Identification and quantification of link vulnerability in multi-level public transport networks: a passenger perspective

Robust public transport networks are important, since disruptions decrease the public transport accessibility of areas. Despite this importance, the full passenger impacts of public transport network vulnerability have not yet been considered in science and practice. We have developed a methodology to identify the most vulnerable links in the total, multi-level public transport network and to quantify the societal costs of link vulnerability for these identified links. Contrary to traditional single-level network approaches, we consider the integrated, total multi-level PT network in the identification and quantification of link vulnerability, including PT services on other network levels which remain available once a disturbance occurs. We also incorporate both exposure to large, non-recurrent disturbances and the impacts of these disturbances explicitly when identifying and quantifying link vulnerability. This results in complete and realistic insights into the negative accessibility impacts of disturbances. Our methodology is applied to a case study in the Netherlands, using a dataset containing 2.5 years of disturbance information. Our results show that especially crowded links of the light rail/metro network are vulnerable, due to the combination of relatively high disruption exposure and relatively high passenger flows. The proposed methodology allows quantification of robustness benefits of measures, in addition to the costs of these measures. Showing the value of robustness, our work can support and rationalize the decision-making process of public transport operators and authorities regarding the implementation of robustness measures.     

Planning for the unexpected: The value of reserve capacity for public transport network robustness

Public transport networks (PTN) are subject to recurring service disruptions. Most studies of the robustness of PTN have focused on network topology and considered vulnerability in terms of connectivity reliability. While these studies provide insights on general design principles, there is lack of knowledge concerning the effectiveness of different strategies to reduce the impacts of disruptions. This paper proposes and demonstrates a methodology for evaluating the effectiveness of a strategic increase in capacity on alternative PTN links to mitigate the impact of unexpected network disruptions. The evaluation approach consists of two stages: identifying a set of important links and then for each identified important link, a set of capacity enhancement schemes is evaluated. The proposed method integrates stochastic supply and demand models, dynamic route choice and limited operational capacity. This dynamic agent-based modelling of network performance enables to capture cascading network effects as well as the adaptive redistribution of passenger flows. An application for the rapid PTN of Stockholm, Sweden, demonstrates how the proposed method could be applied to sequentially designed scenarios based on their performance indicators. The method presented in this paper could support policy makers and operators in prioritizing measures to increase network robustness by improving system capacity to absorb unexpected disruptions.     

Road network vulnerability analysis of area-covering disruptions: A grid-based approach with case study

We present an approach to systematically analysing the vulnerability of road networks under disruptions covering extended areas. Since various kinds of events including floods, heavy snowfall, storms and wildfires can cause such spatially spread degradations, the analysis method is an important complement to the existing studies of single link failures. The methodology involves covering the study area with grids of uniformly shaped and sized cells, where each cell represents the extent of an event disrupting any intersecting links. We apply the approach to the Swedish road network using travel demand and network data from the Swedish national transport modelling system Sampers. The study shows that the impacts of area-covering disruptions are largely determined by the level of internal, outbound and inbound travel demand of the affected area itself. This is unlike single link failures, where the link flow and the redundancy in the surrounding network determine the impacts. As a result, the vulnerability to spatially spread events shows a markedly different geographical distribution. These findings, which should be universal for most road networks of similar scale, are important in the planning process of resource allocation for mitigation and recovery.     

Large-scale road network vulnerability analysis: a sensitivity analysis based approach

Traditionally, an assessment of transport network vulnerability is a computationally intensive operation. This article proposes a sensitivity analysis-based approach to improve computational efficiency and allow for large-scale applications of road network vulnerability analysis. Various vulnerability measures can be used with the proposed method. For illustrative purposes, this article adopts the relative accessibility index (AI), which follows the Hansen integral index, as the network vulnerability measure for evaluating the socio-economic effects of link (or road segment) capacity degradation or closure. Critical links are ranked according to the differences in the AIs between normal and degraded networks. The proposed method only requires a single computation of the network equilibrium problem. The proposed technique significantly reduces computational burden and memory storage requirements compared with the traditional approach. The road networks of the Sioux Falls city and the Bangkok metropolitan area are used to demonstrate the applicability and efficiency of the proposed method. Network manager(s) or transport planner(s) can use this approach as a decision support tool for identifying critical links in road networks. By improving these critical links or constructing new bypass roads (or parallel paths) to increase capacity redundancy, the overall vulnerability of the networks can be reduced.     

An analysis of the Spanish high capacity road network criticality

The analysis of complex networks has been carried out in different fields using an ample variety of method and concepts. Recently, in the general literature of regional economics, the concepts of resilience, connectivity, vulnerability and criticality have been gaining their momentum. The aim of this paper is to provide an analytical framework, using well-known accessibility indicators, in order to calculate the critical links or road sections of the Spanish high-capacity road network. Our analysis will be based on approximately four hundred sections that will be classified in five different groups according to their criticality degree in the whole network. Our analysis will be complemented with the comparison of the results obtained in five different scenarios, namely the average criticality using the effects on the whole country, Madrid, Barcelona, Valencia and Pontevedra. Furthermore, the paper will also analyze what kind of intrinsic characteristics of the sections favor or not the links’ criticality using a method based on a classification and regression tree. This analysis is crucial to understand other important concepts that are recently being studied in network and spatial economics, like, for example, resilience and vulnerability. It is concluded that the number of relations or routes, being a trunk or not, the road density and the time to Madrid capital play an important role in the criticality of the roads section in the high capacity road network.     

Vulnerability analysis for large-scale and congested road networks with demand uncertainty

To assess the vulnerability of congested road networks, the commonly used full network scan approach is to evaluate all possible scenarios of link closure using a form of traffic assignment. This approach can be computationally burdensome and may not be viable for identifying the most critical links in large-scale networks. In this study, an “impact area” vulnerability analysis approach is proposed to evaluate the consequences of a link closure within its impact area instead of the whole network. The proposed approach can significantly reduce the search space for determining the most critical links in large-scale networks. In addition, a new vulnerability index is introduced to examine properly the consequences of a link closure. The effects of demand uncertainty and heterogeneous travellers’ risk-taking behaviour are explicitly considered. Numerical results for two different road networks show that in practice the proposed approach is more efficient than traditional full scan approach for identifying the same set of critical links. Numerical results also demonstrate that both stochastic demand and travellers’ risk-taking behaviour have significant impacts on network vulnerability analysis, especially under high network congestion and large demand variations. Ignoring their impacts can underestimate the consequences of link closures and misidentify the most critical links.     

Assessing potential likelihood and impacts of landslides on transportation network vulnerability

As one of the devastating natural disasters, landslide may induce significant losses of properties and lives area-wide, and generate dramatic damages to transportation network infrastructure. Accessing the impacts of landslide-induced disruptions to roadway infrastructure can be extremely difficult due to the complexity of involved impact factors and uncertainties of vulnerability related events. In this study, a data-driven approach is developed to assess landslide-induced transportation roadway network vulnerability and accessibility. The vulnerability analysis is conducted by integrating a series of static and dynamic factors to reflect the landslide likelihood and the consequences of network accessibility disruptions. The analytical hierarchy process (AHP) model was developed to assess and map the landslide likelihood. A generic vulnerability index (VI) was calculated for each roadway link in the network to identify critical links. Spatial distributions of landslide likelihood, consequences of network disruptions, and network vulnerability degrees were fused and analyzed. The roadway network on Oahu Island in Hawaii is utilized to demonstrate the effectiveness of the proposed approach with all the geo-coded information for its network vulnerability analysis induced by area-wide landslides. Specifically, the study area was classified into five categories of landslide likelihood: very high, high, moderate, low, and stable. About 34% of the study area was assigned as the high or very high categories. The results of network vulnerability analyses highlighted the importance of three highway segments tunnel through the Ko‘olau Range from leeward to windward, connecting Honolulu to the windward coast including the Pali highway segment, Likelike highway segment, and Interstate H-3 highway segment. The proposed network vulnerability analysis method provides a new perspective to examine the vulnerability and accessibility of the roadway network impacted by landslides.     

Importance and exposure in road network vulnerability analysis

The reliability and vulnerability of critical infrastructures have attracted a lot of attention recently. In order to assess these issues quantitatively, operational measures are needed. Such measures can also be used as guidance to road administrations in their prioritisation of maintenance and repair of roads, as well as for avoiding causing unnecessary disturbances in the planning of roadwork. The concepts of link importance and site exposure are introduced. In this paper, several link importance indices and site exposure indices are derived, based on the increase in generalised travel cost when links are closed. These measures are divided into two groups: one reflecting an “equal opportunities perspective”, and the other a “social efficiency perspective”. The measures are calculated for the road network of northern Sweden. Results are collected in a GIS for visualisation, and are presented per link and municipality. In view of the recent great interest in complex networks, some topological measures of the road network are also presented.     

Assessing network vulnerability of heavy rail systems with the impact of partial node failures

Much of the literature in recent years has examined the vulnerability of transportation networks. To identify appropriate and operational measures of nodal centrality using connectivity in the case of heavy rail systems, this paper presents a set of comprehensive measures in the form of a Degree of Nodal Connection (DNC) index. The DNC index facilitates a reevaluation of nodal criticality among distinct types of transfer stations in heavy rail networks that present a number of multiple lines between stations. Specifically, a new classification of transfer stations—mandatory transfer, non-mandatory transfer, and end transfer—and a new measure for linkages—link degree and total link degree—introduces the characteristics of heavy rail networks when we accurately expose the vulnerability of a node. The concept of partial node failure is also introduced and compare the results of complete node failure scenarios. Four local and global indicators of network vulnerability are derived from the DNC index to assess the vulnerability of major heavy rail networks in the United States. Results indicate that the proposed DNC indexes can inform decision makers or network planners as they explore and compare the resilience of multi-hubs and multi-line networks in a comprehensive but accurate manner regardless of their network sizes.

     

The role of travel demand and network centrality on the connectivity and resilience of an urban street system

In the transportation literature, two major and parallel approaches exist to identify the critical elements of a transportation system. On the one hand, conventional transportation engineering emphasizes travel demand, often in terms of traffic volume (i.e., demand side). On the other hand, newer techniques from Network Science emphasize network topology (i.e., supply side). To better understand the relationship between the two approaches, we first investigate whether they correlate by comparing traffic volume and node centrality. Second, we assess the impact of the two approaches on the connectivity and resilience of a transportation network; connectivity is measured by the relative size of the giant component, and resilience is measured by the network’s adaptive capacity (the amount of extra flow it can handle). The urban road system of Isfahan (Iran) is used as a practical case study. Overall, we find that traffic volume indeed correlates with node centrality. In addition, we find that the weighted degree of a node, i.e., the sum of the capacities of its incident links (for small disruptions) and node betweenness (for large disruptions), best captures node criticality. Nodes with high weighted degree and betweenness should therefore be given higher priority to enhance connectivity and resilience in urban street systems. Regarding link criticality, roads with higher capacities showed a more important role as opposed to betweenness, flow, and congestion.

     

Vulnerability and resilience of transport systems – A discussion of recent research

The transport system is critical to the welfare of modern societies. This article provides an overview of recent research on vulnerability and resilience of transport systems. Definitions of vulnerability and resilience are formulated and discussed together with related concepts. In the increasing and extensive literature of transport vulnerability studies, two distinct traditions are identified. One tradition with roots in graph theory studies the vulnerability of transport networks based on their topological properties. The other tradition also represents the demand and supply side of the transport systems to allow for a more complete assessment of the consequences of disruptions or disasters for the users and society. The merits and drawbacks of the approaches are discussed. The concept of resilience offers a broader socio-technical perspective on the transport system’s capacity to maintain or quickly recover its function after a disruption or a disaster. The transport resilience literature is less abundant, especially concerning the post-disaster phases of response and recovery. The research on transport system vulnerability and resilience is now a mature field with a developed methodology and a large amount of research findings with large potential practical usefulness. The authors argue that more cross-disciplinary collaborations between authorities, operators and researchers would be desirable to transform this knowledge into practical strategies to strengthen the resilience of the transport system.     

Predicting disruptions and their passenger delay impacts for public transport stops

Disruptions in public transport can have major implications for passengers and service providers. Our study objective is to develop a generic approach to predict how often different disruption types occur at different stations of a public transport network, and to predict the impact related to these disruptions as measured in terms of passenger delays. We propose a supervised learning approach to perform these predictions, as this allows for predictions for individual stations for each time period, without the requirement of having sufficient empirical disruption observations available for each location and time period. This approach also enables a fast prediction of disruption impacts for a large number of disruption instances, hence addressing the computational challenges that rise when typical public transport assignment or simulation models would be used for real-world public transport networks. To improve transferability of our study results, we cluster stations based on their contribution to network vulnerability using unsupervised learning. This supports public transport agencies to apply the appropriate type of measure aimed to reduce disruptions or to mitigate disruption impacts for each station type. Applied to the Washington metro network, we predict a yearly passenger delay of 5.9 million hours for the total metro network. Based on the clustering, five different types of station are distinguished. Stations with high train frequencies and high passenger volumes located at central trunk sections of the network show to be most critical, along with start/terminal and transfer stations. Intermediate stations located at branches of a line are least critical.

     

Indicators of reliability and vulnerability: Similarities and differences in ranking links of a complex road system

This article investigates two performance attributes of road networks, reliability and vulnerability, analyzing their similarities as well as the differences that justify distinct definitions, based on consolidation of recent studies. We also discuss the indicators found in the literature for these two performance attributes. Since various authors treat vulnerability as an aspect of reliability instead of a specific attribute, we carried out an application to a complex road network representative of the city of Rio de Janeiro to check the suitability of this approach. The results show that the vulnerability indicators are more strongly affected by the characteristics of alternative routes while the reliability metrics are more sensitive to the congestion level. The conclusion is that reliability and vulnerability should be treated distinctly for evaluating the performance of road network links.     

An integrated measure of accessibility and reliability of mass transit systems

The growth of a city or a metropolis requires well-functioning transit systems to accommodate the ensuing increase in travel demand. As a result, mass transit networks have to develop and expand from simple to complex topological systems over time to meet this demand. Such an evolution in the networks’ structure entails not only a change in network accessibility, but also a change in the level of network reliability on the part of stations and the entire system as well. Network accessibility and reliability are popular measures that have been widely applied to evaluate the resilience and vulnerability of a spatially networked system. However, the use of a single measure, either accessibility or reliability, provides different results, which demand an integrated measure to evaluate the network’s performance comprehensively. In this paper, we propose a set of integrated measures, named ACCREL (Integrated Accessibility and Reliability indicators) that considers both metrics in combination to evaluate a network’s performance and vulnerability. We apply the new measures for hypothetical mass transit system topologies, and a case study of the metro transit system in Seoul follows, highlighting the dynamics of network performance with four evolutionary stages. The main contribution of this study lies in the results from the experiments, which can be used to inform how transport network planning can be prepared to enhance the network functionality, thereby achieving a well-balanced, accessible, and reliable system. Insights on network vulnerability are also drawn for public transportation planners and spatial decision makers.     

Transport network criticality metrics: a comparative analysis and a guideline for selection

ABSTRACT

Transport network criticality analysis aims at ranking transport infrastructure elements based on their contribution to the performance of the overall infrastructure network. Despite the wide variety of transport network criticality metrics, little guidance is available on selecting metrics that are fit for the specific purpose of a study. To address this gap, this study reviews, evaluates and compares seventeen criticality metrics. First, we conceptually evaluate these metrics in terms of the functionality of the transport system that the metrics try to represent (either maintaining connectivity, reducing travel cost, or improving accessibility), the underlying ethical principles (either utilitarianism or egalitarianism), and the spatial aggregation considered by the metrics (either network-wide or localised). Next, we empirically compare the metrics by calculating them for eight transport networks. We define the empirical similarity between two metrics as the degree to which they yield similar rankings of infrastructure elements. Pairs of metrics that have high empirical similarity highlight the same set of transport infrastructure elements as critical. We find that empirical similarity is partly dependent on the network’s topology. We also observe that metrics that are conceptually similar do not necessarily have high empirical similarity. Based on the insights from the conceptual and empirical comparison, we propose a five-step guideline for transport authorities and analysts to identify the set of criticality metrics to use which best aligns with the nature of their policy questions.     

Competition in multi-modal transport networks: A dynamic approach

We analyze the behavior of market participants in a multi-modal commuter network, where roads are not priced, but public transport has a usage fee, which is set while taking the effects on the roads into account. In particular, we analyze the difference between markets with a monopolistic public transport operator, which operates all public transport links, and markets in which separate operators own each public transport link. To do so, we consider a simple dynamic transport network consisting of two serial segments and two parallel congestible modes of transport. We obtain a reduced form of the public transport operator’s optimal fare setting problem and show that, even if the total travel demand is inelastic, serial Bertrand–Nash competition on the public transport links leads to different fares than a serial monopoly; a result not observed in a static model. This results from the fact that trip timing decisions, and therefore the generalized prices of all commuters, are influenced by all fares in the network. We then use numerical simulations to show that, contrary to the results obtained in classic studies on vertical competition, monopolistic fares are not always lower than duopolistic fares; the opposite can also occur. We also explore how different parameters influence the price differential, and how this affects welfare.     

A bi-criteria indicator to assess supply chain network performance for critical needs under capacity and demand disruptions

In this paper, we develop a supply chain/logistics network model for critical needs in the case of disruptions. The objective is to minimize the total network costs, which are generalized costs that may include the monetary, risk, time, and social costs. The model assumes that disruptions may have an impact on both the network link capacities as well as on the product demands. Two different cases of disruption scenarios are considered. In the first case, we assume that the impacts of the disruptions are mild and that the demands can be met. In the second case, the demands cannot all be satisfied. For these two cases, we propose two individual performance indicators. We then construct a bi-criteria indicator to assess the supply chain network performance for critical needs. An algorithm is described which is applied to solve a spectrum of numerical examples in order to illustrate the new concepts.     

Basic concepts and future directions of road network reliability analysis

The stability of road networks has become an increasingly important issue in recent times, since the value of time has increased considerably and unexpected delay can results in substantial loss to road users. Road network reliability has now become an important performance measure for evaluating road networks, especially when considering changes in OD traffic demand and link flow capacity over time. This paper outlines the basic concepts, remaining problems and future directions of road network reliability analysis. There are two common definitions of road network reliability, namely, connectivity reliability and travel time reliability. As well, reliability analysis is generally undertaken in both normal and abnormal situations. In order to analyse the reliability of a road network, the reliability of the links within the network must be first determined. A method for estimating the reliability of links within road networks is also suggested in this paper.     

Identification of vehicle sensor locations for link-based network traffic applications

Information on link flows in a vehicular traffic network is critical for developing long-term planning and/or short-term operational management strategies. In the literature, most studies to develop such strategies typically assume the availability of measured link traffic information on all network links, either through manual survey or advanced traffic sensor technologies. In practical applications, the assumption of installed sensors on all links is generally unrealistic due to budgetary constraints. It motivates the need to estimate flows on all links of a traffic network based on the measurement of link flows on a subset of links with suitably equipped sensors. This study, addressed from a budgetary planning perspective, seeks to identify the smallest subset of links in a network on which to locate sensors that enables the accurate estimation of traffic flows on all links of the network under steady-state conditions. Here, steady-state implies that the path flows are static. A “basis link” method is proposed to determine the locations of vehicle sensors, by using the link-path incidence matrix to express the network structure and then identifying its “basis” in a matrix algebra context. The theoretical background and mathematical properties of the proposed method are elaborated. The approach is useful for deploying long-term planning and link-based applications in traffic networks.     

Measuring vulnerability of urban metro network from line operation perspective

Urban metro systems are subject to recurring service disruption for various reasons, such as mechanical or electrical failure, adverse weather, or other accidents. In recent years, studies on metro networks have attracted increasing attention because the consequence of operational accidents is barely affordable. This study proposes to measure the metro network vulnerability from the perspective of line operation by taking the Shanghai metro network as a case study. As opposed to previous studies that focused largely on disruption of important nodes or links, this study investigates the disruption from the line operation perspective. Betweenness centrality (BC) and passenger betweenness centrality (PBC), number of missed trips, weighted average path length, and weighted global efficiency were analyzed considering relative disruption probability of each line. Passenger flow distribution and re-distribution were simulated for different disruption scenarios based on all-or-nothing assignment rule. The results indicate that the metro lines carrying a large number of passengers generally have a significant impact on the network vulnerability. The lines with circular topological form also have a significant influence on passenger flow re-distribution in case of a disruption. The results of this study provide suggestions on metro system administration for potential improvement of the performance of operation, and passengers may meanwhile have an improved alternate plan for their commute trip when a disruption occurs.