A methodological approach to analyze vulnerability of interdependent infrastructures

Abstract

The infrastructures are interconnected and interdependent on multiple levels, the failure of one infrastructure can result in the disruption of other infrastructures, which can cause severe economic disruption and loss of life or failure of services. A methodological approach to analyze vulnerability of interdependent infrastructures has been introduced in this paper, two types of vulnerability are studied: structural vulnerability and functional vulnerability. Infrastructure topologies are only used for analysis on structural vulnerability while operating regimes of different infrastructures are further considered to analyze functional vulnerability. For these two types of vulnerability, interdependent effects are mainly studied and the effects of interdependence strength between infrastructures have also been analyzed. The analysis on structural vulnerability will be helpful to design or improve the infrastructures in the long run while the discussion on functional vulnerability will be useful to protect them in the short term. The methodology introduced in this paper will be advantageous to comprehensively analyze the vulnerability of interdependent infrastructures and protect them more efficiently.

Introduction

The infrastructures on which our society depends are interconnected and interdependent on multiple levels. For example, natural gas may fuel critical gas-fired generators in the electric power system, while at the same time electric power may be used to operate critical systems needed for delivering gas [1]. The failure of one infrastructure can result in the disruption of other infrastructures, which can cause severe economic disruption and loss of life or failure of services which impede public health and well-being. The major power blackout on August 14, 2003, lasted up to 4 days in various parts of the eastern USA, caused traffic’s congestion and affected many other critical infrastructures, the estimated direct costs were between $4 billion and $10 billion [2].

In the past few years, many researchers have concentrated on the modeling and analysis of interdependent infrastructures. Related work tends to fall into two broad categories, structural analysis and functional analysis. Based on complex network theories [3], [4], many researchers have focused on structural vulnerability of different types of single infrastructure [5], [6], [7] or interdependent infrastructures [8], [9], [10]. Their responses to attacks are measured by their global and local connectivity, their vertex degree distributions, and their redundancy ratios and so on. However, considering infrastructure topologies alone are not enough to reflect real vulnerability of those different types of infrastructures, so many other researchers have studied functional vulnerability by further taking their operation regimes into consideration. An interdependent layer network model has been formulated by Earl et al. In their works, definitions of five types of infrastructure interdependencies have been presented and incorporated into a network flows mathematical representation [11]. This model has been used to simulate the September 11 attacks on the WTC. A graph Model of Critical Infrastructure has been used for the analysis of infrastructure interdependencies which could take into account not only abstract interdependencies but also selected properties of infrastructure types such as buffering of resources [12], [13], [14], [15]. This model tries to use one universal model to describe several kinds of infrastructures, which seem to be difficult, because operating regimes for various infrastructures are varied and simulation steps for various infrastructures should be also different. Recently, Rosato et al. have used the DC power flow model and a model of the TCP/IP basic features to analyze the functional vulnerability of interdependent Italian electrical transmission network and the backbone of the internet network [16]. Their studies have opened the way to the use of simulations of the behavior of interdependent infrastructures based on the use of phenomenological master equations [17].

In this paper, we will introduce a methodological approach to comprehensively analyze the vulnerability of interdependent infrastructures, two types of vulnerability will be considered: structural vulnerability and functional vulnerability. Relationships between these two types of vulnerability will be also investigated. The interdependent infrastructure topologies will be generated based on geographical proximity. Vulnerability is related to attacks and can be described as the decrease of efficiency after attack. For structural vulnerability, the infrastructures topologies are the only information and the average reciprocal shortest path lengths of infrastructure networks are used to measure structural efficiency. For functional vulnerability, operating regimes of different infrastructures are further considered and the functionality levels of these infrastructures are considered as functional efficiency. When infrastructures are subjected to attacks, infrastructure efficiencies decrease and their vulnerability can be analyzed. Electrical network and gas pipeline network are mainly discussed in this paper. The gas pipeline consists of metering stations, valves, compressors and gas storages, all these components depend on power supply. Some electric power is provided from turbines driven with gas from the pipelines [12]. For different infrastructures, various models will be used to describe their operating regimes.

The rest of this paper is organized as follows: Section 2 introduces the methodological approach to comprehensively analyze the vulnerability of interdependent infrastructures. The analysis on structural and functional vulnerability, including the operating regimes for different infrastructures will be also introduced in this section. In Section 3, based on the methodological approach, artificial interdependent infrastructures will be generated and simulations are then performed to analyze their vulnerability, and effects of interdependence strength between these two infrastructures are also discussed. Finally, what we found in our paper are summarized in Section 4, and future directions are proposed.