Tunnel, Ceneri Pass, Chiasso | Gotthard Base Tunnel, New Ceneri base tunnel, Chiasso | |

Milan—Antwerp/Rotterdam | Travel time | Chiasso, Ceneri Pass, Gotthard Base tunnel | Chiasso, New Ceneri base tunnel, Gotthard base tunnel |

Monetary cost | Chiasso, Ceneri Pass, Gotthard Base tunnel | Chiasso, New Ceneri base tunnel, Gotthard base tunnel | |

Generalized cost | Chiasso, Ceneri Pass, Gotthard Base tunnel | Chiasso, New Ceneri base tunnel, Gotthard base tunnel | |

Antwerp/Rotterdam—Milan | Travel time | Gotthard Base Tunnel, Ceneri Pass, Chiasso | Gotthard Base Tunnel, New Ceneri base tunnel, Chiasso |

Monetary cost | Gotthard Base Tunnel, Ceneri Pass, Chiasso | Gotthard Base Tunnel, New Ceneri base tunnel, Chiasso | |

Generalized cost | Gotthard Base Tunnel, Ceneri Pass, Chiasso | Gotthard Base Tunnel, New Ceneri base tunnel, Chiasso | |

Milan—Duisburg | Travel time | Chiasso, Ceneri Pass, Gotthard Base tunnel | Chiasso, New Ceneri base tunnel, Gotthard base tunnel |

Monetary cost | Chiasso, Ceneri Pass, Gotthard Base tunnel | Chiasso, New Ceneri base tunnel, Gotthard base tunnel | |

Generalized cost | Chiasso, Ceneri Pass, Gotthard Base tunnel | Chiasso, New Ceneri base tunnel, Gotthard base tunnel | |

Duisburg—Milan | Travel time | Gotthard Base Tunnel, Ceneri Pass, Chiasso | Gotthard Base Tunnel, New Ceneri base tunnel, Chiasso |

Monetary cost | Gotthard Base Tunnel, Ceneri Pass, Chiasso | Gotthard Base Tunnel, New Ceneri base tunnel, Chiasso | |

Generalized cost | Gotthard Base Tunnel, Ceneri Pass, Chiasso | Gotthard Base Tunnel, New Ceneri base tunnel, Chiasso | |

Milan—Hamburg | Travel time | Chiasso, Ceneri Pass, Gotthard Base tunnel | Chiasso, New Ceneri base tunnel, Gotthard base tunnel |

Monetary cost | Chiasso, Ceneri Pass, Gotthard Base tunnel | Chiasso, New Ceneri base tunnel, Gotthard base tunnel | |

Generalized cost | Chiasso, Ceneri Pass, Gotthard Base tunnel | Chiasso, New Ceneri base tunnel, Gotthard base tunnel | |

Hamburg/Milan | Travel time | Gotthard Base Tunnel, Ceneri Pass, Chiasso | Gotthard Base Tunnel, New Ceneri base tunnel, Chiasso |

Monetary cost | Gotthard Base Tunnel, Ceneri Pass, Chiasso | Gotthard Base Tunnel, New Ceneri base tunnel, Chiasso | |

Generalized cost | Gotthard Base Tunnel, Ceneri Pass, Chiasso | Gotthard Base Tunnel, New Ceneri base tunnel, Chiasso | |

Milan—Berlin | Travel time | Chiasso, Ceneri Pass, Gotthard Base tunnel | Chiasso, New Ceneri base tunnel, Gotthard base tunnel |

Monetary cost | Chiasso, Ceneri Pass, Gotthard Base tunnel | Chiasso, New Ceneri base tunnel, Gotthard base tunnel | |

Generalized cost | Chiasso, Ceneri Pass, Gotthard Base tunnel | Chiasso, New Ceneri base tunnel, Gotthard base tunnel | |

Berlin—Milan | Travel time | Gotthard Base Tunnel, Ceneri Pass, Chiasso | Gotthard Base Tunnel, New Ceneri base tunnel, Chiasso |

Monetary cost | Gotthard Base Tunnel, Ceneri Pass, Chiasso | Gotthard Base Tunnel, New Ceneri base tunnel, Chiasso | |

Generalized cost | Gotthard Base Tunnel, Ceneri Pass, Chiasso | Gotthard Base Tunnel, New Ceneri base tunnel, Chiasso | |

Genoa—Zurich | Travel time | Giovi Pass, Luino, Gotthard base tunnel | Third Pass of Giovi, Luino, Gotthard base tunnel |

Monetary cost | Giovi Pass, Luino, Gotthard base tunnel | Third Pass of Giovi, Luino, Gotthard base tunnel | |

Generalized cost | Giovi Pass, Luino, Gotthard base tunnel | Third Pass of Giovi, Luino, Gotthard base tunnel | |

Zurich—Genoa | Travel time | Gotthard base tunnel, Luino, Giovi Pass | Gotthard base tunnel, Luino, Third Pass of Giovi |

Monetary cost | Gotthard base tunnel, Luino, Giovi Pass | Gotthard base tunnel, Luino, Third Pass of Giovi | |

Generalized cost | Gotthard base tunnel, Luino, Giovi Pass | Gotthard base tunnel, Luino, Third Pass of Giovi | |

Turin—Munich | Travel time | Luino, Gotthard base tunnel, Zimmerberg old line | Brenner base tunnel |

Monetary cost | Luino, Gotthard base tunnel, Zimmerberg old line | Brenner base tunnel | |

Generalized cost | Luino, Gotthard base tunnel, Zimmerberg old line | Brenner base tunnel | |

Munich—Turin | Travel time | Zimmerberg old line, Gotthard base tunnel, Luino | Brenner base tunnel |

Monetary cost | Zimmerberg old line, Gotthard base tunnel, Luino | Brenner base tunnel | |

Generalized cost | Zimmerberg old line, Gotthard base tunnel, Luino | Brenner base tunnel | |

Milan—Munich | Travel time | Brenner Pass | Brenner base tunnel |

Monetary cost | Brenner Pass | Brenner base tunnel | |

Generalized cost | Brenner Pass | Brenner base tunnel | |

Munich—Milan | Travel time | Brenner Pass | Brenner base tunnel |

Monetary cost | Brenner Pass | Brenner base tunnel | |

Generalized cost | Brenner Pass | Brenner base tunnel | |

Leghorn—Berlin/Munich | Travel time | Brenner Pass | Brenner base tunnel |

Monetary cost | Brenner Pass | Brenner base tunnel | |

Generalized cost | Brenner Pass | Brenner base tunnel | |

Berlin/Munich—Leghorn | Travel time | Brenner Pass | Brenner base tunnel |

Monetary cost | Brenner Pass | Brenner base tunnel | |

Generalized cost | Brenner Pass | Brenner base tunnel | |

Venice—Munich | Travel time | Tarvisio, Tauern | Brenner base tunnel |

Monetary cost | Tarvisio, Tauern | Brenner base tunnel | |

Generalized cost | Tarvisio, Tauern | Brenner base tunnel | |

Munich—Venice | Travel time | Tauern, Tarvisio | Brenner base tunnel |

Monetary cost | Tauern, Tarvisio | Brenner base tunnel | |

Generalized cost | Tauern, Tarvisio | Brenner base tunnel | |

Leghorn—Prague | Travel time | Tarvisio, Tauern | Brenner base tunnel |

Monetary cost | Tarvisio, Tauern | Brenner base tunnel | |

Generalized cost | Tarvisio, Tauern | Brenner base tunnel | |

Prague—Leghorn | Travel time | Tauern, Tarvisio | Brenner base tunnel |

Monetary cost | Tauern, Tarvisio | Brenner base tunnel | |

Generalized cost | Tauern, Tarvisio | Brenner base tunnel | |

Milan—Vienna | Travel time | Tarvisio, Klagenfurt—Bruck old line, Semmering Pass | Tarvisio, Koralmbahn, Semmering base tunnel |

Monetary cost | Tarvisio, Klagenfurt—Bruck old line, Semmering Pass | Tarvisio, Koralmbahn, Semmering base tunnel | |

Generalized cost | Tarvisio, Klagenfurt—Bruck old line, Semmering Pass | Tarvisio, Koralmbahn, Semmering base tunnel | |

Vienna—Milan | Travel time | Semmering Pass, Bruck—Klagenfurt old line, Tarvisio | Semmering base tunnel, Koralmbahn, Tarvisio |

Monetary cost | Semmering Pass, Bruck—Klagenfurt old line, Tarvisio | Semmering base tunnel, Koralmbahn, Tarvisio | |

Generalized cost | Semmering Pass, Bruck—Klagenfurt old line, Tarvisio | Semmering base tunnel, Koralmbahn, Tarvisio | |

Milan—Budapest | Travel time | Tarvisio, Klagenfurt—Bruck old line, Semmering Pass | Tarvisio, Koralmbahn, Semmering base tunnel |

Monetary cost | Villa Opicina, Divaca, Ljubljana, Ormoz | Villa Opicina, Divaca, Ljubljana, Ormoz | |

Generalized cost | Villa Opicina, Divaca, Ljubljana, Ormoz | Villa Opicina, Divaca, Ljubljana, Ormoz | |

Budapest—Milan | Travel time | Semmering Pass, Bruck—Klagenfurt old line, Tarvisio | Semmering base tunnel, Koralmbahn, Tarvisio |

Monetary cost | Ormoz, Ljubljana, Divaca, Villa Opicina | Ormoz, Ljubljana, Divaca, Villa Opicina | |

Generalized cost | Ormoz, Ljubljana, Divaca, Villa Opicina | Ormoz, Ljubljana, Divaca, Villa Opicina | |

Trieste—Vienna | Travel time | Tarvisio, Klagenfurt-Bruck old line, Semmering Pass | Tarvisio, Koralmbahn, Semmering base tunnel |

Monetary cost | Villa Opicina, Divaca, Ljubljana, Maribor, Semmering Pass | New Trieste—Divaca line, Ljubljana, Maribor, Semmering base tunnel | |

Generalized cost | Tarvisio, Klagenfurt-Bruck old line, Semmering Pass | Tarvisio, Koralmbahn, Semmering base tunnel | |

Vienna—Trieste | Travel time | Semmering Pass, Bruck-Klagenfurt old line, Tarvisio | Semmering base tunnel, Koralmbahn, Tarvisio |

Monetary cost | Semmering Pass, Maribor, Ljubljana, Divaca, Villa Opicina | Semmering base tunnel, Maribor, Ljubljana, new Divaca—Trieste line | |

Generalized cost | Semmering Pass, Bruck-Klagenfurt old line, Tarvisio | Semmering base tunnel, Koralmbahn, Tarvisio | |

Vienna—Koper | Travel time | Semmering Pass, Bruck-Klagenfurt old line, Tarvisio, Villa Opicina, Divaca-Koper old line | Semmering base tunnel, Koralmbahn, Tarvisio, Villa Opicina, Divaca-Koper new line |

Monetary cost | Semmering Pass, Maribor, Ljubljana, Divaca-Koper old line | Semmering base tunnel, Maribor, Ljubljana, Divaca-Koper new line | |

Generalized cost | Semmering Pass, Maribor, Ljubljana, Divaca-Koper old line | Semmering base tunnel, Maribor, Ljubljana, Divaca-Koper new line | |

Koper—Vienna | Travel time | Koper-Divaca old line, Villa Opicina, Tarvisio, Klagenfurt-Bruck old line, Semmering Pass | Koper-Divaca new line, Villa Opicina, Tarvisio, Koralmbahn, Semmering base tunnel |

Monetary cost | Koper-Divaca old line, Ljubljana, Maribor, Semmering Pass | Koper-Divaca new line, Ljubljana, Maribor, Semmering base tunnel | |

Generalized cost | Koper-Divaca old line, Ljubljana, Maribor, Semmering Pass | Koper- Divaca new line, Ljubljana, Maribor, Semmering base tunnel | |

Hamburg—Zagreb | Travel time | Tauern, Karavanke, Ljubljana | Semmering base tunnel, Graz-Maribor line |

Monetary cost | Tauern, Karavanke, Ljubljana | Semmering base tunnel, Graz-Maribor line | |

Generalized cost | Tauern, Karavanke, Ljubljana | Semmering base tunnel, Graz-Maribor line | |

Zagreb—Hamburg | Travel time | Ljubljana, Karavanke, Tauern | Maribor-Graz line, Semmering base tunnel |

Monetary cost | Ljubljana, Karavanke, Tauern | Maribor-Graz line, Semmering base tunnel | |

Generalized cost | Ljubljana, Karavanke, Tauern | Maribor-Graz line, Semmering base tunnel | |

Vienna—Lyon | Travel time | Not through the Alps but via Munich, Bregenz, Zurich, Bern, Lausanne | Semmering base tunnel, Koralmbahn, Tarvisio, new Frejus base tunnel |

Monetary cost | Semmering Pass, Bruck-Klagenfurt old line, Tarvisio, Frejus old tunnel | Semmering base tunnel, Koralmbahn, Tarvisio, new Frejus base tunnel | |

Generalized cost | Not through the Alps but via Munich, Bregenz, Zurich, Bern, Lausanne | Semmering base tunnel, Koralmbahn, Tarvisio, new Frejus base tunnel | |

Lyon—Vienna | Travel time | Not through the Alps but via Lausanne, Bern, Zurich, Bregenz, Munich | New Frejus base tunnel, Tarvisio, Koralmbahn, Semmering base tunnel |

Monetary cost | Frejus old line, Tarvisio, Klagenfurt—Bruck old line, Semmering Pass | New Frejus base tunnel, Tarvisio, Koralmbahn, Semmering base tunnel | |

Generalized cost | Not through the Alps but via Lausanne, Bern, Zurich, Bregenz, Munich | New Frejus base tunnel, Tarvisio, Koralmbahn, Semmering base tunnel | |

Munich—Avignon rail junction | Travel time | Not through the Alps but via Bregenz, Zurich, Bern, Lausanne | Brenner base tunnel, new Frejus base tunnel |

Monetary cost | Not through the Alps but via Bregenz, Zurich, Bern, Lausanne | Brenner base tunnel, new Frejus base tunnel | |

Generalized cost | Not through the Alps but via Bregenz, Zurich, Bern, Lausanne | Brenner base tunnel, new Frejus base tunnel | |

Avignon rail junction—Munich | Travel time | Not through the Alps but via Lausanne, Bern, Zurich, Bregenz | New Frejus base tunnel, Brenner base tunnel |

Monetary cost | Not through the Alps but via Lausanne, Bern, Zurich, Bregenz | New Frejus base tunnel, Brenner base tunnel | |

Generalized cost | Not through the Alps but via Lausanne, Bern, Zurich, Bregenz | New Frejus base tunnel, Brenner base tunnel | |

Munich—Marseilles | Travel time | Brenner Pass, Giovi Pass, Ventimiglia | Brenner base tunnel, Third Pass of Giovi, Ventimiglia |

Monetary cost | Brenner Pass, Giovi Pass, Ventimiglia | Brenner base tunnel, Third Pass of Giovi, Ventimiglia | |

Generalized cost | Brenner Pass, Giovi Pass, Ventimiglia | Brenner base tunnel, Third Pass of Giovi, Ventimiglia | |

Marseilles—Munich | Travel time | Ventimiglia, Giovi Pass, Brenner Pass | Ventimiglia, Third Pass of Giovi, Brenner base tunnel |

Monetary cost | Ventimiglia, Giovi Pass, Brenner Pass | Ventimiglia, Third Pass of Giovi, Brenner base tunnel | |

Generalized cost | Ventimiglia, Giovi Pass, Brenner Pass | Ventimiglia, Third Pass of Giovi, Brenner base tunnel |

## Appendix B

**Table A2.**Travel times [h], monetary costs [€/train] and generalized costs [€/train], in the ‘current scenario’ and in the ‘project scenario’, ordered by the considered O–D pairs.

O–D Pair | Travel Time (h) | Monetary Cost (€/train) | Generalized Cost (€/train) | |||
---|---|---|---|---|---|---|

Current Scenario | Project Scenario | Current Scenario | Project Scenario | Current Scenario | Project Scenario | |

Turin—Paris | 11.14 | 10.34 | 15,553.7 | 14,788.0 | 23,049.5 | 21,744.5 |

Paris—Turin | 11.07 | 10.33 | 15,492.3 | 14,782.2 | 22,994.5 | 21,739.5 |

Genoa—Paris | 13.40 | 12.26 | 17,941.1 | 16,866.4 | 26,967.5 | 25,113.5 |

Paris—Genoa | 13.33 | 12.25 | 17,898.4 | 16,833.5 | 26,928.5 | 25,083.5 |

Leghorn—Paris | 16.30 | 15.16 | 20,398.3 | 19,323.6 | 31,431.5 | 29,577.5 |

Paris—Leghorn | 16.27 | 15.11 | 20,355.7 | 19,290.7 | 31,392.5 | 29,547.5 |

Milan—Avignon rail junction | 8.97 | 8.17 | 13,186.1 | 12,420.4 | 19,236.5 | 17,931.5 |

Avignon rail junction—Milan | 8.93 | 8.15 | 13,124.7 | 12,414.6 | 19,181.5 | 17,926.5 |

Turin—Rotterdam | 16.87 | 16.28 | 21,347.1 | 20,581.4 | 33,261.5 | 31,956.5 |

Rotterdam—Turin | 16.83 | 16.25 | 21,285.7 | 20,575.7 | 33,206.5 | 31,951.5 |

Turin—Antwerp | 15.83 | 15.24 | 19,694.8 | 18,929.1 | 30,577.5 | 29,272.5 |

Antwerp—Turin | 15.79 | 15.24 | 19,633.4 | 18,923.4 | 30,522.5 | 29,267.5 |

Novara—Paris | 11.99 | 11.54 | 16,938.9 | 16,173.2 | 25,014.5 | 23,929.5 |

Paris—Novara | 11.93 | 11.52 | 16,877.5 | 16,167.5 | 24,998.5 | 23,924.5 |

Novara—Antwerp | 14.67 | 14.67 | 19,281.3 | 19,281.3 | 29,495.5 | 29,495.5 |

Antwerp—Novara | 14.64 | 14.64 | 18,994.7 | 18,994.7 | 28,918.5 | 28,918.5 |

Novara—Rotterdam | 15.71 | 15.71 | 20,933.4 | 20,933.4 | 32,179.5 | 32,179.5 |

Rotterdam—Novara | 15.68 | 15.68 | 20,647.2 | 20,647.2 | 31,602.5 | 31,602.5 |

Turin—Hamburg | 18.55 | 18.55 | 27,055.3 | 27,055.3 | 39,137.5 | 39,137.5 |

Hamburg—Turin | 18.52 | 18.52 | 27,048.9 | 27,048.9 | 39,121.5 | 39,121.5 |

Milan—Paris | 12.18 | 11.98 | 17,692.9 | 17,080.2 | 25,773.5 | 25,067.5 |

Paris—Milan | 12.15 | 11.97 | 17,613.2 | 16,986.1 | 25,691.5 | 24,964.5 |

Milan—Antwerp | 14.56 | 14.36 | 19,462.7 | 18,849.9 | 29,273.5 | 28,567.5 |

Antwerp—Milan | 14.50 | 14.33 | 19,382.9 | 18,755.9 | 29,191.5 | 28,464.5 |

Milan—Rotterdam | 15.60 | 15.40 | 21,115.0 | 20,502.2 | 31,957.5 | 31,251.5 |

Rotterdam—Milan | 15.56 | 15.37 | 21,035.2 | 20,408.2 | 31,875.5 | 31,148.5 |

Milan—Duisburg | 12.81 | 12.61 | 20,290.5 | 19,677.7 | 28,590.5 | 27,884.5 |

Duisburg—Milan | 12.75 | 12.55 | 20,210.7 | 19,583.6 | 28,508.5 | 27,781.5 |

Milan—Hamburg | 17.28 | 17.08 | 26,254.0 | 25,641.2 | 37,430.5 | 36,724.5 |

Hamburg—Milan | 17.24 | 17.05 | 26,174.2 | 25,547.1 | 37,348.5 | 36,621.5 |

Milan—Berlin | 16.59 | 16.22 | 25,060.2 | 24,130.1 | 36,248.5 | 34,679.5 |

Berlin—Milan | 16.53 | 16.17 | 24,839.4 | 23,987.2 | 36,051.5 | 34,493.5 |

Genoa—Zurich | 6.05 | 5.57 | 10,476.1 | 10,143.7 | 14,542.5 | 13,860.5 |

Zurich—Genoa | 6.06 | 5.54 | 10,488.4 | 10,110.1 | 14,542.5 | 13,819.5 |

Turin—Munich | 10.52 | 9.84 | 16,014.0 | 15,084.0 | 22,976.5 | 21,611.5 |

Munich—Turin | 10.48 | 9.82 | 15,793.2 | 14,941.1 | 22,960.5 | 21,425.5 |

Milan—Munich | 8.30 | 7.36 | 13,549.5 | 12,619.5 | 19,032.5 | 17,463.5 |

Munich—Milan | 8.04 | 7.31 | 13,328.7 | 12,476.5 | 18,835.5 | 17,277.5 |

Livorno—Berlin | 19.23 | 18.29 | 27,161.9 | 26,231.8 | 39,759.5 | 38,190.5 |

Berlin—Livorno | 19.18 | 18.25 | 26,941.0 | 26,088.9 | 39,562.5 | 38,004.5 |

Livorno—Munich | 10.37 | 9.43 | 15,651.2 | 14,721.1 | 22,543.5 | 20,974.5 |

Munich—Livorno | 10.26 | 9.37 | 15,430.3 | 14,578.2 | 22,346.5 | 20,788.5 |

Venice—Munich | 7.53 | 7.08 | 13,088.2 | 12,158.2 | 18,257.5 | 16,829.5 |

Munich—Venice | 7.47 | 7.01 | 12,867.4 | 12,015.3 | 18,201.5 | 16,643.5 |

Leghorn—Prague | 16.62 | 15.68 | 23,573.3 | 22,643.2 | 34,514.5 | 32,945.5 |

Prague—Leghorn | 16.57 | 15.61 | 23,352.4 | 22,500.3 | 34,317.5 | 32,759.5 |

Milan—Vienna | 11.32 | 10.18 | 16,727.6 | 16,226.5 | 24,349.5 | 22,932.5 |

Vienna—Milan | 11.48 | 10.21 | 16,806.5 | 16,270.7 | 24,419.5 | 22,972.5 |

Milan—Budapest | 14.46 | 13.22 | 18,074.1 | 18,074.1 | 28,797.5 | 27,380.5 |

Budapest—Milan | 14.51 | 13.25 | 18,125.3 | 18,125.3 | 28,867.5 | 27,420.5 |

Trieste—Vienna | 8.14 | 6.90 | 12,107.5 | 11,450.2 | 18,141.5 | 16,724.5 |

Vienna- Trieste | 8.16 | 6.92 | 12,134.2 | 11,400.3 | 18,211.5 | 16,764.5 |

Vienna—Koper | 9.61 | 8.41 | 12,287.9 | 11,357.2 | 19,620.5 | 17,340.5 |

Koper—Vienna | 9.69 | 8.49 | 12,340.6 | 11,401.2 | 19,667.5 | 17,379.5 |

Hamburg—Zagreb | 21.06 | 20.18 | 28,858.6 | 28,597.6 | 42,684.5 | 42,461.5 |

Zagreb—Hamburg | 21.13 | 20.22 | 29,040.8 | 28,836.2 | 42,848.5 | 42,607.5 |

Vienna—Lyon | 18.08 | 16.89 | 24,347.8 | 23,046.3 | 36,996.5 | 34,244.5 |

Lyon—Vienna | 17.99 | 16.86 | 24,207.5 | 22,996.3 | 36,871.5 | 34,199.5 |

Munich—Avignon rail junction | 15.93 | 15.45 | 21,636.4 | 20,834.4 | 32,675.5 | 31,146.5 |

Avignon rail junction—Munich | 15.99 | 15.52 | 21,652.9 | 20,971.6 | 32,675.5 | 31,327.5 |

Munich—Marseilles | 15.96 | 14.78 | 20,882.5 | 19,764.5 | 31,757.5 | 29,832.5 |

Marseilles—Munich | 16.25 | 14.95 | 21,084.6 | 19,934.6 | 31,938.5 | 30,043.5 |

## References

- Kim, N.S.; Van Wee, B. The relative importance of factors that influence the break-even distance of intermodal freight transport systems. J. Transp. Geogr.
**2011**, 19, 859–875. [Google Scholar] [CrossRef] - Brümmersted, K.; Flitsch, V.; Jahn, C. Cost function in Freight Transport Models. In Operational Excellence in Logistics and Supply Chains; Blecker, T., Kersten, W., Ringle, C.M., Eds.; Epubli GmbH: Berlin, Germany, 2015. [Google Scholar]
- Sawadogo, M.; Anciaux, D.; Roy, D. Sustainable Intermodal Freight by route choice with practicality constraints. In Proceedings of the European Transport Conference, Glasgow, Scotland, 10–12 October 2011; pp. 1–20. [Google Scholar]
- Janic, M. Modelling the full costs of an intermodal and road freight transport network. Transp. Res. Part D
**2007**, 12, 33–44. [Google Scholar] [CrossRef] - Grosso, M. Intermodal Transport: A tool for the calculation of the cost function. In Proceedings of the 12th SIET (Società Italiana degli Economisti dei Trasporti) National Conference, Rome, Italy, 17–18 June 2010. [Google Scholar]
- Baumgartner, J.P. Prices and Costs in the Railway Sector; LITEP (Laboratoire d’Intermodalitè des Transports Et de Planification), Ecole Politechnique Federale de Lausanne: Lausanne, Switzerland, 2001. [Google Scholar]
- Dolinayovà, A.; Loch, M.; Kanis, J. Modelling the influence of wagon technical parameters on variable costs in rail freight transport. Res. Transp. Econ.
**2015**, 54, 33–40. [Google Scholar] [CrossRef] - PLANCO Consulting GmbH and Bundesanstalt für Gewässerkunde (German Federal Institute for Hydrology). Verkehrswirtschaftlicher und Ökologischer Vergleich der Verkehrsträger Straße, Schiene und Wasserstraße (Traffic and Ecological Comparison of the Modes of Transport Road, Rail and Waterway); German Federal Institute for Hydrology: Koblenz, Germany, 2007. [Google Scholar]
- Trenitalia, S.p.A. Relazione Finanziaria Annuale (Annual Financial Report). 31 December 2016. Available online: http://www.sipotra.it/wp-content/uploads/2017/06/TRENITALIA-S.p.A-RELAZIONE-FINANZIARIA-ANNUALE-AL-31-DICEMBRE-2016.pdf (accessed on 13 December 2019).
- European Union Council. Relazione della Commissione al Parlamento Europeo e al Consiglio (Report of the Commission to the European Parliament and to the Council); European Union Council: Bruxelles, Belgium, 2012; Available online: http://www.parlamento.it/web/docuorc2004.nsf/00672360b4d2dc27c12576900058cad9/ad633aa27f6c38bcc1257aa30036abb0/$FILE/15773-12IT.PDF (accessed on 26 October 2012).
- Rete Ferroviaria Italiana (RFI). Nuovo pedaggio di infrastruttura. Pacchetto Minimo di Accesso. Importi Medi Unitari per segmento di mercato. Periodo Tariffario 2016–2021. 2016. Available online: http://www.rfi.it/cms-file/allegati/rfi_2014/48-v5-Importi-Medi-Unitari-PMdA-2018-2021-I-II.pdf (accessed on 13 December 2019).
- International Transport Forum. Charges for the Use of Rail Infrastructure; International Transport Forum: Paris, France, 2008; pp. 47–48. [Google Scholar]
- Terminali Italia. Tariffe Servizi Terminalistici (Fares of Terminal Services). Available online: http://www.terminaliitalia.it/content/dam/terminaliitalia/allegati/terminaliitalia_2014/Circolare_THC_2019_IT_%20_EN.pdf (accessed on 8 January 2020).
- Mayer, L. Impianti Ferroviari; Guida, P.L., Milizia, E., Eds.; CIFI: Rome, Italy, 2005. [Google Scholar]
- Rete Ferroviaria Italiana (RFI). Norme di Esercizio (Operating Rules). Available online: http://site.rfi.it/quadroriferimento/pgos.htm (accessed on 8 January 2020).
- Micucci, A.; Mantecchini, L. Alcune considerazioni sulle resistenze al moto per carri ferroviari merci | Some observations on the resistance to motion for freight railway wagons. Ing. Ferrov.
**2006**, 60, 599–609. [Google Scholar] - Vicuna, G. Organizzazione e Tecnica Ferroviaria; Collegio Ingegneri Ferroviari Italiani (CIFI): Rome, Italy, 1989. [Google Scholar]
- Szanto, F. Rolling resistance revisited. In Proceedings of the Conference Of Railway Excellence (CORE) 2016, Melbourne, Australia, 16–18 May 2016. [Google Scholar]
- Lai, Y.C.; Barkan, C.P.L.; Onal, H. Optimizing the aerodynamic efficiency of intermodal freight trains. Transp. Res. Part E
**2008**, 44, 820–834. [Google Scholar] [CrossRef] - Rail Traction Company. Characteristics of the E189 Locomotive. Available online: http://www.railtraction.it/index.php?option=com_content&view=article&id=73%3Asiemens-e189a&catid=15&Itemid=117&lang=it (accessed on 5 April 2018).
- Mercitalia Rail. Typologies of wagons. Available online: http://areariservata.cargo.trenitalia.it/flex/simulatore/perOgniMerce.jsp (accessed on 9 January 2020).
- Lupi, M.; Pratelli, A.; Canessa, M.; Lorenzini, A.; Farina, A. A study on contestable regions in Europe through the use of a new rail cost function. An application to the hinterland of the new container terminal of Leghorn port. J. Adv. Transp.
**2019**, 2019, 1–35. [Google Scholar] [CrossRef] - Eurostat. Electricity Prices for Non-Household Consumers–Bi-Annual Data (from 2007 Onwards). Available online: https://appsso.eurostat.ec.europa.eu/nui/show.do?dataset=nrg_pc_205&lang=en (accessed on 5 April 2018).
- Rete Ferroviaria Italiana (RFI). Prefazione Generale all’Orario di Servizio (PGOS). Available online: http://site.rfi.it/quadroriferimento/utilities/istruzioni/Prefazione%20generale%20all%27orario%20di%20servizio.pdf (accessed on 9 January 2020).
- Rete Ferroviaria Italiana (RFI). Procedura di Interfaccia. Modifiche alla Prefazione Generale all’Orario di Servizio. Disposition n° 18 of 19 November 2015. 2015. Available online: http://site.rfi.it/quadroriferimento/disposizioni_esercizio_rfi.htm#d2015 (accessed on 5 April 2018).
- Piro, G.; Vicuna, G. Il Materiale Rotabile Motore; CIFI: Rome, Italy, 2000. [Google Scholar]
- Lupi, M.; Farina, A.; Pratelli, A.; Orsi, D. The capability of Motorways of the Sea of being competitive against road transport. The case of the Italian mainland and Sicily. J. Transp. Geogr.
**2017**, 58, 9–21. [Google Scholar] [CrossRef] [Green Version] - De Jong, G. Value of freight travel-time savings. In Handbook of Transport Modelling; Hensher, D.A., Button, K.J., Eds.; Pergamon: New York, NY, USA, 2007; pp. 649–663. [Google Scholar]
- Ehrbar, H.; Kellenberger, J. Risk Management during Construction of the Gotthard Base Tunnel. 2003. Available online: http://www.heinzehrbarpartners.com/files/2503-2003-ehrbar-kellenberger-karlsruhe_risk_management.pdf (accessed on 10 January 2020).
- SBB (Swiss Rail Infrastructuremanager). Switzerland through and through. The North-South Gotthard Corridor. 2016. Available online: https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=3&ved=2ahUKEwiYu_yI6L_nAhWnx4UKHbSJD74QFjACegQIARAB&url=https%3A%2F%2Fcompany.sbb.ch%2Fcontent%2Fdam%2Fsbb%2Fde%2Fpdf%2Fsbb-konzern%2Fmedien%2Fhintergrund-dossier%2FGotthard%2FBasispraesentation_Gotthard_TP_KOM_PONS_en_2016.pdf.sbbdownload.pdf&usg=AOvVaw0hdXKnKi8qTr2kDoYJowis (accessed on 10 January 2020).
- Lupi, M.; Pratelli, A.; Giachetti, A.; Farina, A. Rail freight transport in Italy: An analysis of combined transport connections | Il trasporto ferroviario in Italia: Una analisi dei collegamenti ferroviari di trasporto combinato. Ing. Ferrov.
**2018**, 73, 209–245. [Google Scholar] - Zurlo, R. Galleria di Base del Brennero—Brenner Basistunnel. 2014. Available online: http://www.lucazeni.it/download/2014_01_31%20PPT%20ING%20ZURLO%20a%20MULES.PDF (accessed on 10 January 2020).
- Schmittner, H. Complessità e prospettive per il trasporto ferroviario delle merci sull’asse del Brenner. In Proceedings of the International Conference ‘La Competitività del Trasporto Intermodale Sull’asse del Brennero | Die Wettbewerbsfähigkeit des Intermodalen Transports auf der Brennerachse’, Trento, Italy, 15 April 2016. [Google Scholar]
- Cox, P. Annual Activity Report 2012–2013 for Priority Project 1—Railway axis Berlin–Verona/Milano–Bologna–Napoli–Messina–Palermo; European Commission: Brussels, Belgium, 2013; Available online: https://ec.europa.eu/transport/sites/transport/files/themes/infrastructure/ten-t-policy/priority-projects/doc/progress-reports/2012-2013/pp1_en.pdf (accessed on 13 January 2020).
- RFI and LTF. Potenzialità, Prestazioni e Criticità Della Linea Storica Torino—Lione; Quaderno 1 of the Osservatorio Val di Susa; Osservatorio per il collegamento ferroviario Torino—Lione: Rome, Italy, 2007; pp. 112–128. [Google Scholar]
- Ferrari, P. The effects of the evolution of rail transport through the Swiss Alps on the freight traffic through the Frejus pass | Le conseguenze dell’evoluzione del trasporto ferroviario attraverso le Alpi Svizzere sul traffico delle merci al valico del Frejus. Ing. Ferrov.
**2014**, 69, 111–124. [Google Scholar] - SBB (Swiss Rail Infrastructure Manager) Website—Infrastructure. Available online: https://company.sbb.ch/de/sbb-als-geschaeftspartner/leistungen-evu.html (accessed on 13 January 2020).
- Basler, E. Verkehrliche und Räumliche Auswirkungen des Lötschberg-Basistunnels (Traffic and Spatial Effects of the Lötschberg Base Tunnel); Bundesamt für Raumentwicklung (Swiss Federal Office for Spatial Development): Ittigen, Switzerland, 2012. [Google Scholar]
- OBB (Austrian Rail Infrastructure Manager). Semmering Base Tunnel. 2008. Available online: https://www.oebb.at/infrastruktur/en/Servicebox/Brochures_and_Folders/2008_08__FSBT_en.pdf (accessed on 14 January 2020).
- Dijkstra, E.W. A note on two problems in connexion with graphs. Numer. Math.
**1959**, 1, 269–271. [Google Scholar] [CrossRef] [Green Version]

**Figure 1.**The European area taken into account in this study, circled in dark blue (the Avignon rail junction, mentioned several times in the paper, has been underlined in red).

**Figure 2.**Alpine passes taken into account in this study. Alpine railway lines currently in operation (‘current scenario’) are represented in light blue; Alpine railway lines under construction or planned (‘project scenario’) are represented in dark blue.

**Figure 3.**Enlargement of Figure 2. Railway lines currently in operation (‘current scenario’) are represented in red, and railway lines across Alpine Passes are represented in light blue; Alpine railway lines under construction or planned (‘project scenario’) are represented in dark blue.

**Table 2.**Alpine Passes crossed by minimum travel time and cost routes in the ‘current scenario’ and in the ‘project scenario’. Only some reference O–D pairs are reported (see Appendix A for a larger number of O–D pairs).

O–D Pair | Current Scenario | Project Scenario | |
---|---|---|---|

Leghorn—Paris | Travel time | Giovi Pass, Frejus old tunnel | Third Pass of Giovi, New Frejus base tunnel |

Monetary cost | Giovi Pass, Frejus old tunnel | Third Pass of Giovi, New Frejus base tunnel | |

Generalized cost | Giovi Pass, Frejus old tunnel | Third Pass of Giovi, New Frejus base tunnel | |

Milan—Avignon junction | Travel time | Giovi Pass, Ventimiglia | New Frejus base tunnel |

Monetary cost | Giovi Pass, Ventimiglia | New Frejus base tunnel | |

Generalized cost | Giovi Pass, Ventimiglia | New Frejus base tunnel | |

Novara—Paris | Travel time | Luino, Gotthard base tunnel | New Frejus base tunnel |

Monetary cost | Luino, Gotthard base tunnel | New Frejus base tunnel | |

Generalized cost | Luino, Gotthard base tunnel | New Frejus base tunnel | |

Milan—Paris | Travel time | Chiasso, Ceneri Pass, Gotthard base tunnel | Chiasso, New Ceneri base tunnel, Gotthard base tunnel |

Monetary cost | Chiasso, Ceneri Pass, Gotthard base tunnel | Chiasso, New Ceneri base tunnel, Gotthard base tunnel | |

Generalized cost | Chiasso, Ceneri Pass, Gotthard base tunnel | Chiasso, New Ceneri base tunnel, Gotthard base tunnel | |

Novara—Rotterdam | Travel time | Luino, Gotthard base tunnel | Luino, Gotthard base tunnel |

Monetary cost | Luino, Gotthard base tunnel | Luino, Gotthard base tunnel | |

Generalized cost | Luino, Gotthard base tunnel | Luino, Gotthard base tunnel | |

Milan—Duisburg | Travel time | Chiasso, Ceneri Pass, Gotthard base tunnel | Chiasso, New Ceneri base tunnel, Gotthard base tunnel |

Monetary cost | Chiasso, Ceneri Pass, Gotthard base tunnel | Chiasso, New Ceneri base tunnel, Gotthard base tunnel | |

Generalized cost | Chiasso, Ceneri Pass, Gotthard base tunnel | Chiasso, New Ceneri base tunnel, Gotthard base tunnel | |

Milan—Hamburg | Travel time | Chiasso, Ceneri Pass, Gotthard base tunnel | Chiasso, New Ceneri base tunnel, Gotthard base tunnel |

Monetary cost | Chiasso, Ceneri Pass, Gotthard base tunnel | Chiasso, New Ceneri base tunnel, Gotthard base tunnel | |

Generalized cost | Chiasso, Ceneri Pass, Gotthard base tunnel | Chiasso, New Ceneri base tunnel, Gotthard base tunnel | |

Milan—Berlin | Travel time | Chiasso, Ceneri Pass, Gotthard base tunnel | Chiasso, New Ceneri base tunnel, Gotthard base tunnel |

Monetary cost | Chiasso, Ceneri Pass, Gotthard base tunnel | Chiasso, New Ceneri base tunnel, Gotthard base tunnel | |

Generalized cost | Chiasso, Ceneri Pass, Gotthard base tunnel | Chiasso, New Ceneri base tunnel, Gotthard base tunnel | |

Milan—Munich | Travel time | Brenner Pass | Brenner base tunnel |

Monetary cost | Brenner Pass | Brenner base tunnel | |

Generalized cost | Brenner Pass | Brenner base tunnel | |

Venice—Munich | Travel time | Tarvisio, Tauern | Brenner base tunnel |

Monetary cost | Tarvisio, Tauern | Brenner base tunnel | |

Generalized cost | Tarvisio, Tauern | Brenner base tunnel | |

Milan—Vienna | Travel time | Tarvisio, Klagenfurt—Bruck old line, Semmering Pass | Tarvisio, Koralmbahn, Semmering base tunnel |

Monetary cost | Tarvisio, Klagenfurt—Bruck old line, Semmering Pass | Tarvisio, Koralmbahn, Semmering base tunnel | |

Generalized cost | Tarvisio, Klagenfurt—Bruck old line, Semmering Pass | Tarvisio, Koralmbahn, Semmering base tunnel | |

Trieste—Vienna | Travel time | Tarvisio, Klagenfurt-Bruck old line, Semmering Pass | Tarvisio, Koralmbahn, Semmering base tunnel |

Monetary cost | Villa Opicina, Divaca, Ljubljana, Maribor, Semmering Pass | New Trieste—Divaca line, Ljubljana, Maribor, Semmering base tunnel | |

Generalized cost | Tarvisio, Klagenfurt-Bruck old line, Semmering Pass | Tarvisio, Koralmbahn, Semmering base tunnel | |

Koper—Vienna | Travel time | Koper-Divaca old line, Villa Opicina, Tarvisio, Klagenfurt—Bruck old line, Semmering Pass | Koper-Divaca new line, Villa Opicina, Tarvisio, Koralmbahn, Semmering base tunnel |

Monetary cost | Koper—Divaca old line, Ljubljana, Maribor, Semmering Pass | Koper-Divaca new line, Ljubljana, Maribor, Semmering base tunnel | |

Generalized cost | Koper—Divaca old line, Ljubljana, Maribor, Semmering Pass | Koper—Divaca new line, Ljubljana, Maribor, Semmering base tunnel | |

Vienna—Lyon | Travel time | Not through the Alps but via Munich, Bregenz, Zurich, Bern, Lausanne | Semmering base tunnel, Koralmbahn, Tarvisio, new Frejus base tunnel |

Monetary cost | Semmering Pass, Bruck—Klagenfurt old line, Tarvisio, Frejus old tunnel | Semmering base tunnel, Koralmbahn, Tarvisio, new Frejus base tunnel | |

Generalized cost | Not through the Alps but via Munich, Bregenz, Zurich, Bern, Lausanne | Semmering base tunnel, Koralmbahn, Tarvisio, new Frejus base tunnel | |

Munich—Avignon rail junction | Travel time | Not through the Alps but via Bregenz, Zurich, Bern, Lausanne | Brenner base tunnel, new Frejus base tunnel |

Monetary cost | Not through the Alps but via Bregenz, Zurich, Bern, Lausanne | Brenner base tunnel, new Frejus base tunnel | |

Generalized cost | Not through the Alps but via Bregenz, Zurich, Bern, Lausanne | Brenner base tunnel, new Frejus base tunnel | |

Munich—Marseilles | Travel time | Brenner Pass, Giovi Pass, Ventimiglia | Brenner base tunnel, Third Pass of Giovi, Ventimiglia |

Monetary cost | Brenner Pass, Giovi Pass, Ventimiglia | Brenner base tunnel, Third Pass of Giovi, Ventimiglia | |

Generalized cost | Brenner Pass, Giovi Pass, Ventimiglia | Brenner base tunnel, Third Pass of Giovi, Ventimiglia |

**Table 3.**Travel times [h], monetary costs [€/train] and generalized costs [€/train] between selected O–D pairs. (see the Appendix B for a larger number of O–D pairs).

O–D Pair | Travel Time (h) | Monetary Cost (€/train) | Generalized Cost (€/train) | |||
---|---|---|---|---|---|---|

Current Scenario | Project Scenario | Current Scenario | Project Scenario | Current Scenario | Project Scenario | |

Leghorn—Paris | 16.30 | 15.16 | 20,398.3 | 19,323.6 | 31,431.5 | 29,577.5 |

Milan—Avignon rail junction | 8.97 | 8.17 | 13,186.1 | 12,420.4 | 19,236.5 | 17,931.5 |

Novara—Paris | 11.99 | 11.54 | 16,938.9 | 16,173.2 | 25,014.5 | 23,929.5 |

Milan—Paris | 12.18 | 11.98 | 17,692.9 | 17,080.2 | 25,773.5 | 25,067.5 |

Novara—Rotterdam | 15.71 | 15.71 | 20,933.4 | 20,933.4 | 32,179.5 | 32,179.5 |

Milan—Duisburg | 12.81 | 12.61 | 20,290.5 | 19,677.7 | 28,590.5 | 27,884.5 |

Milan—Hamburg | 17.28 | 17.08 | 26,254.0 | 25,641.2 | 37,430.5 | 36,724.5 |

Milan—Berlin | 16.59 | 16.22 | 25,060.2 | 24,130.1 | 36,248.5 | 34,679.5 |

Milan—Munich | 8.30 | 7.36 | 13,549.5 | 12,619.5 | 19,032.5 | 17,463.5 |

Venice—Munich | 7.53 | 7.08 | 13,088.2 | 12,158.2 | 18,257.5 | 16,829.5 |

Milan—Vienna | 11.32 | 10.18 | 16,727.6 | 16,226.5 | 24,349.5 | 22,932.5 |

Trieste—Vienna | 8.14 | 6.90 | 12,107.5 | 11,450.2 | 18,141.5 | 16,724.5 |

Koper—Vienna | 9.69 | 8.49 | 12,340.6 | 11,401.2 | 19,667.5 | 17,379.5 |

Vienna—Lyon | 18.08 | 16.89 | 24,347.8 | 23,046.3 | 36,996.5 | 34,244.5 |

Munich—Avignon rail junction | 15.93 | 15.45 | 21,636.4 | 20,834.4 | 32,675.5 | 31,146.5 |

Munich—Marseilles | 15.96 | 14.78 | 20,882.5 | 19,764.5 | 31,757.5 | 29,832.5 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Lupi, M.; Pratelli, A.; Conte, D.; Farina, A.
Railway Lines across the Alps: Analysis of Their Usage through a New Railway Link Cost Function. *Appl. Sci.* **2020**, *10*, 3120.
https://doi.org/10.3390/app10093120

**AMA Style**

Lupi M, Pratelli A, Conte D, Farina A.
Railway Lines across the Alps: Analysis of Their Usage through a New Railway Link Cost Function. *Applied Sciences*. 2020; 10(9):3120.
https://doi.org/10.3390/app10093120

**Chicago/Turabian Style**

Lupi, Marino, Antonio Pratelli, Daniele Conte, and Alessandro Farina.
2020. "Railway Lines across the Alps: Analysis of Their Usage through a New Railway Link Cost Function" *Applied Sciences* 10, no. 9: 3120.
https://doi.org/10.3390/app10093120