2.5.3 How to measure resilience: resilience metrics

In order to incorporate resilience into asset management processes, the transportation organization needs quantitative methods to measure resilience of their transport systems to threats that may cause failures. However, especially at an early stage of a resilience implementation process, it is suggested that qualitative measures should also be considered in addition to only a quantitative measure and analysis by using, for example, an Multi Criteria Analysis approach.

Generally, there are two steps to measure a resilience-related parameter. The first step is to assign a metric for measurement, and the second step is to establish evaluation criteria to assess the compliance with the metric. Currently, there is no overall measurement standard for resilience within the roadway network, both in terms of metrics and methods of assessment. Resilience metrics for transportation infrastructure used so far, can be divided into two categories: topological metrics and performance-based metrics (Nicolosi et al., 2022).

Metrics belonging to the first group use topological properties of transportation networks, such as shortest path length, average node degree or centrality (Aydin, 2018) and primarily focus on the layout of the transportation systems while ignoring the dynamic features and the operating condition. In other terms, topological properties such as, for example, the ratio between the number of links and number of nodes that is a numerical parameter related to the redundancy of network as far as the connectivity level is concerned, are mainly based on network layout.

The performance-based metrics measure systems’ resilience based on their performance over the period affected by disasters (disruption, period of reduced functionality and recovery according to Fig. 1). Three most widely used performance-based Measures of Resilience “MoR” identified in the literature are:

1. degradation of system functionality over time,
2. time-dependent ratio of recovery to loss,
3. expected fraction of demand satisfied in post-disaster network using specific recovery costs and socio-economic impacts.

An example of a performance-based MoR of the type 1 is proposed in (Bruneau et al 2003 , Bocchini and Frangopol, 2010) and it is represented through Equation 1:

where: RL is defined as the resilience loss, Q(t) is the performance  level of the system expressed in terms of percentage of the original asset condition value (prior to disruption event). The latter can be associated to a single or to an aggregate key performance indicator of the asset, or other functionality-based performance index such as the overall travelled time, the overall travelled distance or the overall generalized transport cost within the examined road network. It is worthy to note that the MoR parameter can be graphically defined as the shaded area shown in Figure 1.

For the second type of indicator, resilience is dynamically represented not merely as single parameter but rather as a time dependent function (as opposed to the other types of indicators, where resilience is a steady indicator) that represents the overall effects of disruption in the 3 phases following the occurrence of the event.

In the third type of MoR, resilience is defined as the expected ratio of demand satisfied  by the network in the post-disaster phases with specific recovery costs. These indicators thus have two characteristics: 1) they explicitly consider transportation demand; and 2 ) they consider the dependence of the post-disruption phases on the economic resources committed.

Generally, the researchers consider the performance-based metrics more appropriate than topological metrics to measure the resilience of transportation systems, as the latter do not consider traffic flows  in the network. However, it is worthy to highlight that some topological metrics have been suggested in order to evaluate redundancy properties of networks affecting overall resilience (Jovanović et al. 2018) and therefore such metrics may be justified in an early stage of a resilience implementation process within Road Asset Management. Among all the performance-based metrics, the third type MoR are preferable as they account for the performance of the system during the whole process, the real operating traffic condition s and the economic resources mobilized. Furthermore, the metrics that include economic resources required for recovery, which influence the recovery time, within the assessment of resilience, are more valuable than the others that usually consider recovery resources as constraints.

In the literature several approaches were proposed to measure the level of functionality of transportation systems and calculate performance based resilience metrics. These performance evaluation approaches were categorized as:  optimization models, simulation models, probability theory models, fuzzy logic models, and data-driven models. Among all of them, optimization models are the most widely used.