1. Introduction

Nowadays, Critical Infrastructures (CI) (roads and railways, electrical and telecommunication networks, gas and water pipelines, etc.), supplying primary services to citizens, are mutually connected as they provide their services not only to final users but also to other infrastructures. In this aspect, infrastructures are said to be dependent on each other and” interdependent.” The concept of dependency stands on the fact that an infrastructure (e.g., the electrical network) provides service to another (e.g., the telecommunication network), and, thus, the latter is said to be dependent on the former. CI interdependencies can involve different abstraction layers. For instance, a general statement about the dependency between a railway and a power station involves a different layer related to a railway and a power station located in a given city. For the sake of simplicity, in the following, we refer to the former as system dependency and to the latter as urban dependency.

Whereas repositories of system dependencies already exist¹, these are not sufficient to build urban dependencies due to several factors including lack of integration of knowledge held by different critical infrastructure operators and privacy restrictions. Furthermore, these data are constantly changing and difficult to collect because different stakeholders keep them. In order to build simulation models, the unavailability of information on real interdependencies is generally overcome using literature data or through survey data analysis addressed to critical infrastructure experts [1]. However, interdependency data would allow more reliable simulation for risk assessment and crisis management in case of natural events, such as earthquakes, or other events, such as cyber-attacks.

In this context, this paper aims to define a methodology to generate one of the possible graphs modeling CI interdependencies at an urban scale starting from uncertain data. The proposed methodology, named MARIS (Modeling infrAstructuRe dependencIes at an urban Scale), allows the discover of possible hidden dependencies using Geographical Information System (GIS) Open data of CIs and Points of Interest (e.g., the location of substations of an electric distribution network serving an urban area) and to apply proximity criteria to model dependencies when these are not known.

In addition, the paper presents the results of a survey on CIs conducted by several experts from Italy, aiming at quantifying the dependencies between critical infrastructures. This can be a valuable input for applying the MARIS methodology to produce realistic graphs of interdependencies in an urban context.

The rest of the paper is organized as it follows. Section 2 gives an overview of the present work on CI interdependencies. Section 3 presents the MARIS methodology. Section 4 presents a survey analysis of experts on the dependencies between Critical Infrastructures. Section 5 describes a case study related to Rome in Italy. Finally, Section 6 concludes the paper.

2. Related work

Modeling of CI interdependencies has been considered as a relevant problem since the seminal paper of [2].

In Chiara et al. [3], the authors proposed the Mixed Holistic Reductionist (MHR) methodology based on the interaction of three layers: (i) a holistic layer where CIs are seen as singular entities with defined boundaries and functional properties; (ii) a reductionist layer modeling the behavior of individual CI components; and (iii) a service layer that describes the functional relationships between components and the infrastructure at different levels of granularity.

An ontology design pattern to model CI interdependencies was proposed by Ref. [4] as part of the TERMINUS ontology. Crisis management [5] and risk assessment [6, 7] are two possible applications of ontologies modeling critical infrastructures [8].

In Rosato et al. [9], the authors focus on modeling cyber dependencies of a set of infrastructures in an urban context. In particular, a dependency matrix [10] was used to reveal the potential vulnerability of a given node to the unavailability, corruption, or disclosure of data from an interdependent node regardless of the current state of the shared data infrastructure.

The work of Michel et al. [11] allowed us to define a dependency matrix generated based on the analysis of CI disruptions gathered from public media in the Netherlands from 2004 to 2010. In particular, a specific set of news sources containing impact keywords were acquired by Google News and further organized to save information including the affected CI sector and service, the initiating event (if any), and its dependency on another affected CI service.

In Franchina et al. [12], the authors present a methodology able to classify critical infrastructures starting from citizenship basic needs and foresee possible cascading effects.

In the MARIS methodology, we address all types of dependencies (logical, cyber, and physical) that are modeled by a specific system dependency layer and acquire open data of CIs and points of interest in order to create an urban dependency layer that can be valuable for further CI dependency analysis.

3. The MARIS methodology

3.1 Overview

Dependencies and interdependencies increase the vulnerability of infrastructures as they allow failures and perturbations to propagate from one system to another with the consequence that an infrastructure, which is not directly affected by some event that undermines its functioning, can be perturbed by the lack of functionality coming from another infrastructure which is turn hit by the event. Whereas from a conceptual side, the phenomenon is clear, on the practical side, dependencies and interdependencies are responsible for producing complex phenomena as, for instance, propagation time-scales can be quite different depending on the first perturbed infrastructure and on the infrastructure where perturbation will flow. For example, whereas perturbation on an electrical line may affect a very short time scale (seconds or less), an electrical perturbation to the traffic system or the water distribution network may take hours to produce sizeable effects. In that, if one would consider a” dependency matrix” where row and columns represent infrastructures and the i-j element their interaction, such a matrix is highly nonsymmetric (the ij element may be largely different from the ji one) as some infrastructure might perturb (severely and rapidly) other infrastructures which, in turn, have a very poor effect on the former when, in turn, perturbed. In some cases (i.e. when perturbation originates from the electrical system), the” coupling” strength is often very strong (i.e. many systems depend primarily on the electrical power), and the resulting reduction (or loss) of function established in a very short time scale. The presence of such strong coupling between infrastructures leads the system to be a” unique” system that cannot be treated and approximated as a system of independent (or nearly independent) infrastructure but as a” system of systems” that cannot be linearized A further element which leads the interdependency problem even more complex to be treated originates from the possibility of closed loops involving more than a couple of infrastructures. Perturbation from a first infrastructure might flow on several infrastructures before returning to the first one, providing negative feedback.

All these issues lead to an operational approach to interdependency that is extremely complex due primarily to an incomplete description of system’s dependencies, time scales, and latencies. All dependency and interdependency data can be achieved through direct and indirect methods [12], but a complete theory of interdependency is still lacking.

Despite all that, it is possible to empirically deal with the problem of describing a number of dependent and interdependent systems with the aim of providing some type of decision support systems (DSS) enable to support decision makers (e.g., CI and Civil Protection managers) in the risk management process.

The MARIS methodology makes it possible to transform the layer of interdependencies known at the system level into a layer of interdependencies at the level of the physical components that lie in an urban context, as shown in Figure 1.

Figure 1.
Georeferenced dependency upscaling.

In the following, first, we give some definitions of the main concepts involved in the MARIS methodology, and then, we give an overview of its main steps.

3.2 Definitions

The MARIS methodology is based on seven fundamental concepts pertaining to the two above-mentioned layers. The ones dealing with the system dependency layer are the following:

System: It denotes a Critical infrastructure from an overarching perspective [13]. Accordingly, examples are transportation, energy, water, waste, telecommunication, education, and health.
Subsystem: It represents a further refinement of a system; for instance, the Water system includes several subsystems such as drinking water, wastewater/sewage, and stemming of surface water.
Subsystem Dependencies: These can be physical, logical, and cyber. For example, a hospital depends on an electric distribution network.

Those pertaining to the urban infrastructure layer are:

Entity Type: It represents a physical component of a subsystem that is responsible for the provision of a service (e.g., the generic substation component of a distribution power grid).
Item: It represents the resource, good, data, or functionality provided to a customer (or a citizen) that is produced and/or consumed by an entity.
Entity: It represents the specific instance of an Entity Type (e.g., the set of substations of a distribution power grid in the area of interest).
Urban dependencies: These can be physical, logical, and cyber. Unlike SD, UD involves Entity only. For example, a specific substation of a distribution power grid may depend on a nearby base transceiver station (BTS) that provides communication functionality required by the power grid’s supervisory control and data acquisition (SCADA) system.

3.3 Main steps

Figure 2 describes the main steps of the MARIS methodology. First, dependencies at system scale are collected through a survey eliciting knowledge on the dependencies between critical infrastructures. As mentioned, these dependencies concern subsystems. Information on entities are retrieved from a GIS (Geographical Information System) such as OpenStreetMap (OSM). Then, similar to the approach presented in Ref. [14], subsystems are matched with entity types. The resulting pairs are included in an annotation table. Finally, all the above information, i.e., subsystems dependencies, entities, and the annotation table, are used to infer urban dependencies and create an interdependency graph.

Figure 2.
Main steps of the MARIS methodology.

4. Survey analysis on the dependencies between critical infrastructures

In this section, we present the results of a survey on Cis conducted with experts from Italy coming from various economic and social sectors.

This activity, in addition to providing a set of real interdependencies useful for the application of the MARIS methodology, was used as input to the DOMINO simulation model [12], developed by Tesseract Srl company, aiming at studying and quantifying the consequences of negative, unexpected, and disruptive events to the Supply and Value Chain systems of a country. The purpose of this model is to reproduce the impacts that would occur on such systems if relevant functions of the Chains were disrupted by natural or malicious events. This DOMINO approach leverages the concept of an item (as defined in Section 3.1) based on the NACE² and ATECO³ classifications. The survey was conducted by involving industry experts to detail the direct consequences produced by their own organizations due to the loss (or degradation) of a specific item. In particular, for each of the 117 items considered (Table A1 in the Appendix section), a set of the impacted items was collected. In addition, data regarding the duration of the propagation (in terms of hours, days, months, and years) were also collected in order to perform impact analysis through the DOMINO model.

The overall model will thus consider all the interdependencies between the various sectors (including Cis) that make up the Country Supply Chain System, based on the data reported by the various experts.

In the following, two examples of dependency trees are discussed. Figures 3 and 4 show the direct dependencies of the Drinking water and Bank items respectively. At the top of each tree a timeline is displayed to show the “falling time” of each ITEM, starting from the “time zero,” corresponding to the root node.

Figure 3.
DOMINO model from tesseract Srl: Drinking water dependency tree.

Figure 4.
DOMINO model from tesseract Srl: Bank dependency tree (items with impact higher than 30 days have been removed for the sake of space).

In the first dependency tree, it can be noted that, following the disruption of the Drinking Water item, two items, i.e., Education and Research, are impacted in the range of only 4 hours. On day 1, 45 items are impacted. Most of the dependencies represented are directly linked to the root node, but few of them are activated due to second (or higher) order effects (i.e., Maintenance services, Agriculture, and products).

In the second dependency tree, a few items are impacted in the order of a few minutes. However, most of the items are impacted after 3 days from the initiating failure.

5. Case study

The case study concerns an area of the city of Rome characterized by a high concentration of various business activities and power centers, as well as the presence of CIs, which are essential to maintaining vital societal functions. As shown in Table 1, the mentioned area includes 𝑁 = 10 systems and 11 subsystems.

System	Subsystem	Entity type	Entity occurrences
Education	University	Univ. building	27
	School	School building	181
	College	College building	11
Energy	Power	Substation facility	1000
Financial services	Bank	Bank building	413
	Insurance	Insurance building	40
Food	Restaurant	Restaurant building	2492
	Fast food	Fast food building	701
Government	Embassy	Embassy building	184
	Parliament	Parliament	2
Health	Clinic	Clinic building	40
	Pharmacy	Pharmacy building	506
	Hospital	Hospital facility	31
	Dentist	Dentist building	48
Internet	Internet services	Street cabinet	34
Telecommunication	Telecom	BTS building	122
Transportation	Railway	Railway Station	188
	Airports	Airport facility	4
Water	Water Supply	Water tower	2
Total:			6025

Table 1.

Dataset of infrastructure types in this study, categorized under 11 subsystems and 10 systems in the area of interest.

5.1 System dependency layer

In this step, we imported the subset of subsystem dependencies that were collected by means of the survey described in Section 4. It is worth noting that these dependencies expand those more generic related to the system level, which are addressed, for instance, in Rinaldi et al. [2]. Figure 5 shows an example of how system dependencies are extended to subsystem dependencies.

Figure 5.
(a) Example of system dependency layer; (b) example of subsystem dependency layer obtained from open data in the area of interest; (c) a fragment of the entity layer.

5.2 Territorial open-data acquisition

The development of the local dataset in the case study is based on the integration of open data collected and provided by OSM. The aim of this platform is to provide free geospatial information of world features. OSM uses open tagging mechanism to add meaning to geographic objects, so that any OSM user can add a new tag to them. For instance, some keys can be used to classify OSM entities into classes (e.g., highway, building, and amenity) while other keys play the role of attributes (e.g., name and maxspeed). OSM also allows to set attribute values, while values for classes are used to classify class members into categories (e.g., residential, hotel, monument).

In order to facilitate the understanding of OSM data and reduce the number of incorrect entity-classes associations [15], we used the Taginfo platform⁴ to gather tag statistics (e.g., providing the tags are actually in the database, the number of users choosing those tags) and to semantically enrich the entities. For example, when analyzing the railway subsystem, by setting the tag railway = station in Taginfo, we were able to select the railway station entities located in the area of interest and discard those combinations (e.g., railway = crossing, railway = radio) that were associated with different concepts.

Then, we used Overpass turbo⁵, a web-based data mining tool for OSM, to acquire the OSM data of interest representing entity type occurrences of Table A1 (e.g., university buildings and water towers) according to a geoJSON data format.

Therefore, the GIS open data acquired for CIs and Points of Interest were classified according to the specific subsystem.

5.3 Urban infrastructure layer

Regarding the dependencies to be associated to the entity layer, we considered those at the subsystem level and scaled them to the entity level. In other words, given that, according to the system dependency layer, the health system depends on the energy system, when scaling to the entity layer, we adopted the criterion that the specific hospital X depends on the energy supplied by the electrical substation Y (in particular, the one closest to the hospital).

Figure 5 shows the result of the application of the MARIS workflow, i.e., a fragment of the dependency at an urban level graph. It can be noticed that a geographical proximity criterion was applied to set up dependencies between CI components.

6. Conclusion

The presented MARIS methodology allows the generation of a graph at urban scale that can capture the known dependencies of CIs and Points of interest and model those dependencies that are unknown (because of partial, uncertain, or sensitive data) through the application of proximity criteria.

The use of open software and data (Taginfo, Overpass turbo, OSM) and the knowledge of CI interdependencies data at the system level were used to estimate the interdependencies at an urban level and to produce a realistic graph of interdependencies.

The methodology was applied to the city of Rome to create an interdependency graph characterized by 6025 entities representing real CIs and Points of interest. Future developments will concern the application of dynamic simulation models to the interdependency graph, obtained through the MARIS methodology, in order to reproduce the impacts that would occur on such systems when relevant functions of the supply chain of an area of interest were disrupted by natural or anthropic events.

Appendix A

List of items considered in the DOMINO model

System	Item
Water	Irrigation Water
Water	Water For Industrial Use
Water	Water For Industrial Use
Agriculture, Livestock, Fisheries, Forests	Agriculture And Products
Agriculture, Livestock, Fisheries, Forests	Farming And Products
Agriculture, Livestock, Fisheries, Forests	Forests
Agriculture, Livestock, Fisheries, Forests	Lumber
Agriculture, Livestock, Fisheries, Forests	Fisheries And Products
Environment	Waste Water
Environment	Dams
Environment	Nonhazardous Waste
Environment	Hazardous Waste
Environment	Meteorology and Climate Services
Food Chain	Long-Life Foods
Food Chain	Perishable Foods
Food Chain	Frozen Foods
Food Chain	Drinks and Bottled Water
Trade	Retail Trade
Trade	Wholesale
Culture, Icons, Venues	Arts and Sports
Culture, Icons, Venues	Associationism
Culture, Icons, Venues	Education
Culture, Icons, Venues	Religion
Culture, Icons, Venues	Research
Energy	Coal
Energy	Fuels (Oil, Diesel, Biodiesel, etc.)
Energy	Electricity distribution
Energy	Renewable Sources Biomass
Energy	Wind Renewable Sources
Energy	Geothermal Renewable Sources
Energy	Renewable Water Sources
Energy	Solar Renewable Sources
Energy	Liquid Natural Gas
Energy	Greggio
Energy	Methane
Energy	Nuclear
Energy	Electric Transport
Energy	Electricity Production
Finance	Insurance, Reinsurance, and Pension Funds
Finance	Cash
Finance	Stock Market
Finance	Loans And Mortgages
Finance	Banks
Finance	Services and Payment Systems (Excluding Cash)
Industry	Clothes and Footwear
Industry	Other
Industry	Paper Production
Industry	Chemical Industry
Industry	Construction
Industry	Electrical Devices Production
Industry	Electronics
Industry	Rubber and Plastics Production
Industry	Metal Machinery
Industry	Metallurgy
Industry	Nonmetal Mining
Industry	Metal Mining
Industry	Furniture and Supply Chain
Industry	Leather Goods
Industry	Ceramic Production
Industry	Wood Goods
Industry	Metal Goods Production
Industry	Textile Industry
Industry	Glass and the Supply Chain
Institutions and Public Administration	Central Public Administrations
Institutions and Public Administration	Local Public Administrations
Institutions and Public Administration	Civil Defense and Firefighters
Institutions and Public Administration	Police and Law Enforcement
Institutions and public administration	Local political institutions
Institutions and Public Administration	National Political Institutions
Institutions and Public Administration	Civil Protection
Institutions and Public Administration	Government Financial Services
Institutions and Public Administration	Prison System
Institutions and Public Administration	Defense
Manpower	Physical Manpower
Manpower	Virtual Manpower
Healthcare	Social Assistance
Healthcare	Production of Medicines and Medical Devices
Healthcare	Health Emergency Services
Healthcare	Private Medical Services
Healthcare	Public Medical Services
Healthcare	Veterinary Services
Healthcare	Sale of Medicines and Medical Devices
Services	Other (Opticians and Photographers)
Services	Legal Estate Services
Services	Legal Advisory Services
Services	Informatics Industry
Services	Temporary Employment
Services	Marketing and Advertising
Services	Restaurants
Services	Accommodation Services
Services	Maintenance Services
Services	Cleaning Services
Services	Private Security Services
Services	Software Industry
ICT	Digital Terrestrial Connection System
ICT	Data Processing, Hosting
ICT	Provision of Internet Services (Isp)
ICT	Web Portals
ICT	Television Production
ICT	Publishing (Books, Periodicals, and Newspapers)
ICT	Radio Broadcasting
ICT	Radio and Communication Services
ICT	Satellite Services
ICT	Fixed Telecommunications
ICT	Fiber Optic Telecommunications
ICT	Mobile Telecommunications
Transport and Logistics	Air Transport of Goods and Logistics
Transport and Logistics	Passenger Air Transport
Transport and logistics	Logistics by sea and ocean
Transport And Logistics	Logistics By Road
Transport And Logistics	Transport On Inland Waterways
Transport And Logistics	Rail Freight And Logistics Transport
Transport And Logistics	Passenger Rail Transport

Table A1.

List of items.

Dominic Pepperell

Chapters authored

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