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.     

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 fault tolerance approach for railway scheduling and train control

This paper makes two contributions. It firstly proposes the use of a fault tolerance approach for railway operations and secondly it develops a minimum time gap matrix model for capacity computation and the study of perturbation effects through the generation of a compressed timetable. A fault tolerance approach is proposed to improve the operational efficiency of the railway network in terms of the network capacity and the robustness of train timetables. The term fault tolerance is used in a broad sense, to represent any abnormalities or unexpected events in operations or equipment. Enhanced fault tolerance capability provides safety assurance so that, in normal operating conditions, trains can adopt much faster speed profiles when approaching a ‘to-be-cleared’ signal block at stations and junctions than those currently permitted, effectively turning the status of ‘be ready to stop’ to that of ‘proceed with caution’. In the rare event of a ‘fault’ in the system, e.g. if a conflicting train fails to move out of a signalling block as expected or a switch fails to operate as required, the train would be re-routed to take an alternative path. In this study, the new approach is developed on three scenarios i.e., a standard classic right turn junction, a terminus station, and a small network combining both of these elements to demonstrate the performance gains, but the concept can be readily extended for other types of junctions/stations. Results so far show great potential in the proposed fault tolerance approach to increase the capacity and enhance operational robustness to perturbations at such locations. A novel method for capacity computation called minimum time gap matrix model is also introduced that has capability to produce compressed timetables directly from a given train sequence.     

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.     

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.     

An artificial neural network approach for evaluating transportation network improvements

As demand increases over time, new links or improvements in existing links may be considered for increasing a network's capacity. The selection and timing of improvement projects is an especially challenging problem when the benefits or costs of those projects are interdependent. Most existing models neglect the interdependence of projects and their impacts during intermediate periods of a planning horizon, thus failing to identify the optimal improvement program. A multiperiod network design model is proposed to select the best combination of improvement projects and schedules. This model requires the evaluation of numerous network improvement alternatives in several time periods. To facilitate efficient solution methods for the network design model, an artificial neural network approach is proposed for estimating total travel times corresponding to various project selection and scheduling decisions. Efficient procedures for preparing an appropriate training data set and an artificial neural network for this application are discussed. The Calvert County highway system in southern Maryland is used to illustrate these procedures and the resulting performance.     

Improving recovery-to-optimality robustness through efficiency-balanced design of timetable structure

To improve the service quality of the railway system (e.g., punctuality and travel times) and to enhance the robust timetabling methods further, this paper proposes an integrated two-stage approach to consider the recovery-to-optimality robustness into the optimized timetable design without predefined structure information (defined as flexible structure) such as initial departure times, overtaking stations, train order and buffer time. The first-stage timetabling model performs an iterative adjustment of all departure and arrival times to generate an optimal timetable with balanced efficiency and recovery-to-optimality robustness. The second-stage dispatching model evaluates the recovery-to-optimality robustness by simulating how each timetable generated from the first-stage could recover under a set of restricted scenarios of disturbances using the proposed dispatching algorithm. The concept of recovery-to-optimality is examined carefully for each timetable by selecting a set of optimally refined dispatching schedules with minimum recovery cost under each scenario of disturbance. The robustness evaluation process enables an updating of the timetable by using the generated dispatching schedules. Case studies were conducted in a railway corridor as a special case of a simple railway network to verify the effectiveness of the proposed approach. The results show that the proposed approach can effectively attain a good trade-off between the timetable efficiency and obtainable robustness for practical applications.     

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.     

The reliable hub-and-spoke design problem: Models and algorithms

Hub-and-spoke structure is widely adopted in industry, especially in transportation and telecommunications applications. Although hub-and-spoke paradigm demonstrates significant advantages in improving network connectivity with less number of routes and saving operating cost, the failure of hubs and reactive disruption management could lead to substantial recovery cost to the operators. Thus, we propose a set of reliable hub-and-spoke network design models, where the selection of backup hubs and alternative routes are taken into consideration to proactively handle hub disruptions. To solve these nonlinear mixed integer formulations for reliable network design problems, Lagrangian relaxation and Branch-and-Bound methods are developed to efficiently obtain optimal solutions. Numerical experiments are conducted with respect to real data to demonstrate algorithm performance and to show that the resulting hub-and-spoke networks are more resilient to hub unavailability.     

Vehicle scheduling under stochastic trip times: An approximate dynamic programming approach

Due to unexpected demand surge and supply disruptions, road traffic conditions could exhibit substantial uncertainty, which often makes bus travelers encounter start delays of service trips and substantially degrades the performance of an urban transit system. Meanwhile, rapid advances of information and communication technologies have presented tremendous opportunities for intelligently scheduling a bus fleet. With the full consideration of delay propagation effects, this paper is devoted to formulating the stochastic dynamic vehicle scheduling problem, which dynamically schedules an urban bus fleet to tackle the trip time stochasticity, reduce the delay and minimize the total costs of a transit system. To address the challenge of “curse of dimensionality”, we adopt an approximate dynamic programming approach (ADP) where the value function is approximated through a three-layer feed-forward neural network so that we are capable of stepping forward to make decisions and solving the Bellman’s equation through sequentially solving multiple mixed integer linear programs. Numerical examples based on the realistic operations dataset of bus lines in Beijing have demonstrated that the proposed neural-network-based ADP approach not only exhibits a good learning behavior but also significantly outperforms both myopic and static polices, especially when trip time stochasticity is high.     

Disruption risk management in railroad networks: An optimization-based methodology and a case study

We propose an optimization-based methodology for recovery from random disruptions in service legs and train services in a railroad network. A network optimization model is solved for each service leg to evaluate a number of what-if scenarios. The solutions of these optimization problems are then used in a predictive model to identify the critical disruption factors and accordingly design a suitable mitigation strategy. A mitigation strategy, such as adding flexible or redundant capacity in the network, is an action that is deliberately taken by management in order to hedge against the cost and impact of disruption if it occurs. It is important that managers consider the trade-offs between the cost of mitigation strategy and the expected cost of disruption. The proposed methodology is applied to a case study built using the realistic infrastructure of a railroad network in the mid-west United States. The resulting analysis underscores the importance of accepting a slight increase in pre-disruption transportation costs, which in turn will enhance network resiliency by building dis-similar paths for train services, and by installing alternative links around critical service legs.     

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.     

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.     

Modeling the interaction between buses,passengers and cars on a bus route using a multi-agent system

This paper models part of a public transport network (PTN), specifically, a bus route, as a small-size multi-agent system (MAS). The proposed approach is applied to a case study considering a ‘real world’ bus line within the PTN in Auckland, New Zealand. The MAS-based analysis uses modeling and simulation to examine the characteristics of the observed system – autonomous agents interacting with one another – under different scenarios, considering bus capacity and frequency of service for existing and projected public transport (PT) demand. A simulation model of a bus route is developed, calibrated and validated. Several results are attained, such as when the PT passenger load is not close to bus capacity, this load has no effect on average passenger waiting time at bus stops. The model proposed can be useful to practitioners as a tool to model the interaction between buses and other agents.     

Formulating and solving the network design problem by decomposition

The optimal transportation network design problem is formulated as a convex nonlinear programming problem and a solution method based on standard traffic assignment algorithms is presented. The technique can deal with network improvements which introduce new links, which increase the capacity of existing links, or which decrease the free-flow (uncongested) travel time on existing links (with or without simultaneously increasing link capacity). Preliminary computational experience with the method demonstrates that it is capable of solving very large problems with reasonable amounts of computer time.     

Validation of a schedule‐based capacity restraint transit assignment model for a large‐scale network

This paper describes the application of a capacity restraint trip assignment algorithm to a real, large‐scale transit network and the validation of the results. Unlike the conventional frequency‐based approach, the network formulation of the proposed model is dynamic and schedule‐based. Transit vehicles are assumed to operate to a set of pre‐determined schedules. Passengers are assumed to select paths based on a generalized cost function including in‐vehicle and out‐of‐vehicle time and line change penalty. The time‐varying passenger demand is loaded onto the network by a time increment simulation method, which ensures that the capacity restraint of each vehicle during passenger boarding is strictly observed. The optimal‐path and path‐loading algorithms are applied iteratively by the method of successive averages until the network converges to the predictive dynamic user equilibrium. The Hong Kong Mass Transit Railway network is used to validate the model results. The potential applications of the model are also discussed.     

Design and evaluation of dynamic traffic management strategies for congested conditions

This paper presents a procedure for dynamic design and evaluation of traffic management strategies in oversaturated conditions. The method combines a dynamic control algorithm and a disutility function. The dynamic algorithm designs signal control parameters to manage formation and dissipation of queues on system links with explicit consideration of current and projected queue lengths and demands. The disutility function measures the relative performance of the dynamic control algorithm based on preset system performance goals. The user may statically select the management strategy, or alternatively the system may be instructed to set off different management schemes based on predefined performance thresholds. The problem was formulated as one of output maximization subject to state, control, and traffic management strategy choices. Solutions were obtained using genetic algorithms. Four traffic management plans were tested to show the capabilities of the new procedure. The results show that the procedure is able to generate suitable signal control schemes that are favorable to attaining the desired traffic management goals. The results showed that multiple, or hybrids of single measures of effectiveness may need to be examined in order to correctly assess system performance. The procedure has potential for real-time implementation in an intelligent transportation system setting.     

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.     

A computational model for the probit‐based dynamic stochastic user optimal traffic assignment problem

This paper focuses on computational model development for the probit‐based dynamic stochastic user optimal (P‐DSUO) traffic assignment problem. We first examine a general fixed‐point formulation for the P‐DSUO traffic assignment problem, and subsequently propose a computational model that can find an approximated solution of the interest problem. The computational model includes four components: a strategy to determine a set of the prevailing routes between each origin–destination pair, a method to estimate the covariance of perceived travel time for any two prevailing routes, a cell transmission model‐based traffic performance model to calculate the actual route travel time used by the probit‐based dynamic stochastic network loading procedure, and an iterative solution algorithm solving the customized fixed‐point model. The Ishikawa algorithm is proposed to solve the computational model. A comparison study is carried out to investigate the efficiency and accuracy of the proposed algorithm with the method of successive averages. Two numerical examples are used to assess the computational model and the algorithm proposed. Results show that Ishikawa algorithm has better accuracy for smaller network despite requiring longer computational time. Nevertheless, it could not converge for larger network. Copyright © 2010 John Wiley & Sons, Ltd.     

Decomposition of general facility disruption correlations via augmentation of virtual supporting stations

Infrastructure facilities may be subject to probabilistic disruptions that compromise individual facility functionality as well as overall system performance. Disruptions of distributed facilities often exhibit complex spatial correlations, and thus it is difficult to describe them with succinct mathematical models. This paper proposes a new methodological framework for analyzing and modeling facility disruptions with general correlations. This framework first proposes pairwise transformations that unify three probabilistic representations (i.e., based on conditional, marginal, and scenario probabilities) of generally correlated disruption profile among multiple distributed facilities. Then facilities with any of these disruption profile representations can be augmented into an equivalent network structure consisting of additional supporting stations that experience only independent failures. This decomposition scheme largely reduces the complexity associated with system evaluation and optimization. We prove analytical properties of the transformations and the decomposition scheme, and illustrate the proposed methodological framework using a set of numerical case studies and sensitivity analyses. Managerial insights are also drawn.