**3. Case study 1: vulnerabilities of urban systems**

An urban system is a complex system comprising an infrastructure-actor network, whose complexity is confounded by their close physical proximity and functional interdependencies. An understanding of its complexities can support policymakers to maintain quality of life amidst perturbations, growth and decay, discontinuities, and stress in the system. Building upon [8], we aim to establish the level of influence and vulnerability of a network of multiple infrastructure-actor networks in urban systems.

#### **3.1. A typology of urban system complexities**

An overall urban system comprises several individual systems such as energy, water, telecommunication, and transportation. We develop a typology for classifying different types of system interdependency (**Figure 4**), which is based on (1) whether the network accounts for the connectivity within an individual system (i.e., intrasystem) or across systems (i.e., intersystem) and (2) whether the context of such connectivity takes place in an emergency condition (i.e., with drastic service discontinuities) or in a non-emergency one.

**3.3. Results and implications**

**Figure 4.** A typology of urban system complexities.

tion is described later.

*3.3.1. Centrality degree*

*3.3.2. Betweenness centrality*

*3.3.3. Eigen-vector centrality*

A summary of the network measures is given in **Table 2**. Each of the measures and its implica-

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It counts the number of outgoing (i.e., influence) and incoming (i.e., dependence) links. For the case study, road infrastructure exerts the most influence to others, whereas (waste) water plant and electricity transmission receive most influence from others and hence are most vulnerable. This insight can inform prioritizing infrastructures that need to be decoupled from other.

This measures node importance in terms of its role as an 'intermediary' in a failure path. The electricity plan appears to play the most dominant role. Consequently, urban system needs to

It measures the importance of an infrastructure not only by the number of nodes it affects but also the importance of the nodes to which it affects. It appears that the supervisory control

be disconnected with electricity plant by, for example, having own backup power.

To a certain extent, each of the resulting quadrants has a different focus of inquiry and hence policy implications in terms of actors' actions and coordination. For instance, the first quadrant (Q1) focuses on connectivity within a single sector (e.g., transportation) in a non-emergency condition. An example of inquiry in this sector may revolve around the issue of reducing traffic congestion. By contrast, in the third quadrant (Q3), the inquiry considers interdependencies among multiple sectors (e.g., a city as a whole) and addresses broader issues (e.g., impacts of extreme weather events). In this chapter, we focus on the fourth quadrant.

#### **3.2. Network theory perspective and the network model**

Network theory is employed to obtain measures that can illuminate the degree of infrastructure influence and vulnerability within an urban system. We consider a particular infrastructure as a node. A directional link between two nodes means that the failure in the source affects the end node. This formulation implies that fewer links among nodes are actually desirable. We use and interpret sample data from [9] to model the (inter)dependencies among infrastructure and the repair team for the urban systems in Florida during the 2004 hurricane season. The resulting network model of infrastructure-actor connectivity is depicted in **Figure 5**. To generate some network measures, we employ the UCINET software [10].

Dealing with Complexities and Uncertainties in a System-of-Systems: Case Studies on Urban… http://dx.doi.org/10.5772/intechopen.73706 101

**Figure 4.** A typology of urban system complexities.

### **3.3. Results and implications**

A summary of the network measures is given in **Table 2**. Each of the measures and its implication is described later.

#### *3.3.1. Centrality degree*

This way of characterizing SoS uncertainty space highlights its path dependency nature.

An urban system is a complex system comprising an infrastructure-actor network, whose complexity is confounded by their close physical proximity and functional interdependencies. An understanding of its complexities can support policymakers to maintain quality of life amidst perturbations, growth and decay, discontinuities, and stress in the system. Building upon [8], we aim to establish the level of influence and vulnerability of a network of multiple

An overall urban system comprises several individual systems such as energy, water, telecommunication, and transportation. We develop a typology for classifying different types of system interdependency (**Figure 4**), which is based on (1) whether the network accounts for the connectivity within an individual system (i.e., intrasystem) or across systems (i.e., intersystem) and (2) whether the context of such connectivity takes place in an emergency condi-

To a certain extent, each of the resulting quadrants has a different focus of inquiry and hence policy implications in terms of actors' actions and coordination. For instance, the first quadrant (Q1) focuses on connectivity within a single sector (e.g., transportation) in a non-emergency condition. An example of inquiry in this sector may revolve around the issue of reducing traffic congestion. By contrast, in the third quadrant (Q3), the inquiry considers interdependencies among multiple sectors (e.g., a city as a whole) and addresses broader issues (e.g.,

impacts of extreme weather events). In this chapter, we focus on the fourth quadrant.

**Figure 5**. To generate some network measures, we employ the UCINET software [10].

Network theory is employed to obtain measures that can illuminate the degree of infrastructure influence and vulnerability within an urban system. We consider a particular infrastructure as a node. A directional link between two nodes means that the failure in the source affects the end node. This formulation implies that fewer links among nodes are actually desirable. We use and interpret sample data from [9] to model the (inter)dependencies among infrastructure and the repair team for the urban systems in Florida during the 2004 hurricane season. The resulting network model of infrastructure-actor connectivity is depicted in

tion (i.e., with drastic service discontinuities) or in a non-emergency one.

**3.2. Network theory perspective and the network model**

, the uncertainty space that is path dependent on the initial condition (s1

*]*). One future path (illustrated by the dashed arrows), for example, can be

]. The evolution of uncertainty space progresses over time until the

, there will be a set of uncertainty spaces, each

(i.e., the initial condi-

) 0 is

*) n-1],…,* 

is the realization of the uncertainty space in period<sup>0</sup>

. In *Periodn*

originated from the realizations of all the preceding periods (i.e., uncertainty space<sup>1</sup> *([(si*

Suppose that *(s1*

100 System of System Failures

tion). In period1

represented by *(s1*

*[(si ) 2 ], [(si ) 1 ], [(si ) 0*

the uncertainty space1

*) 0*

end of analysis' time horizon, *Periodn*

*) 0 (s1 ) 1 (s1 ) 2 … (s1 ) n* .

 [*(s1 )0*

infrastructure-actor networks in urban systems.

**3.1. A typology of urban system complexities**

**3. Case study 1: vulnerabilities of urban systems**

It counts the number of outgoing (i.e., influence) and incoming (i.e., dependence) links. For the case study, road infrastructure exerts the most influence to others, whereas (waste) water plant and electricity transmission receive most influence from others and hence are most vulnerable. This insight can inform prioritizing infrastructures that need to be decoupled from other.

#### *3.3.2. Betweenness centrality*

This measures node importance in terms of its role as an 'intermediary' in a failure path. The electricity plan appears to play the most dominant role. Consequently, urban system needs to be disconnected with electricity plant by, for example, having own backup power.

#### *3.3.3. Eigen-vector centrality*

It measures the importance of an infrastructure not only by the number of nodes it affects but also the importance of the nodes to which it affects. It appears that the supervisory control and data acquisition (SCADA) system is the infrastructure with the highest score because it affects three very important nodes such as electricity transmission, electricity plant, and phone/Internet infrastructure.

Our initial work employs network theory to establish the degree and influence and vulnerability of infrastructure-actor interdependency in urban systems. The insight obtained from the work can potentially be used to set priority of actions and to find a balance between vul-

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Uncertainties abound in making investment decisions in energy infrastructure such as electricity power plant. There are some major uncertainties they have to deal with in liberalized energy markets ([11]). It is difficult to predict the future electricity demand price as well as the price of input fuels. In addition, there are several structural uncertainties. These include regulation on price mechanisms (e.g., price cap) and environment (e.g., cooling water, emissions, and waste), the developments in the natural gas industry (e.g., the extraction of gas through fracking), and the unbundling of the energy industry into separate electricity genera-

An SoS model for electricity power plant investment is given in **Figure 6**. It consists of two engineered (power plant and house building technologies) and three actor systems (utility

**4. Case study 2: investments in energy infrastructure**

nerability and performance.

tion, transmission, and distribution function.

**Figure 6.** SoS model for electricity power plant investment.

**4.1. SoS model of investment in energy infrastructure**

companies, household consumers, and public utilities commission).

**Figure 5.** Infrastructure-actor network in the context of Florida urban systems.


**Table 2.** Summary results of network analysis of urban infrastructure systems.

Our initial work employs network theory to establish the degree and influence and vulnerability of infrastructure-actor interdependency in urban systems. The insight obtained from the work can potentially be used to set priority of actions and to find a balance between vulnerability and performance.
