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.     

Depot location in degradable transport networks

Areas subject to natural or man-made disasters, such as earthquakes, fires, floods or attacks, are reliant on the residual transport network for the rescue of survivors and subsequent recovery. Pre-disaster planning requires assumptions about how the transport network may degrade. This paper presents a game theoretic approach modelling network degradation and applies this to depot location, with a case study based on Sichuan province in China, which is prone to earthquakes. To facilitate a cautious approach to depot location, the method assumes that the transport network is subject to attack by node-specific demons with the power to degrade links. The mixed strategy Nash equilibrium for the non-cooperative zero sum game between dispatchers and demons is used to define rescue hyperpaths. These in turn define the best depot locations. Two forms of the drop heuristic are used to find good depot locations.     

Network impacts of a road capacity reduction: Empirical analysis and model predictions

In spite of their widespread use in policy design and evaluation, relatively little evidence has been reported on how well traffic equilibrium models predict real network impacts. Here we present what we believe to be the first paper that together analyses the explicit impacts on observed route choice of an actual network intervention and compares this with the before-and-after predictions of a network equilibrium model. The analysis is based on the findings of an empirical study of the travel time and route choice impacts of a road capacity reduction. Time-stamped, partial licence plates were recorded across a series of locations, over a period of days both with and without the capacity reduction, and the data were ‘matched’ between locations using special-purpose statistical methods. Hypothesis tests were used to identify statistically significant changes in travel times and route choice, between the periods of days with and without the capacity reduction. A traffic network equilibrium model was then independently applied to the same scenarios, and its predictions compared with the empirical findings. From a comparison of route choice patterns, a particularly influential spatial effect was revealed of the parameter specifying the relative values of distance and travel time assumed in the generalised cost equations. When this parameter was ‘fitted’ to the data without the capacity reduction, the network model broadly predicted the route choice impacts of the capacity reduction, but with other values it was seen to perform poorly. The paper concludes by discussing the wider practical and research implications of the study’s findings.     

Multi-scale robustness model for highway networks under flood events

Transportation system infrastructure often experiences severe flood-related disruptions such as overtopping, erosion, and scour. The ensuing damages can result in enormous direct and indirect economic losses to the traffic network and consequently the individuals through conditions like inaccessibility to commuters and reduction in traffic safety. Many studies have claimed that a robust transportation system could significantly prevent such consequences from natural hazards such as floods, highlighting the importance of robustness measures that could be used by decision-makers to properly manage flooded transportation system. Most available measures related to network robustness assessment are qualitative, and while some recent studies have focused on such evaluation using quantitative assessment approaches related to environmental or social-economic operations, they lack the holistic view towards robustness under flood events. This study develops a composite multi-scale transportation-system robustness model considering flood hazards by synthesizing geographical damage recognition, topological functionality analysis, network operation evaluation, and traffic-user loss estimation. This integrated model has been applied in a real-world highway network, mainly revealing that a given intensive flood occurrence at different locations may result in a variety of after-flood disruptions in the transportation network. To assist the asset owners with developing more reasonable prevention and recovery plans, the developed multi-scale robustness index presents both visible multi-denominational flood consequences and an overall post-event transportation-system robustness indicator.     

A kinematic wave approach to traffic statics and dynamics in a double-ring network

Recently there has been much interest in understanding macroscopic fundamental diagrams of stationary road networks. However, there lacks a systematic method to define and solve stationary states in a road network with complex junctions. In this study we propose a kinematic wave approach to defining, analyzing, and simulating static and dynamic traffic characteristics in a network of two ring roads connected by a 2 × 2 junction, which can be either an uninterrupted interchange or a signalized intersection. This study is enabled by recently developed macroscopic junction models of general junctions. With a junction model based on fair merging and first-in-first-out diverging rules, we first define and solve stationary states and then derive the macroscopic fundamental diagram (MFD) of a stationary uninterrupted network. We conclude that the flow-density relationship of the uninterrupted double-ring network is not unique for high average network densities (i.e., when one ring becomes congested) and unveil the existence of infinitely many stationary states that can arise with a zero-speed shockwave. From simulation results with a corresponding Cell Transmission Model, we verify that all stationary states in the MFD are stable and can be reached, but show that randomness in the retaining ratio of each ring drives the network to more symmetric traffic patterns and higher flow-rates. Furthermore we model a signalized intersection as two alternate diverge junctions and demonstrate that the signalized double-ring network can reach asymptotically periodic traffic patterns, which are therefore defined as “stationary” states in signalized networks. With simulations we show that the flow-density relation is well defined in such “stationary” states, and asymptotic traffic patterns can be impacted by signal cycle lengths and retaining ratios. But compared with uninterrupted interchanges, signalized intersections lead to more asymmetric traffic patterns, lower flow-rates, and even gridlocks when the average density is higher than half of the jam density. The results are consistent between this study and existing studies, but the network kinematic wave model, with appropriate junction models, is mathematically tractable and physically meaningful. It has offered a more complete picture regarding the number and type of stationary states, their stability, and MFD in freeway and signalized networks.     

Transportation serviceability analysis for metropolitan commuting corridors based on modal choice modeling

Major commuting corridors in metropolitan areas generally comprise multiple transportation modes for commuters, such as transit (subways or buses), private vehicles, or park-and-ride combinations. During the morning peak hour, the commuters would choose one of the available transportation modes to travel through the corridors from rural/suburban living areas to urban working areas. This paper introduces a concept of transportation serviceability to evaluate a transportation mode’s service status in a specific link, route, road, or network during a certain period. The serviceability can be measured by the possibility that travelers choose a specific type of transportation service at a certain travel cost. The commuters’ modal-choice possibilities are calculated using a stochastic equilibrium model based on general travel cost. The modeling results illustrate how transportation serviceability is influenced by background traffic flow in a corridor, value of comfort for railway mode, and parking fee distribution.     

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.     

On the existence of stationary states in general road networks

Our daily driving experience and empirical observations suggest that traffic patterns in a road network are relatively stationary during peak periods. In numerous transportation network studies, there has been an implicit conjecture that stationary states exist in a network when origin demands, route choice proportions, and destination supplies are constant. In this study, we first rigorously formulate the conjecture within the framework of a network kinematic wave theory with an invariant junction model. After defining stationary states, we derive a system of algebraic equations in 3-tuples of stationary link flow-rates, demands, and supplies. We then introduce a new definition of junction critical demand levels based on effective demands and supplies. With a map in critical demand levels, we show that its fixed points and, therefore, stationary states exist with the help of Brouwer’s fixed point theorem. For two simple road networks, we show that the map is well-defined and can be used to solve stationary states with a brute-force method. Finally we summarize the study and present some future extensions and applications.     

Spillback congestion in dynamic traffic assignment: A macroscopic flow model with time-varying bottlenecks

In this paper, we propose a new model for the within-day Dynamic Traffic Assignment (DTA) on road networks where the simulation of queue spillovers is explicitly addressed, and a user equilibrium is expressed as a fixed-point problem in terms of arc flow temporal profiles, i.e., in the infinite dimension space of time’s functions. The model integrates spillback congestion into an existing formulation of the DTA based on continuous-time variables and implicit path enumeration, which is capable of explicitly representing the formation and dispersion of vehicle queues on road links, but allows them to exceed the arc length. The propagation of congestion among adjacent arcs will be achieved through the introduction of time-varying exit and entry capacities that limit the inflow on downstream arcs in such a way that their storage capacities are never exceeded. Determining the temporal profile of these capacity constraints requires solving a system of spatially non-separable macroscopic flow models on the supply side of the DTA based on the theory of kinematic waves, which describe the dynamic of the spillback phenomenon and yield consistent network performances for given arc flows. We also devise a numerical solution algorithm of the proposed continuous-time formulation allowing for “long time intervals” of several minutes, and give an empirical evidence of its convergence. Finally, we carry out a thorough experimentation in order to estimate the relevance of spillback modeling in the context of the DTA, compare the proposed model in terms of effectiveness with the Cell Transmission Model, and assess the efficiency of the proposed algorithm and its applicability to real instances with large networks.     

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.     

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.     

Cumulative impacts of road developments in floodplains

This paper investigates the impact of differing road development strategies in floodplains for increasing levels of road expansion, focusing on hydraulic characteristics of floods such as water level, velocity and inundation duration and extent. Cumulative impacts are presented in term of both a resistant approach where road transport infrastructure has the secondary purpose of flood dykes and, a resilience approach that maintains the floodplain hydraulics through the use of flow through structures. Each method is examined in the context of road development in the Cambodian Mekong floodplain. Results indicate that resistance approaches necessitate higher levels of road structures, designed to higher technical specifications, whilst resilience approaches maintain the hydraulic character of floodplains but require the inclusion of well-designed flow through structures with localized scour protection.     

Modelling the resilience,friability and costs of an air transport network affected by a large-scale disruptive event

This paper deals with developing a methodology for estimating the resilience, friability, and costs of an air transport network affected by a large-scale disruptive event. The network consists of airports and airspace/air routes between them where airlines operate their flights. Resilience is considered as the ability of the network to neutralize the impacts of disruptive event(s). Friability implies reducing the network’s existing resilience due to removing particular nodes/airports and/or links/air routes, and consequently cancelling the affected airline flights. The costs imply additional expenses imposed on airports, airlines, and air passengers as the potentially most affected actors/stakeholders due to mitigating actions such as delaying, cancelling and rerouting particular affected flights. These actions aim at maintaining both the network’s resilience and safety at the acceptable level under given conditions.Large scale disruptive events, which can compromise the resilience and friability of a given air transport network, include bad weather, failures of particular (crucial) network components, the industrial actions of the air transport staff, natural disasters, terrorist threats/attacks and traffic incidents/accidents.The methodology is applied to the selected real-life case under given conditions. In addition, this methodology could be used for pre-selecting the location of airline hub airport(s), assessing the resilience of planned airline schedules and the prospective consequences, and designing mitigating measures before, during, and in the aftermath of a disruptive event. As such, it could, with slight modifications, be applied to transport networks operated by other transport modes.     

Reprint of “Modelling the resilience,friability and costs of an air transport network affected by a large-scale disruptive event”

This paper deals with developing a methodology for estimating the resilience, friability, and costs of an air transport network affected by a large-scale disruptive event. The network consists of airports and airspace/air routes between them where airlines operate their flights. Resilience is considered as the ability of the network to neutralize the impacts of disruptive event(s). Friability implies reducing the network’s existing resilience due to removing particular nodes/airports and/or links/air routes, and consequently cancelling the affected airline flights. The costs imply additional expenses imposed on airports, airlines, and air passengers as the potentially most affected actors/stakeholders due to mitigating actions such as delaying, cancelling and rerouting particular affected flights. These actions aim at maintaining both the network’s resilience and safety at the acceptable level under given conditions.Large scale disruptive events, which can compromise the resilience and friability of a given air transport network, include bad weather, failures of particular (crucial) network components, the industrial actions of the air transport staff, natural disasters, terrorist threats/attacks and traffic incidents/accidents.The methodology is applied to the selected real-life case under given conditions. In addition, this methodology could be used for pre-selecting the location of airline hub airport(s), assessing the resilience of planned airline schedules and the prospective consequences, and designing mitigating measures before, during, and in the aftermath of a disruptive event. As such, it could, with slight modifications, be applied to transport networks operated by other transport modes.     

A universal distribution law of network detour ratios

Using trajectory data of normal taxis and ride-sourcing vehicles for 10 cities with various sizes in China, we analyze trip distance characteristics by examining the distribution of network detour ratios. The detour ratio for a specific ride is the ratio of the actual driving distance to the corresponding Euclidean (straight-line) distance. We find that, in spite of their different sizes and geographical features, the various cities exhibit an amazingly similar distribution law of network detour ratios: the mean of the detour ratios is inversely proportional to the Euclidean distance with an intercept. We further verify our findings with extensive simulation experiments for a hypothetical circular city with a directional grid street network. Our finding of this universal distribution law of network detour ratios contrasts sharply with the traditional wisdom of modeling throughout the past 50 years that have typically assumed a constant road detour ratio or factor within the range of 1.25–1.41. Our finding in the urban context also has far-reaching implications for fundamental research in many fields such as human mobility, human geography, facility location problems, logistic distribution networks and urban transportation planning.     

Clustering of heterogeneous networks with directional flows based on “Snake” similarities

Aggregated network level modeling and control of traffic in urban networks have recently gained a lot of interest due to unpredictability of travel behaviors and high complexity of physical modeling in microscopic level. Recent research has shown the existence of well-defined Macroscopic Fundamental Diagrams (MFDs) relating average flow and density in homogeneous networks. The concept of MFD allows to design real-time traffic control schemes specifically hierarchical perimeter control approaches to alleviate or postpone congestion. Considering the fact that congestion is spatially correlated in adjacent roads and it propagates spatiotemporaly with finite speed, describing the main pockets of congestion in a heterogeneous city with small number of clusters is conceivable. In this paper, we propose a three-step clustering algorithm to partition heterogeneous networks into connected homogeneous regions, which makes the application of perimeter control feasible. The advantages of the proposed method compared to the existing ones are the ability of finding directional congestion within a cluster, robustness with respect to parameters calibration, and its good performance for networks with low connectivity and missing data. Firstly, we start to find a connected homogeneous area around each road of the network in an iterative way (i.e. it forms a sequence of roads). Each sequence of roads, defined as ‘snake’, is built by starting from a single road and iteratively adding one adjacent road based on its similarity to join previously added roads in that sequence. Secondly, based on the obtained sequences from the first step, a similarity measure is defined between each pair of the roads in the network. The similarities are computed in a way that put more weight on neighboring roads and facilitate connectivity of the clusters. Finally, Symmetric Non-negative Matrix Factorization (SNMF) framework is utilized to assign roads to proper clusters with high intra-similarity and low inter-similarity. SNMF partitions the data by providing a lower rank approximation of the similarity matrix. The proposed clustering framework is applied in medium and large-size networks based on micro-simulation and empirical data from probe vehicles. In addition, the extension of the algorithm is proposed to deal with the networks with sparse measurements where information of some links is missing. The results show the effectiveness and robustness of the extended algorithm applied to simulated network under different penetration rates (percentage of links with data).     

Identifying critical road segments and measuring system-wide robustness in transportation networks with isolating links: A link-based capacity-reduction approach

A wide range of relatively short-term disruptive events such as partial flooding, visibility reductions, traction hazards due to weather, and pavement deterioration occur on transportation networks on a daily basis. Despite being relatively minor when compared to catastrophes, these events still have profound impacts on traffic flow. To date there has been very little distinction drawn between different types of network-disruption studies and how the methodological approaches used in those studies differ depending on the specific research objectives and on the disruption scenarios being modeled.In this paper, we advance a methodological approach that employs different link-based capacity-disruption values for identifying and ranking the most critical links and quantifying network robustness in a transportation network. We demonstrate how an ideal capacity-disruption range can be objectively determined for a particular network and introduce a scalable system-wide performance measure, called the Network Trip Robustness (NTR) that can be used to directly compare networks of different sizes, topologies, and connectivity levels.Our approach yields results that are independent of the degree of connectivity and can be used to evaluate robustness on networks with isolating links. We show that system-wide travel-times and the rank-ordering of the most critical links in a network can vary dramatically based on both the capacity-disruption level and on the overall connectivity of the network. We further show that the relationships between network robustness, the capacity-disruption level used for modeling, and network connectivity are non-linear and not necessarily intuitive. We discuss our findings with respect to Braess’ Paradox.     

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.     

Private road competition and equilibrium with traffic equilibrium constraints

Toll road competition is one of the important issues under a build-operate-transfer (BOT) scheme, which is being encountered nowadays in many cities. When there are two or more competing firms and each firm operates a competitive toll road, their profits are interrelated due to the competitors' choices and demand inter-dependence in the network. In this paper we develop game-theoretic approaches to the study of the road network, on which multiple toll roads are operated by competitive private firms. The strategic interactions and market equilibria among the private firms are analyzed both in determining their supply (road capacity) and price (toll level) over the network. The toll road competition problems in general traffic equilibrium networks are formulated as an equilibrium program with equilibrium constraints or bi-level variational inequalities. Heuristic solution methods are proposed and their convergences are demonstrated with simple network examples. It is shown that private pricing and competition can be both profitable and welfare-improving.     

西部地区公路地质灾害监测预报技术研究

“西部地区公路地质灾害监测预报技术研究”项目针对西部地区公路地质灾害危险性区划、滑坡、崩塌与泥石流监测预报及地质灾害安全管理等关键技术问题进行深入系统研究,形成了公路滑坡、崩塌与泥石流监测预报成套技术,建立了公路地质灾害数据标准,构建了“基于GIS的公路地质灾害监测预报信息系统”平台,实现了公路地质灾害监测实时分析处理和动态预报,为地质灾害综合管理提供技术支撑。