Vulnerability and robustness of interdependent transport networks in north-western Italy

Economic activity is deeply dependent on network infrastructure, be it electricity, transport, water or communication networks (see, among others, [15]. Infrastructure networks have become increasingly complex, showing progressively higher levels of interdependence that make them even more vulnerable, as shown by several worldwide emergency episodes caused by both natural and man-made disasters [35]. Since networks-of-networks are inherently more fragile than isolated ones [8], identifying and understanding interdependencies is one of the biggest challenges in analyzing the complex infrastructures on which our national systems rely [37].

The focus of this analysis is on transport infrastructures, which are fundamental to the functioning of societies. These systems not only must be able to meet mobility needs and guarantee access to resources and markets [38], but in emergency situations they make it possible to rescue people and also repair other damaged infrastructure systems [31]. The study of the vulnerability and robustness of transport networks in the event of emergencies is of prime importance for making the transport systems resilient.

This work originates from the collapse of the Morandi bridge in Genoa in August 2018 when both urban and motorway mobility of people and goods was drastically disrupted, and the underlying rail network was also damaged. In addition, the flows of goods originating from the port of Genoa, one of the largest in the Mediterranean, were inevitably impacted. Episodes like this show that damage to one component of the network can spread and cause damage on a large scale. The importance of having a robust transport system from an economic and social welfare perspective has led to the emergence of a large body of literature on the mechanisms that can cause system vulnerability, including interdependence [31]. This work fits into this literature by proposing an empirical analysis of the robustness and vulnerability of the motorway and railway networks in north-western Italy.

We adopt a network-based approach, i.e. we describe the network using nodes representing the network components and links representing the physical connection between each pair of nodes [31].¹ Indeed, network theory is recognized as an effective methodology for studying complex networks (see, among others, [11, 12, 29]. Although it is necessary to recognize the importance of the dynamic study of networks, the structural analysis of networks such as transport networks can also be very informative, since the robustness of the system is a prerequisite for efficient rescue and recovery planning after the occurrence of a shock [11, 12].

The objective of the study is twofold. First, the identification of critical components, i.e. nodes crucial for the functioning of a network [28], of the transport network in the northwest of Italy, by accounting for the geographic interdependence of two transport infrastructures, i.e. motorway and railway networks. In particular, we consider the case in which the condition of one infrastructure does not influence the condition of another, but their elements are in close spatial proximity [37]. To determine whether and to what extent each of the nodes in the network contributes to the vulnerability of the interconnected system, we first calculate the loss of efficiency associated to the removal of each node of the network by relying on the efficiency measure proposed by Latora and Marchiori [27]. Furthermore, we observe which vertex when removed causes a reduction in the size of the largest connected component, i.e. we detect cut vertices, and we calculate each vertex betweenness centrality, as a proxy for the ability of a node to connect other nodes in the system.

Turning to the second objective, we consider the concept of functional interdependence in the spirit of Zhang and Peeta [50] and we analyze functional connection between the two transport networks to investigate the robustness of the resulting multimodal graph. This analysis is based on a multi-layer graph in which in each main city in the northwest of Italy the modal change can take place and the motorway exits and the railway stations are connected. Following previous literature, we use as a measure of the robustness of the network the size of the giant component during all possible “attacks” on the system (see, among others, [13, 40]. We perform the robustness analysis to observe the different behaviour of the multimodal network with respect to the corresponding uni-modal ones.

Results from both these analyses show that interdependence (in its various definitions) is a determining factor in topological analyses. In our framework, considering interconnections turns out to be fundamental for the analysis to be informative.

The major contribution of this work is to focus on the vulnerability and the robustness of two interdependent systems by performing the empirical analysis on two transport networks, i.e. motorways and railways, in a multi-regional scale. Indeed, the economic literature has recognised the importance of studying concepts such as resilience and vulnerability within the framework of complex networks, and it has been argued that it is crucial to study the critical components of a system accounting for (geographic) interdependence of networks [29]. Nevertheless, even though there exist some important exceptions such as Schintler et al. [39], Jin et al. [26], Bocewicz [6] and Apricio et al. [2], multilayer transportation systems have received little attention in the literature [48], and studies in transport economics often focus on one transport mode only.² Furthermore, investigating vulnerability in multimodal transport networks appears to be one of the directions in which research into transportation network performance should be directed [19], and we believe that our robustness analysis moves precisely in this direction. In addition, along with the valuable contribution of jointly analyzing two transportation networks, the analysis focuses on a geographic area never analyzed in previous studies. Moreover, in this case study we analyse an area that includes multiple NUTS-2 regions: with some exceptions, such as Schintler et al. [39], where the authors analyze Florida’s road and rail network, studies often focus on urban areas (see, for example, Jin et al. [26] for a case applied to the public transportation system in the central part of the city of Singapore, and Apricio et al. [2] for a case study related to the city of Lisbon).

This work was produced on the basis of considerations emerged from the New Economic Regulation For Transport In Case Of Emergency Events project, a project funded by the European Union via the Structural Reform Support Programme.³

The rest of the paper is organized as follows. Relevant literature is analysed in Sect. 2. In Sect. 3 the methodology is presented. Section 4 shows the case study and results. Finally, conclusions are drawn in Sect. 5.

This study contributes to literature on the vulnerability and the resilience of transport infrastructures. Important surveys on resilience and vulnerability in transportation studies are, among others, Reggiani et al. [36], Mattsson and Jenelius [31], Gu et al. [19], Sun et al. [41].⁴

Even though there is no a common definition of vulnerability, there are definitions that summarize much of the literature on the subject. Berdica [5] argues that vulnerability in the road transportation system is “the susceptibility to incidents that can result in considerable reduction in road network serviceability,” and according to Jenelius and Mattsson [24] vulnerability of all transport system is the “society’s risk of transport system disruptions and degradations.” From an empirical perspective, the vulnerability of infrastructures is investigated under two main approaches: network topology and system-based [31]. The network topology approach relies on graph theory and is strictly connected to the concept of efficiency, which in turn refers to average minimum distance between pairs of nodes in the network [27]. Typically, network efficiency indicators are used to evaluate the vulnerability of transport networks and typically researchers focus on the variation in levels of efficiency after the removal of a network component. In Latora and Marchiori [28], the authors evaluate the drop in network performance caused by the removal of a network component using efficiency as a proxy for system performance.⁵ Another important index belonging to the category of topology-based vulnerability indices is closeness, which relies to the average shortest distances between all nodes, while efficiency relies on the reciprocal of distances [19]. Other methods used in the literature to investigate critical network components include that of Demšar et al. [10] according to which two measures have to be used to identify critical locations in vulnerability analysis: cut vertices (a vertex is a cut vertex if its removal causes an increase in the number of connected component) and each node betweenness centrality (the higher the value of this measure, the more critical a node is).⁶ The second approach, the system-based one, also considers the effect of congestion, and thus travel cost issues [19] and is deeply related to the concept of accessibility: “a network node is vulnerable if loss (or substantial degradation) of a small number of links significantly diminishes the accessibility of the node, as measured by a standard index of accessibility; a network link is critical if loss (or substantial degradation) of the link significantly diminishes the accessibility of the network or of particular nodes, as measured by a standard index of accessibility” [44]. Within this approach, the graph theory is integrated with transport supply and demand analysis with the aim of investigating real responses to shocks by analyzing demand and supply of transport according to different vulnerability scenario. The advantage of the topology-based approach is related to the limited need for data and also the relative simplicity of the methodology used, but at the same time it does not allow for the incorporation of a realistic description of the response to a destructive event. In this sense, the system-based approach can be interpreted as an attempt to overcome the limitations of the topology-based approach, even though this requires a volume of information that is not always available and also makes comparability between different networks less immediate [31].

When it comes to the resilience of transportation network, literature is not yet so well established as literature on vulnerability [31].⁷ Following Reggiani et al. [36] it is possible to distinguish between ecological and engineering studies. The latter refers to the ability of a system to return to the old steady state equilibrium, while the former to the ability of a system to get to a new steady state equilibrium. Moreover, according to the authors, in this literature the concept of robustness is often used, and it seems to be used with a similar meaning to that of resilience. Robustness describes the performance that can be preserved under disturbance, and can be considered as the inverse of vulnerability (see, among others, [19, 36].⁸ The concepts of resilience and robustness lead to similar results, but through different processes: in fact, a system is more resilient the greater its ability to recover after a shock, while a system is robust if it remains intact after a destructive event [16, 17].⁹ With regard to quantitative resilience indices [51, 52], refer to three categories: topological metrics, attributes-based metrics, and performance-based metrics.¹⁰ Metrics belonging to the first category, are often similar to those of vulnerability. This is due to the fact that, as already pointed out, vulnerability captures the ability of a network to withstand shocks, and this is one of the components of the multi-faceted concept of resilience [19]. Examples of metrics belonging to the second category are those that focus on the recovery phase, i.e. recovery speed and recovery efficiency. As argued by [51, 52], most of the methods proposed in the literature to assess resilience are hardly applicable to large-scale transportation network. Only topological methods can be considered more efficient in this sense, although it is necessary to recognize the limitation of not including traffic flow aspects. Because of these reasoning, since our case study refers to a multiregional scale, we refer to topological robustness measures in this analysis.

Finally, this paper also relates to the literature on critical interdependent infrastructures. Researchers have often described interdependence in terms of criticality, since when two networks are involved in a shock the final effect is more than proportional to the sum of the outcomes that would occur in the case of destructive events involving only one of the two infrastructures [34]. Moreover, there are often several organizations in charge of each single infrastructure, which leads to coordination issues in emergency management [1]. Hasan and Foliente [20] argue that when a disruptive event occurs also indirect effects that percolate through the set of interconnected networks have to be considered. Ouyang [35] identify different categories of approaches to investigate infrastructure interdependencies and this work is related to the literature that adopts the network-based approach, where vertices represent different components of the infrastructure, links represent the physical or virtual connections among them, and inter-links describe interdependencies between infrastructures. Typically, researchers using this approach model the failure of one of the network components to observe its cascading effects on the entire interdependent infrastructure. Depending on how the infrastructure is modelled, within this approach we can furthermore distinguish between analytical methods and simulation methods (for an in-depth analysis of these approaches see Okuyama [34].

A graph, \(G = \left( {v,e} \right)\), is a symbolic representation of a network and its connectivity. A vertex, \(v\), is a terminal point or an intersection point of a graph. In our study, each vertex can be the abstraction of a transport terminal (a motorway exit in the motorway graph and a railway station in the railroad graph, respectively) or, alternatively, an intersection point. An edge \(e\) is a link between two nodes. The link \(\left( {i,j} \right)\) is of initial extremity i and of final extremity \(j\). Each link is the abstraction of a transport infrastructure supporting movements between nodes, i.e. an existing highway or a railway line.¹¹ We rely on both unweighted and weighted graphs; in the latter case the weight used is the distance (expressed in kilometers). In this study both the railway and the highway networks are symmetrical.

Since our analysis focuses on interconnected infrastructures, defining the way motorways and railways networks are interconnected, i.e. to identify inter-links, is fundamental. Critical infrastructures are interdependent in several ways, and scholars provide different classifications (see [14, 37, 47, 50, 53]).¹² We use two different definitions of interconnection, serving to different purposes. Indeed, depending on how two infrastructures are connected, different aspects of the multi-layer network arise.

Our case study refers to the north-west of Italy as shown in Fig. 1.¹⁷

To conduct the analysis and construct the graphs, the first methodological choice concerns the identification of relevant railway lines. The latter are selected starting from the full list provided by RFI, the company managing the railway infrastructure in Italy, in its Online Network Statement, and focusing on the lines classified as fundamental. In some cases, urban junction lines are also considered to allow fundamental lines to be connected. On the other hand, as far as motorways are concerned, we consider the most important exit stations and also relevant intersections.¹⁸ Finally, all vulnerability and robustness analyses are performed using iGraph R Package.

In this work we have focused on the motorway and rail network in the north-western part of Italy, and we analyzed different aspects of these networks in the context of interdependent transport infrastructures. Based on a network topological approach, we relied on two different concepts of interdependence to build two multi-level networks that serve two different purposes. Firstly, we analyzed the concept of geographical interdependence, and then we mapped the points at which motorways pass over railways, or vice versa, in the whole of the territory under analysis. Thus, we constructed a multi-level network in which it was possible to consider the points at which, if a shock occurred, it would also have cascading repercussions on the network not directly involved, precisely because it was geographically’close’. Using this multi-layer graph it was possible to evaluate the changes in network efficiency after removing one by one the nodes of the interconnected network. As expected, the removal of the nodes of geographic proximity generally leads to a strong decrease in network vulnerability, as measured by a typical efficiency measure. Even following other criteria, i.e. the identification of cut vertices and the analysis of betweenness centrality, the results confirm that points of geographical proximity are always very critical points and therefore points that worsen the vulnerability of the system. This analysis therefore provides a list of nodes (and links) that should be the focus of prevention policies to reduce the possibility of damage, but also gives an indication of which nodes (and links) should be restored as quickly as possible whenever an emergency and destructive event renders them inaccessible.

Second, using the concept of functional interdependence we assumed that in each of the main cities of north-western Italy a modal shift was possible. Using this second multi-layer network it was possible to evaluate the robustness of a multimodal network in comparison with the corresponding uni-modal networks. The analysis reveals that the intermodal network involves more fragility: multimodal networks have the advantage of being able to transfer demand from one mode to another, but this means that any problem occurring on one transport infrastructure also affects all the other infrastructures in the network. This result has a very important relevance for the debate on regulation and coordination between competent authorities since often the infrastructures are managed by different operators and the main problems concern the coordination of decisions. In this context, it is necessary to direct researches towards analyzing possible ways of increasing the resilience of multimodal networks.