Transportation Geography and Network Science/Vulnerability

Vulnerability has been treated with varying degrees of complexity. In its simplest treatment, vulnerability is effectively the inverse of reliability: as a network’s reliability decreases, its vulnerability increases and vice versa.

A more complex theory of vulnerability connects the ideas of reliability and network resilience by considering how network structure mitigates or aggravates the effect of link degradation. Vulnerability is evaluated for each link in the network and reflects the degree to which network performance (by some chosen measure) is affected if a particular link is degraded. A link is highly vulnerable if a small degradation results in a large reduction of network performance.

This approach to vulnerability could be extended to encompass whole-network vulnerability by computing the ratios of links in a network that have various values of vulnerability. A network with a high proportion of highly vulnerable links would be described as highly vulnerable.

Road network vulnerability
The vulnerability of road network reflects the effect of a failure node, link, or network on quality of transportation networks. The change of some important variables for network could evaluate the vulnerability, which are showed as variations, such as capacity, accessibility and connectivity. Hence, in a simple way, the vulnerability is viewed as the inverse of the conception of reliability, which means that the higher reliability stands for the lower vulnerability for transportation network.

For vulnerability, many different definitions are proposed and non of them has been generally accepted. Berdica defined vulnerability for transportation network as the susceptibility to incidents, which could cause significant reductions of serviceability.

D’ESTE and Tylor, on the other hand, used accessibility measurement as per the following definition to evaluate the consequences of failures in a road network (i.e., vulnerability). (1) For a node, it is vulnerable if the accessibility of the node could be significantly reduced by the shutdown of a small number of links. (2) For a link, it is critical if the accessibility for the network or certain nodes could be significantly reduced by the shutdown of the link. An example of the Australian national highway network in the Figure shows the consequences of a failure link. The origin and destination for this example is Perth and Adelaide in Australia, respectively. The common used route is the route showed as blue in the Figure. However, the Eyre Highway was cut off once by the flood, so the transportation between Perth and Adelaide needed to use the alternative route, which is showed as red in the Figure. .



Case study: an accessibility approach in assessing regional road network vulnerability
This case study uses the Green Triangle Region in Australia, which shows a great economical development potential because of its forestry and tourism industry, to analyze the vulnerability on the regional road network level. The reducing of the vulnerability for the road network in the Green Triangle Region attracts more demand. The region is located at the southern end of the border and between two metropolitan cities, Adelaide and Melbourne, which is shown in the Figure.



Glenelg Highway is an important road for the green Triangle region, and four critical links in the Glenelg Highway were chosen to analyze its vulnerability, which are Glenelg Highway near Dunkeld, Glenelg Highway near Hamilton, Glenelg Highway near Casterton and Glenelg Highway near Tarpeena. These links were emphasized on Figure 7.

To measure the vulnerability on the regional road network level, Accessibility/Remoteness index of Australia (ARIA) was used to evaluate the accessibility. The ARIA is defined as the accessibility to the services centers which have a population more than 1,000, such as schools, shopping centers, or hospitals.

The ARIA index could be expressed as,

$$ARIA_{iL}=\sum_L min\{3,\frac{x_{iL}}{\overline{x}_L}\}$$

where $$x_{iL}$$ is the distance from point $$i$$ to the nearest service centers, while the $$\overline{x}_L$$ stands for the average value of distance to the nearest service centers. Since the vulnerability shows the changes of accessibility for the before-and –after scenario, Tylor presents the relative accessibility changes as, $$\Delta{RA}=1-\frac{A_i^1}{A_i^0}$$

where $$A_i^0$$ is the accessibility for the complete network, and $${A_i^1}$$ is that for the network with failure links.

The vulnerability of each link measures the changes in the network's ARIA index before-and-after the cut of one link. The results show that the degradation of Glenelg Highway near Dunkeld has significant effects on the accessibility of Dunkeld, and the changes of ARIA index has increased more than 57%. While the degradations of both Glenelg Highway near Hamilton and Glenelg Highway near Casterton have great effects on the accessibility of Casterton, and ARIA indices change around 20%. Combing with the changes of ARIA indices on other service centers, the Glenelg Highway near Dunkeld could be treated as the most critical link in those four.

Vulnerability vs. Reliability vs. Resilience vs. Robustness
This section contrasts Vulnerability with Reliability,  Resilience, and  Robustness. In a nutshell, reliability is the possibility that people or goods could move from one place to another successfully, while vulnerability reflects the effect of a failure node, link or network on the quality of transportation network as a whole. We could treat vulnerability as the inverse of reliability in a simple way that the higher reliability stands for the lower vulnerability for transportation network. Resilience is the ability for the system to maintain its demonstrated level of service or to restore itself to that level of service in a specified timeframe, which could be an important factor to affect the robustness of the road network. As the ability to cope with disturbances happened in the network, network robustness plays a vital role in providing reliability to travelers. A road network with higher robustness could provide users a higher reliability. But unlike reliability, robustness is the property for the network itself rather than for the users.

Further Readings
1. Network Science book: Chapter 8 (Barabasi)