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A Review of Current Practice in Network Disruption Analysis and an Assessment of the Ability to Account for Isolating Links in Transportation Networks
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This paper presents a comprehensive review of the scholarly literature related to the field of network-disruption analysis. Research related to network disruption has progressed immensely since the late 1990s and now includes a wide variety of themes and approaches used to assess the impacts associated with a variety of disruptive events. Of particular relevance are those approaches which use repetitive link and/or node-removal methodologies to develop measures of network robustness or vulnerability (complementary concepts). More recently, various methods have begun to focus on the sequential application of equilibrium-based traffic assignments to measure the cost of a disruption to the network. It is crucial for these types of methods to handle the complexities of real-world transportation networks — one of which is the presence of isolating links in a network, which provide a single link to a particular region or subnetwork. A number of methods have attempted to deal with the problem of isolating links in different ways, but none has been ubiquitously successful. To develop a comprehensive and useful measure of transportation network robustness it is important to successfully address the issue of isolating network links
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... Robustness measures a system's ability to maintain its designed function when faced with perturbations (Jenelius and Cats 2015;Snelder, van Zuylen, and Immers 2012;Zhou, Wang, and Yang 2019). In the context of network analysis, robustness is often framed around the question: how can a network remain functional after a disruptive event (Sullivan, Aultman-Hall, and Novak 2009). For bus networks, robustness ensures that connections for travelers are maintained within expected travel times and costs (Yap and Van Oort 2015). ...
This study revisits bus network robustness by addressing the dependency of bus service networks on the underlying physical road network. A novel methodology integrates resistance distance theory with a multilayer physical-service network framework, accounting for disruptions at the road layer and detour mechanisms. Two robustness indices are introduced: the absolute resistance robustness index, which quantifies the overall impact of disruptions, and the relative resistance robustness index, which reflects network redundancy. Using data from 29 cities, the empirical analysis reveals that geographical and socioeconomic factors significantly influence bus network robustness, with higher GDP, flatter terrains, and concentrated urban areas associated with greater relative robustness. Sensitivity analysis identifies terrain compactness as the most influential factor. This methodology advances the theoretical understanding of transportation network resilience and provides practical tools for urban transportation planning. Future research could extend the approach to directional networks and incorporate travel demand data for more refined analyses.
... Infrastructure interdependencies and network science are essential components of vulnerability assessments [29]. Repetitive link and node removal methodologies can be used to assess network robustness and vulnerability [30]. Many scholars have focused on cascading failures within the context of transportation network vulnerability and reliability. ...
The cascading reliability problem of international railway freight network is becoming noticeable due to the limitation of node transportation capacity with increases in the transport volume of the international railway freight trains. We discuss this problem in this study, thereby focusing on the failure process of the international railway freight network. As the first step, we consider three factors of node degree, node betweenness, and edge betweenness based on the complex network theory, and establish the node model using coupled map lattice method. Next, we select three indicators to evaluate the reliability characteristics of the network and evaluate the robustness of the network with the maximum effective graph and the network efficiency. Finally, we apply the model to the China Railway Express freight network and consider two situations: cascading failures and noncascading failures that are corresponding to two strategies: redistributing cargoes and disbanding cargoes. The results show that the cascading reliability of the China Railway Express freight network is not high. The indicators decrease less than 10% under noncascading failure, while more than 40% under cascading failure, so the network is more reliable under noncascading failure. Our research provides a new way to test the cascading reliability of the international railway freight network and provide different strategies for improving reliability.
... The network performance was found to worsen in cases with node or link disruptions. Consequently, network metrics such as network efficiency and network connectivity were proposed to evaluate the robustness of networks under disruptions [43][44][45]. For example, it was found that the betweenness centrality-based approach is the most effective mode for the railway network in China [46]. ...
Guidance signage systems (GSSs) play a large role in pedestrian navigation for public buildings. A vulnerable GSS can cause wayfinding troubles for pedestrians. In order to investigate the robustness of GSSs, a complex network-based GSS robustness analysis framework is proposed in this paper. First, a method that can transform a GSS into a guidance service network (GSN) is proposed by analyzing the relationships among various signs, and signage node metrics are proposed to evaluate the importance of signage nodes. Second, two network performance metrics, namely, the level of visibility and guidance efficiency, are proposed to evaluate the robustness of the GSN under various disruption modes, and the most important signage node metrics are determined. Finally, a multi-objective optimization model is established to find the optimal weights of these metrics, and a comprehensive evaluation method is proposed to position the critical signage nodes that should receive increased maintenance efforts. A case study was conducted in a subway station and the GSS was transformed into a GSN successfully. The analysis results show that the GSN has scale-free characteristics, and recommendations for GSS design are proposed on the basis of robustness analysis. The signage nodes with high betweenness centrality play a greater role in the GSN than the signage nodes with high degree centrality. The proposed critical signage node evaluation method can be used to efficiently identify the signage nodes for which failure has the greatest effects on GSN performance.
... Much of the mathematical and engineering thinking regarding disruption is based on a notion of equilibrium. Before a disruptive event happens there is an equilibrium state in which the system exists; and, once the cause of the disruption is removed, the system will return to such an equilibrium, or could potentially shift to some new equilibrium if conditions have changed (Sullivan et al., 2009). ...
... Transportation network criticality metrics and network disruption analyses have been summarized in these review papers [5,28,29]. Most studies on pre-disaster component ranking employ a network performance metric such as importance or criticality [30][31][32], adaptability or resilience [33,34], or vulnerability [35]. ...
Transportation networks play a crucial role in society by enabling the smooth movement of people and goods during regular times and acting as arteries for evacuations during catastrophes and natural disasters. Identifying the critical road segments in a large and complex network is essential for planners and emergency managers to enhance the network’s efficiency, robustness, and resilience to such stressors. We propose a novel approach to rapidly identify critical and vital network components (road segments in a transportation network) for resilience improvement or post-disaster recovery. We pose the transportation network as a graph with roads as edges and intersections as nodes and deploy a Graph Neural Network (GNN) trained on a broad range of network parameter changes and disruption events to rank the importance of road segments. The trained GNN model can rapidly estimate the criticality rank of individual road segments in the modified network resulting from an interruption. We address two main limitations in the existing literature that can arise in capital planning or during emergencies: ranking a complete network after changes to components and addressing situations in post-disaster recovery sequencing where some critical segments cannot be recovered. Importantly, our approach overcomes the computational overhead associated with the repeated calculation of network performance metrics, which can limit its use in large networks. To highlight scenarios where our method can prove beneficial, we present examples of synthetic graphs and two real-world transportation networks. Through these examples, we show how our method can support planners and emergency managers in undertaking rapid decisions for planning infrastructure hardening measures in large networks or during emergencies, which otherwise would require repeated ranking calculations for the entire network.
... The investigation of robustness in disrupted networks typically involves the measurement of vulnerability and reliability (Sullivan, Aultman-Hall and Novak, 2009). Vulnerability refers to the extent to which a system cannot function following a disruption. ...
Floods affect an average of 21 million people worldwide each year, and their frequency is expected to increase due to climate warming, population growth, and rapid urbanization. Previous research on the robustness of transportation networks during floods has mainly used percolation theory. However, the component size of disrupted networks cannot capture the entire network's information and, more importantly, does not reflect the local reality. To address this issue, this study introduces a novel approach to context-based bounded centrality to extract the local impact of disruption. In particular, we propose embedding travel behaviour into the road network to calculate bounded centrality and develop new measures characterizing connected component size during flooding. Our analysis can identify critical road segments during floods by comparing the decreasing trend and dispersibility of component size on road networks. To demonstrate the feasibility of these approaches, a case study of the London transportation infrastructure that integrates road networks with relevant urban contexts is presented in this paper. We find that this approach is beneficial for practical risk management, helping decision-makers allocate resources effectively in space and time.
... With the LFPs and RDSs for every link in the Model road network, a new networkcriticality method was developed by the authors, building on previous research into the development of the Network Robustness Index (NRI) (Sullivan et al. 2009(Sullivan et al. , 2010 , considers how critical a roadway is for serving the needs of the region's travelers and incorporates the LFPs and RDSs derived from the vulnerability scoring. To calculate the NCI, traffic assignment is performed using the Model once for the intact network, then once for each of a series of Monte Carlo simulations with disrupted network states. ...
The importance of a reliable transportation system is often taken for granted but its value becomes undeniable when the system is severely disrupted with little warning, the area of impact is extensive, and the amount of time required to restore system connectivity is prolonged. For many states, the largest single cost of flood damage comes from damage to transportation infrastructure and the ensuing disruption of personal, commercial, and emergency-response travel. The goal of transportation risk planning at the state or provincial level is to consider the risks imposed by the vulnerability of network elements to strengthen the system’s ability to withstand a disruptive impact. Although separate measures of vulnerability and criticality are useful, a true risk-based measure would use the vulnerability of links in the network to calculate criticality, so links that are unlikely to be disrupted by a given hazard are left intact in the calculations. This paper details the development and application of the Network Criticality Index (NCI), a new link-specific, risk-based performance measure that uses flood-risk vulnerability scores and a Monte Carlo simulation process for simulating disruptive impacts and measuring link criticality. The paper includes an application of the NCI for flood risk planning to the Deerfield River basin in Vermont. Highly critical segments can be identified as those with the highest NCI values, and mitigation projects can be designed to mitigate the risk. The application finds that relatively high traffic flows can make highly vulnerable links critical due to a lack of redundant routes with adequate capacity to handle flows when they are disrupted by floods. Reducing risk to the highway system from flooding means either (1) improving the segment or crossing and thereby reducing its vulnerability score, or (2) influencing regional traffic flows to prevent disruptive effects on travelers when a disruption occurs. Addressing the vulnerability of the segment or crossing can be done with an engineering design that is sensitive to the project context and the need to improve its ability to withstand higher stream flows in the future.
The robustness of long-distance transport services is paramount for ensuring network connectivity under disruptions. We conduct a comparative analysis of the European rail and air networks of 124 main metropolitan areas, assessing their ability to withstand successive network degradation. We undertake a multi-modal and multi-layer approach in our analysis of the robustness of long-distance transport networks. In particular, we are interested in the role of individual nodes for both air and rail networks as well as for the integrated multi-modal network. Given the hierarchical nature of long-distance transport services, we adopt a multi-layer perspective by means of clustering nodes based on their criticality in order to identify common performance profiles. Original metrics are formulated to measure the impact of nodes on network fragmentation, both at the individual level and as cluster members. Additionally, a new metric is introduced to assess cities’ reliance on air transportation, when considering the integrated multi-layer air-rail network during disruptions in air connections. Our findings indicate that the air network exhibits significantly greater robustness compared to rail, i.e. 10% versus 71% performance loss in the worst case scenario, respectively. Furthermore, primary sub-graph of nodes whose protection from attacks can greatly enhance network’s overall robustness is identified. We discuss our findings in terms of the relationship between network structure, robustness, and the role of critical nodes as well as propose potential mitigation measures.
The robustness of international transport services is paramount for ensuring network connectivity under disruptions. We conduct a comparative analysis of the European rail and air networks of 124 main metropolitan areas, assessing their ability to withstand disruptions through the progressive failure of nodes and links. Various strategies for node selection, including targeted and random failures, are explored. During progressive node failures, network response is measured by considering the size of the largest connected component. Additionally, an aggregate network robustness metric is presented to compare networks and strategies responses. Our findings indicate that the air network exhibits significantly greater robustness compared to rail. Furthermore, original metrics are formulated for measuring the impact of nodes on network fragmentation, both at the individual level and as cluster members. Additionally, a new metric is introduced to assess cities' reliance on air transportation, when considering the integrated multi-layer air-rail network during disruptions in air connections. We discuss our findings in terms of the relationship between network structure, robustness, and the role of critical nodes.
In this paper, we demonstrate how to capture the robustness of a transportation network in the case of degradable links represented by decreasing capacities. The analysis is conducted by utilizing Bureau of Public Road link travel cost functions and a recently proposed network efficiency measure for congested networks. For specific networks we are able to derive lower bounds for the robustness when percentage reductions in the link capacities take place.
A bilevel formulation is developed to identify vulnerable transportation network links. The problem can be viewed as a game between an "evil entity" and the traffic management agency. At the lower level, the traffic management agency routes vehicles according to the system of optimal traffic assignment At the upper level, the evil entity seeks to maximize disruption to the network. A key component of this formulation is the vulnerability index, which is a measure of the importance of a specific link to the connectivity of an origin-destination pair. The vulnerability index accounts for the availability of alternate paths, excess capacity, and travel time. The vulnerability indices are aggregated across all origin-destination pairs into the disruption index. This disruption index is the measure of damage to the network by which the evil entity might rank links as targets. Because the evil entity has a limited amount of resources, it cannot strike all of the potential targets and must choose among subsets of links. Four cases with different types of information availability for the evil entity and the traffic management agency are examined for a simple network. In each case, the evil entity is assumed to aim its strike at the link that has the potential to carry traffic for the most origin-destination pairs.
We investigate the significance of geography for road network vulnerability. By our definitions, a region is exposed if the consequences of a random road closure are severe for this region, and it is important if the consequences of a road closure within the region are severe for the overall network traffic. In a case study of the Swedish road network we study the distribution of exposure and importance among municipalities and counties. We find considerable regional inequity of exposure, in particular for long closure durations. We also identify network regions that are particularly important for the socio-economic efficiency of the road transport system. Furthermore, we have developed simple proxy variables that can be used as rough estimates of exposure and importance and provide a better understanding of the factors underlying these measures. The policy implications of the findings are discussed.
The loss of biodiversity resulting from extinctions is receiving increasing attention. Over several thousands of animal species have been evaluated and recognized as endangered species. Inbreeding depression has been demonstrated in many wild animal species. Here we sequenced 655-978 bp mitochodrial D-loop region of 32 individuals from four regional giant panda populations. Sixteen haplotypes were observed. AMOVE analysis demonstrated that genetic differentiation was not significant in the overall population, except the Qingling pop-ulation. The current panda population may recover from a recent severe bottleneck that occurred about 43 000 years ago. Combining with our results on two endangered snub-nosed monkey species and one common hare species, different scenarios for low genetic variation have been discussed. Our results suggest that low genetic variation does not necessary result from a recent bottleneck, and it is not necessarily an indication of the level of endangerment.
Daily traffic assignments to a large-scale road network are described for build and no-build scenarios to evaluate the addition of two proposed ramps between I-295 and SR-42 in the New Jersey part of the Delaware Valley region. The road network consists of 39,800 links connecting 1,510 zones. The user-equilibrium traffic-assignment problem was solved with a new algorithm called origin-based assignment (OBA), which can achieve highly converged solutions with reasonable computing effort. Following a description of the user-equilibrium traffic-assignment problem and the OBA algorithm, the stability of link-flow differences between the two scenarios in the vicinity of the proposed ramps are examined over a broad range of assignment convergence levels. Then, link-flow differences over this range of convergence levels are compared to link-flow differences between two very highly converged solutions. Examination of the findings reveals, in the writers' view, that a relative gap of 0.01% (0.0001) is required to ensure that the traffic assignments are sufficiently converged to achieve link-flow stability. These convergence levels are then interpreted in terms of the number of Frank-Wolfe iterations needed to achieve comparable relative gaps as well as the computational effort required.
Transport network vulnerability is a relatively new field of research and to this date no commonly agreed definition or quantifiable expression of what vulnerability is exists within the academic community. This paper presents a review of road network vulnerability, seeking to synthesize different terminologies and metrics, among which: reliability, vulnerability, resilience, flexibility, robustness, and adaptive capacity.
As an event-driven system, a supply chain network will face not only the uncertainties in the supply chain, but also the unexpected events outside the supply chain network such as contingency, disruption, disaster and terrorism. These uncertainties and unexpected events have negative impacts on the survival and performance of a supply chain network. Robustness of supply chain networks is an important research issue as a vulnerable supply chain network may not be able to operate at all. While there has been extensive work on the measurement of supply chain performance, little of this work has focused on measuring a supply chain's robustness, that is, the ability to cope with deviation and disruption. This paper presents a system-wide approach to quantifying robustness index of supply chain networks. This approach considers both network structural robustness and network functional robustness. A hypothetical supply chain network is employed to demonstrate the proposed approach.
A new characteristic (residual closeness) which can measure the network resistance is presented. It evaluates closeness after removal of vertices or links, hence two types are considered—vertices and links residual closeness. This characteristic is more sensitive than the well-known measures of vulnerability—it captures the result of actions even if they are small enough not to disconnect the graph. A definition for closeness is modified so it still can be used for unconnected graphs but the calculations are easier.