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.     

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.     

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.     

Exposing the role of exposure: Public transport network risk analysis

Network risk assessment takes into consideration the probability that adverse events occur and the impacts of such disruptions on network functionality. In the context of transport networks, most studies have focused on vulnerability, the reduction in performance indicators given that a disruption occurs. This study presents and applies a method to explicitly account for exposure in identifying and evaluating link criticality in public transport networks. The proposed method is compared with conventional measures that lack exposure information. A criticality assessment is performed by accounting for the probability of a certain event occurring and the corresponding welfare loss. The methodology was applied for a multi-modal public transport network in the Netherlands where data concerning disruptions was available. The results expose the role of exposure in determining link criticality and overall network vulnerability. The findings demonstrate that disregarding exposure risks prioritizing links with high passenger volumes over links with a higher failure probability that are significantly more critical to network performance. The inclusion of exposure allows performing a risk analysis and has consequences on assessing mitigation measures and investment priorities.     

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.     

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.     

A framework for robustness analysis of road networks for short term variations in supply

There is a growing awareness that road networks, are becoming more and more vulnerable to unforeseen disturbances like incidents and that measures need to be taken in order to make road networks more robust. In order to do this the following questions need to be addressed: How is robustness defined? Against which disturbances should the network be made robust? Which factors determine the robustness of a road network? What is the relationship between robustness, travel times and travel time reliability? Which indicators can be used to quantify robustness? How can these indicators be computed? This paper addresses these questions by developing a consistent framework for robustness in which a definition, terms related to robustness, indicators and an evaluation method are included. By doing this, policy makers and transportation analyst are offered a framework to discuss issues that are related to road network robustness and vulnerability which goes beyond the disconnected definitions, indicators and evaluation methods used so far in literature. Furthermore, the evaluation method that is presented for evaluating the robustness of the road network against short term variations in supply (like incidents) contributes to the problem of designing robust road networks because it has a relatively short computation time and it takes spillback effects and alternative routes into account.     

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.     

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.

     

A method to assess demand growth vulnerability of travel times on road network links

Many national governments around the world have turned their recent focus to monitoring the actual reliability of their road networks. In parallel there have been major research efforts aimed at developing modelling approaches for predicting the potential vulnerability of such networks, and in forecasting the future impact of any mitigating actions. In practice—whether monitoring the past or planning for the future—a confounding factor may arise, namely the potential for systematic growth in demand over a period of years. As this growth occurs the networks will operate in a regime closer to capacity, in which they are more sensitive to any variation in flow or capacity. Such growth will be partially an explanation for trends observed in historic data, and it will have an impact in forecasting too, where we can interpret this as implying that the networks are vulnerable to demand growth. This fact is not reflected in current vulnerability methods which focus almost exclusively on vulnerability to loss in capacity. In the paper, a simple, moment-based method is developed to separate out this effect of demand growth on the distribution of travel times on a network link, the aim being to develop a simple, tractable, analytic method for medium-term planning applications. Thus the impact of demand growth on the mean, variance and skewness in travel times may be isolated. For given critical changes in these summary measures, we are thus able to identify what (location-specific) level of demand growth would cause these critical values to be exceeded, and this level is referred to as Demand Growth Reliability Vulnerability (DGRV). Computing the DGRV index for each link of a network also allows the planner to identify the most vulnerable locations, in terms of their ability to accommodate growth in demand. Numerical examples are used to illustrate the principles and computation of the DGRV measure.     

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.     

In search of surrogate safety indicators for vulnerable road users: a review of surrogate safety indicators

Surrogate indicators are meant to be alternatives or complements of safety analyses based on accident records. These indicators are used to study critical traffic events that occur more frequently, making such incidents easier to analyse. This article provides an overview of existing surrogate indicators and specifically focuses on their merit for the analyses of vulnerable road users and the extent to which they have been validated by previous research. Each indicator is evaluated based on its ability to consider the collision risk, which can be further divided into the initial conditions of an event, the magnitude of any evasive action and the injury risk in any traffic event. The results show that various indicators and their combinations can reflect different aspects of any traffic event. However, no existing indicator seems to capture all aspects. Various studies have also focused on the validity of different indicators. However, due to the use of diverse approaches to validation, the large difference in how many locations were investigated and variations in the duration of observation at each location, it is difficult to compare and discuss the validity of the different surrogate safety indicators. Since no current indicator can properly reflect all the important aspects underlined in this article, the authors suggest that the choice of a suitable indicator in future surrogate safety studies should be made with considerations of the context-dependent suitability of the respective indicator.     

Robust network sensor location for complete link flow observability under uncertainty

The link observability problem is to identify the minimum set of links to be installed with sensors that allow the full determination of flows on all the unobserved links. Inevitably, the observed link flows are subject to measurement errors, which will accumulate and propagate in the inference of the unobserved link flows, leading to uncertainty in the inference process. In this paper, we develop a robust network sensor location model for complete link flow observability, while considering the propagation of measurement errors in the link flow inference. Our model development relies on two observations: (1) multiple sensor location schemes exist for the complete inference of the unobserved link flows, and different schemes can have different accumulated variances of the inferred flows as propagated from the measurement errors. (2) Fewer unobserved links involved in the nodal flow conservation equations will have a lower chance of accumulating measurement errors, and hence a lower uncertainty in the inferred link flows. These observations motivate a new way to formulate the sensor location problem. Mathematically, we formulate the problem as min–max and min–sum binary integer linear programs. The objective function minimizes the largest or cumulative number of unobserved links connected to each node, which reduces the chance of incurring higher variances in the inference process. Computationally, the resultant binary integer linear program permits the use of a number of commercial software packages for its globally optimal solution. Furthermore, considering the non-uniqueness of the minimum set of observed links for complete link flow observability, the optimization programs also consider a secondary criterion for selecting the sensor location scheme with the minimum accumulated uncertainty of the complete link flow inference.     

Evaluating the significance of highway network links under the flood damage: An accessibility approach

This paper conducts an analysis to assess the significance of highway network links in Maryland under flood damage. An accessibility index is derived to incorporate the distance-decay effect and the volume of traffic influence on the transportation network. The accessibility level of individual counties and the state as a whole is checked before and after the hypothetical disruption of individual links within the floodplain. The results indicate that critical links identified based on the distance-only and the distance-traffic volume criteria appear to be different, implying that the priority of retrofit might also vary depending on what criterion to choose. The percentage loss of accessibility due to the disruption of a link is generally greater in the latter. However, distance-only consideration results in a more prominent spatial distribution pattern of links in percentage loss induced. Some links remain significant in both cases. Especially if the disruption of a certain link does not have an alternative solution (for example, if the link is the only way in and out of a certain county) and if counties connected by the link are low accessibility counties, the two criteria may produce a similar outcome.     

A framework for neighbour links travel time estimation in an urban network

This paper proposes a solution to the problem of limited network sensor coverage caused by insufficient sample size of probe vehicles or inadequate numbers of fixed sensors. A framework is proposed to estimate link travel times using available data from neighbouring links. Two clues are used for real-time travel time estimation: link historical travel time data and online travel time data from neighbour links. In the absence of online travel time data from neighbour links, historical records only have to be relied upon. However, where the two types of data are available, a data fusion scheme can be applied to make use of the two clues. The proposed framework is validated using real-life data from the City of Vancouver, British Columbia. The estimation accuracy is found to be comparable to the existing literature. Overall, the results demonstrate the feasibility of using neighbour links data as an additional source of information that might not have been extensively explored before.     

A big data approach for clustering and calibration of link fundamental diagrams for large-scale network simulation applications

Existing methods for calibrating link fundamental diagrams (FDs) often focus on a limited number of links and use grouping strategies that are largely dependent on roadway physical attributes alone. In this study, we propose a big data-driven two-stage clustering framework to calibrate link FDs for freeway networks. The first stage captures, under normal traffic state, the variations of link FDs over multiple days based on which links are clustered in the second stage. Two methods, i.e. the standard k-means algorithm combined with hierarchical clustering and a modified hierarchical clustering based on the Fréchet distance, are applied in the first stage to obtain the FD parameter matrix for each link. The calibrated matrices are input into the second stage where the modified hierarchical clustering is re-employed as a static approach resulting in multiple clusters of links. To further consider the variations of link FDs, the static approach is extended by modifying the similarity measure through the principle component analysis (PCA). The resulting multivariate time-series clustering models the distributions of the FD parameters as a dynamic approach. The proposed framework is applied on the Melbourne freeway network using one-year worth of loop detector data. Results have shown that (a) similar roadway physical attributes do not necessarily result in similar link FDs, (b) the connectivity-based approach performs better in clustering link FDs as compared with the centroid-based approach, and (c) the proposed framework helps achieving a better understanding of the spatial distribution of links with similar FDs and the associated variations and distributions of the FD parameters.     

Network design: selection and design of links and facility location

In this paper we introduce new network design problems. A network of potential links is given. Each link can be either constructed or not at a given cost. Also, each constructed link can be constructed either as a one-way or two-way link. The objective is to minimize the total construction and transportation costs. Two different transportation costs are considered: (i) traffic is generated between any pair of nodes and the transportation cost is the total cost for the users and (ii) demand for service is generated at each node and a facility is to be located on a node to satisfy the demand. The transportation cost in this case is the total cost for a round trip from the facility to each node and back. We will consider two options in regard to the links between nodes. They can either be two-way only, or mixed, with both two-way and one-way (in either direction) allowed. When these options are combined with the two objective functions, four basic problems are created. These problems are solved by a descent algorithm, simulated annealing, tabu search, and a genetic algorithm. Extensive computational results are presented.     

Quasi-dynamic traffic assignment with residual point queues incorporating a first order node model

Static traffic assignment models are still widely applied for strategic transport planning purposes in spite of the fact that such models produce implausible traffic flows that exceed link capacities and predict incorrect congestion locations. There have been numerous attempts to constrain link flows to capacity. Capacity constrained models with residual queues are often referred to as quasi-dynamic traffic assignment models. After reviewing the literature, we come to the conclusion that an important piece of the puzzle has been missing so far, namely the inclusion of a first order node model. In this paper we propose a novel path-based static traffic assignment model for finding a stochastic user equilibrium in general transportation networks. This model includes a first order (steady-state) node model that yields more realistic turn capacities, which are then used to determine consistent capacity constrained traffic flows, residual point (vertical) queues (upstream bottleneck links), and path travel times consistent with queuing theory. The route choice part of the model is specified as a variational inequality problem, while the network loading part is formulated as a fixed point problem. Both problems are solved using existing techniques to find a solution. We illustrate the model using hypothetical examples, and also demonstrate feasibility on large-scale networks.     

Optimizing path query performance: graph clustering strategies

Path queries over transportation networks are operations required by many Geographic Information Systems applications. Such networks, typically modeled as graphs composed of nodes and links and represented as link relations, can be very large and hence often need to be stored on secondary storage devices. Path query computation over such large persistent networks amounts to high I/O costs due to having to repeatedly bring in links from the link relation from secondary storage into the main memory buffer for processing. This paper is the first to present a comparative experimental evaluation of alternative graph clustering solutions in order to show their effectiveness in path query processing over transportation networks. Clustering optimization is attractive because it does not incur any run-time cost, requires no auxiliary data structures, and is complimentary to many of the existing solutions on path query processing. In this paper, we develop a novel clustering technique, called spatial partition clustering (SPC), that exploits unique properties of transportation networks such as spatial coordinates and high locality. We identify other promising candidates for clustering optimizations from the literature, such as two-way partitioning and approximate topological clustering. We fine-tune them to optimize their I/O behavior for path query processing. Our experimental evaluation of the performance of these graph clustering techniques using an actual city road network as well as randomly generated graphs considers variations in parameters such as memory buffer size, length of the paths, locality, and out-degree. Our experimental results are the foundation for establishing guidelines to select the best clustering technique based on the type of networks. We find that our SPC performs the best for the highly interconnected city map; the hybrid approach for random graphs with high locality; and the two-way partitioning based on link weights for random graphs with no locality.