Air–Rail Connectivity Index: A Comprehensive Study of Multimodal Journeys ^†

Abstract

To enhance the accessibility and efficiency of airports, the concept of airport connectivity is extended to High-Speed Rail (HSR), as major hub airports now have direct access to an HSR station. The traditional hub connectivity index is supplemented by the number and quality of connections between train and flight departures/arrivals (or timetables). The methodology is tested at the Paris-Charles de Gaulle airport. The results highlight that air–rail and rail–air connections can represent up to 72% of the total hub connectivity. A disaggregated analysis of connectivity across origin–destination pairs was conducted, revealing potential synchronization gaps. These findings demonstrate that this tool can assist transportation service providers in synchronizing their timetables, by measuring the degree to which it contributes to improve connectivity. Moreover, the findings offer new insights into air–rail timetable coordination and provide policy implications regarding the replacement of feeder flights by HSR.

1. Introduction

In 2050, the European Commission envisions a future where airports are turned into multimodal hubs, seamlessly connected with other transportation modes. An integrated transportation network, consisting of air and other transportation modes, is of great importance for passengers, in terms of assessment of all costs and time in door-to-door journeys, taking into account relevant parameters for all travel. Airports, as critical nodes in this network, facilitate trade, tourism, and investment. At the same time, High-Speed Rail (HSR) has become the most efficient mode of transportation for short- and medium-distance travels, providing a sustainable, high-capacity, and reliable alternative to air transport [1]. By merging air and HSR networks, regions can achieve a network expansion with improved accessibility, creating seamless multimodal connections that bring benefit to passengers, operators, and local economies.

The concept of hub connectivity is defined by three components: the number of airports with direct flight services, the frequency of these services, and the timing of arrivals and departures at the hub [2]. Each of these factors contributes to the overall efficiency and attractiveness of an airport as a transfer point. By aligning these elements with rail timetables, airports can enhance connectivity without increasing the number of flights or train departures, thus optimizing the use of existing resources. Moreover, air–rail connectivity fosters regional inclusiveness by connecting under-served or peripheral areas to major hubs, promoting balanced regional development.

In this paper, a novel air–rail connectivity index, inspired by the air connectivity index, is proposed. This air–rail index measures the number and quality of indirect routes available as a result of coordination between airline/airport and rail timetables at major hub airports. The quality of an indirect route is considered through time coordination (maximum acceptable transfer time) and routing factor (ratio between actual flight distance and direct flight distance) constraints.

In the highly competitive aviation market, it is very important to offer the appropriate level of service, i.e., to have a wide range of connections and positions that are easy to access. In the existing literature, various authors provide different connectivity measures in air transport [3,4,5,6]. These measures are good for assessing the direct and indirect service levels available to the passengers at the respective airports. It has been proven that airline hubs with bank structures typically achieve higher connectivity ratios [7]. Moreover, the challenge is to identify a robust network structure and enhance hub connectivity by coordinating different timetables [8].

The structure of this paper is as follows: Section 2 introduces the concept of the air–rail connectivity index. Section 3 provides an overview of the case study and dataset used in the research, along with a detailed discussion and presentation of the results. Section 4 highlights the key conclusions and potential directions for future research.

2. Air–Rail Connectivity Index—Methodology

2.1. Initial NetScan Model

To maximize the number of origin–destination (OD) pairs served, airlines generally operate a hub-and-spoke structure. Such a network consists of a hub, which is a central airport, and many lines, spokes, that extend radially relative to the hub, to many surrounding airports (Figure 1).

In this study, we focus on the metric proposed by [9], later called the NetScan model. As a reminder, the NetScan model for a hub h is computed as follows. $k=(a,b)$ denotes an air–air connection at the hub airport h, between an incoming flight from airport a and an outgoing flight to airport b. For each feasible connection k, the connection time at the hub is denoted by $C{T}_k$. A connection is considered as feasible if two criteria are satisfied. First, the connection time is within a minimum connecting time ($MC{T}_{air,air}$) and a maximum acceptable connecting time ($MAC{T}_{air,air}$), generally of 24 h. Second, the detour induced by the connection is limited: the total distance traveled $a-h-b$, must be lower than the great circle distance between a and b, multiplied by a Maximum Routing Factor (MRF).

The total travel time from a to b, through the hub, is the sum of the in-flight times from a to h ($T_k^{\mathrm{in}}$) and from h to b ($T_k^{\mathrm{out}}$), along with the connection time at the hub $C{T}_k$. Since the connection time is perceived as a time loss by passengers, Ref. [9] introduces the Perceived Travel Time (PTT) concept, where the connection time is weighted by a parameter w to reflect its longer perceived duration, compared to the actual vehicle time. For each connection k, the Perceived Travel Time is computed as

$$PT{T}_k=T_k^{\mathrm{in}}+T_k^{\mathrm{out}}+wC{T}_k.$$

(1)

This value is limited by the Maximum Perceived Travel Time (MAPTT), which sets the value above which the connection is no longer attractive for passengers [9]. For each connection k at the hub, we denote $MAPT{T}_k$ this limit, and it is defined as follows:

$$MAPT{T}_k=(3-0.075\ast T_k^{\mathrm{direct}})T_k^{\mathrm{direct}},$$

(2)

where $T_k^{\mathrm{direct}}$ denotes the non-stop flight time (NST) of a direct flight from a to b. In the following, for an origin–destination airport pair $(a,b)$, the non-stop flight time is computed as

$$NST(a,b)={\displaystyle \frac{40+0.068GCD(a,b)}{60}},$$

(3)

where $GCD$ is the great circle distance between a and b [5].

Finally, the quality of the connection k through the hub equals

$$C{U}_{k,\mathrm{indirect}}=1-{\displaystyle \frac{PT{T}_k---T_k^{\mathrm{direct}}}{MAPT{T}_k---T_k^{\mathrm{direct}}}}.$$

(4)

Let K be the set of each feasible connection at the hub. The hub connectivity index therefore corresponds to the sum the quality of each feasible connection at the airport:

$$C_h=\sum _{k\in K}C{U}_{k,\mathrm{indirect}}.$$

(5)

This metric is further adapted to measure the quality of rail–air and air–rail connections at the airport.

2.2. Air–Rail Connectivity Index

The concept of airport connectivity is expanded to include HSR, as many major hub airports now have direct HSR access. Indeed, integrating HSR improves airport accessibility, facilitates seamless multimodal journeys, and enhances the passenger experience. In addition to air–air connections, we propose to measure the number and the quality of rail–air connections at hub airports. To extend the hub connectivity index $C_h$ to rail, we propose refining air-specific term to become more generic. A trip to/from the airport (either a train or a flight) is now called a leg. The indirect travel time therefore corresponds to the sum of the in-vehicle time of each leg and the connection time at the airport. Connection time at the airport in the case of rail–air connections refers to the total time required for a passenger to transfer from a train arriving at a rail station within or near the airport to their gate of the departing flight and vice versa for air–rail connection. For rail–air, it includes time to exit the train, walking to the terminal, check-in/baggage drop, security screening time, and boarding time. Note that some airports do not have an HSR station. In such a case, an additional transfer time must be considered, in particular in the definition of the minimum connecting times ($MC{T}_{rail,air}$ and $MC{T}_{air,rail}$) and maximum acceptable connecting times ($MAC{T}_{rail,air}$ and $MAC{T}_{air,rail}$).

In the case of air–rail or rail–air connections, it is more reasonable to compare the multimodal options with indirect air–air connections than with direct flights. For a multimodal connection k, we therefore propose refining the computation of $T_k^{\mathrm{direct}}$. For each rail–air connection k, at the hub, $T_k^{\mathrm{direct}}=NST(a,h)+MC{T}_{air,air}+T_k^{\mathrm{out}}$, with $NST(a,h)$ the non-stop flight time from train station a to hub airport h. Similarly, for each air–rail connection k, $T_k^{\mathrm{direct}}=T_k^{\mathrm{in}}+MC{T}_{air,air}+NST(h,b)$, where $NST(h,b)$ is the non-stop flight time from the hub airport h to train station b. This value is larger than a direct flight from the origin to the destination, but represents the ideal indirect connection by air.

Similarly, the detour ratio is no longer compared with the great circle distance from a to b. In the case of a rail–air connection (or air–rail connection), the detour ratio corresponds to the travel time from the origin train station to the final airport (or from the origin airport to the final train station) with an ideal connecting time at the hub, divided by the ideal travel time with an air–air connection:

$$Detou{r}_k={\displaystyle \frac{T_k^{\mathrm{in}}+MC{T}_{rail,air}+T_k^{\mathrm{out}}}{T_k^{\mathrm{direct}}}}$$

(6)

The total connectivity of the airport can therefore be computed as follows:

$$C_h=\sum _{k\in K^{\mathrm{air},\mathrm{air}}}C{U}_{k,\mathrm{indirect}}+\sum _{k\in K^{\mathrm{air},\mathrm{rail}}}C{U}_{k,\mathrm{indirect}}+\sum _{k\in K^{\mathrm{rail},\mathrm{air}}}C{U}_{k,\mathrm{indirect}},$$

(7)

where $K^{\mathrm{air},\mathrm{air}},K^{\mathrm{air},\mathrm{rail}}$, and $K^{\mathrm{rail},\mathrm{air}}$ is the set of feasible air–air, air–rail, and rail–air connections at the hub h.

3. Paris-Charles de Gaulle Case Study

In this section, the methodology detailed above is tested on the case study of Paris-Charles de Gaulle airport (CDG). A description of the airport, the parameters of the study, and the results obtained are presented.

3.1. Case Study Description

Paris-Charles de Gaulle airport is the largest French airport with more than 67 million passengers in 2023 [10] and a connecting rate of 20%. It is the third airport in Europe in terms of passenger traffic in September 2024 [11] and the seventh hub worldwide in terms of connectivity according to OAG [12]. The airport is connected to HSR with a train station located at terminal 2. Each day, more than 60 trains stop at the airport, serving more than 40 destinations across France, Belgium, and Germany. The HSR network is displayed in Figure 2.

For this study, data from the first week of June 2024 are collected. The flight and train schedules are obtained from the OAG [13] and SNCF [14] websites, respectively.

In the following, three adjustments of the initial model are made. First, values for MCT and MACT are revised to avoid too-long connection times, which are in practice not attractive for passengers. The values of the parameters MCT and MACT for each connection type are summarized in

Table 1. Parameters (minutes).

Connection Type	Schengen Connections		Non-Schengen Connections
	MCT	MACT	MCT	MACT
Flight–Flight	45	180	60	300
Train–Flight	90	300	120	300
Flight–Train	60	300	90	300

.

Second, we propose extending the “domestic” concept to the Schengen area. In Europe, an agreement between 29 countries, named the Schengen area, abolishes border controls. France belongs to this agreement. Flights within this space can therefore be seen as domestic flights. Finally, the weighting parameter w (Equation (1)) is set to 1.5. In [9], this value was set to 3, i.e., one hour of connection is perceived as three hours. However, some studies further analyzed this value of waiting time compared to in-vehicle time, and it appears that a lower value seems more realistic [15].

Note that connections to train stations located within the Paris area (i.e., Marne-la-Vallée Chessy and Massy) are not considered in this study, since they are considered direct connections from Paris. No change has been made to the air and rail schedules in terms of departure times, and the MRF is set to 1.7.

3.2. Results

3.2.1. Global Connectivity

The connectivity is computed based on data from the first week of June 2024. The number of feasible connections and the connectivity index per connection type are represented in Figure 3. As a reminder, a connection between two legs (i.e., train or flight) is considered feasible if the transfer time is within the range [MCT, MACT] for the connection type considered and if the detour ratio is lower than MRF.

Air–rail and rail–air connections represent 34% of the feasible connections at CDG airport, for the considered period. Moreover, including the rail in the $C_h$ more than triples the hub connectivity from 34,186 to 124,069. One can observe that the quality of air–rail and rail–air connections is on average higher than flight–flight connections. This is due to the definition of the $T^{\mathrm{direct}}$ parameter for multimodal trips, which is not computed as a non-stop flight time between the origin and destination. As $T^{\mathrm{direct}}$ is generally higher than a direct non-stop flight for multimodal trips, the comparison between the total travel time and $T^{\mathrm{direct}}$ is less restrictive. The average connectivity scores for an air–rail connection and for a rail–air connection equal 0.42 and 0.39, respectively. This is explained by the MCT value for air–rail connection which is lower than for rail–air connection, since there is no processing time at the train station.

3.2.2. Origin–Destination Connectivity Analysis

The connectivity index values per origin train station for rail–air connections, and per destination train station for air–rail connections, are presented in Figure 4a and Figure 4b, respectively. The number of trains to/from each city during the studied period is also displayed.

For both rail–air and air–rail connections, the highest total connectivity is obtained for Lille Europe train station, with a value of 5552 and 6767, respectively. Indeed, for the studied period, 116 trains from Lille Europe stopped at CDG, and 122 departed from CDG to Lille Europe, thereby increasing the potential for connections.

Regarding rail–air connections, cities with the lowest connectivity index are located on two train lines: Perpignan–Narbonne–Béziers–Agde–Sète, and Freiburg–Ringsheim–Lahr–Offenburg–Strasbourg. The first line only stops at CDG four times during the studied period. The second line is an extension of the CDG–Strasbourg line, and the service is run only once in the considered schedule. Such a low frequency limits the connectivity at the hub. However, one can observe that the connectivity is not solely due to the number of trains that arrive at the hub. For instance, although the number of arriving trains from TGV Haute Picardie station is lower than the ones from Lyon Part-Dieu, the rail–air connectivity index for this origin stop is higher, reflecting either a better schedule synchronization or a lower detour.

The connectivity index for each city is generally higher for air–rail connections compared to rail–air connections, even though the number of train stops is of a similar order of magnitude. As mentioned earlier, this is due to a smaller value of MCT for air–rail connections, reducing the Perceived Travel Time term. Similarly to the rail–air connection graph, synchronization patterns can be detected. For instance, trains to Marseille or Avignon have a lower connectivity index than Lille Flandres, while their frequency of departures is higher. On the contrary, trains to Arras or Lyon Saint-Exupéry have a higher air–rail connectivity index than Bordeaux Saint-Jean, for instance, despite fewer trains serving Arras and Lyon compared to Bordeaux.

To facilitate the detection of such phenomenon, Figure 5 displays the connectivity index as a function of the number of arriving trains for rail–air connections (Figure 5a), and as a function of departing trains from CDG for air–rail connections (Figure 5b). A linear regression is performed and represented on the graph. For each train station, the distance to the regression line is calculated. Cities above the line are considered to have good connectivity, while those below are considered to have bad connectivity. For rail–air connections, trains from Lille Europe, TGV Haute Picardie and Champagne-Ardenne TGV stations have good connectivity. This translates to the fact that, on average, the arrival of the train is well synchronized with departing flights, or that the detour induced by the train compared to an air–air connection is low. On the contrary, trains from Avignon, Aix-en-Provence or Marseille Saint-Charles have a low connectivity index for their respective frequency.

Regarding air–rail connections, again, trains to Lille and TGV Haute Picardie are well connected with arriving flights at CDG airport. Lyon Saint-Exupéry also appears among the top five connected cities. This tool highlights that trains from Lyon could easily replace feeder flights to this city, as the quality of the connection remains high. High connectivity can be the first indication of the lines that could replace feeder short-haul flights. Another indicator could be the detour factor. If there is a small or medium difference between train route and air route, then that train service will be a good candidate for substitution. Otherwise, the substitution should be reconsidered due to the additional inconvenience for passengers.

4. Conclusions

This paper extends the hub connectivity concept to the rail transportation network, to account for air–rail connections at the hub airport. The NetScan model is enriched by including a connectivity unit of multimodal connection at the hub airport. The methodology is tested at Paris-Charles de Gaulle airport, equipped with a High-Speed Rail station. Results highlight that considering air–rail connections can triple the hub connectivity index. In addition, an analysis of origin–destination pairs allows us to detect a lack of synchronization between air and rail. In particular, measuring the connectivity index, in parallel with the frequency of trains or the number of feasible connections, may help transportation service providers identify weak links in terms of synchronization. Additionally, achieving a sufficient level of connectivity for air–rail connections could assist transportation service providers in identifying opportunities to remove feeder flights, ensuring that a high-quality rail alternative is available as a replacement.

Several avenues for future work are under consideration. First, in the proposed formula, one can observe that reducing the connection time increases the quality of the connection. However, in practice, more and more passengers are looking for robust connections to avoid missed connections in case of delay. Future works may consist of considering the robustness of the connection in its quality measurement. Second, a parameter sensitivity analysis should be conducted. In particular, different values of MCT, MACT, and the weighting parameter w can be tested, as they directly impact the connection quality. Finally, a timetable coordination method could be further developed, based on the connectivity index. Such a tool could have a significant impact on operator capacity utilization. It would be valuable to analyze how such changes might affect stakeholders’ operations and passenger experience.