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.

     

Estimating the influence of common disruptions on urban rail transit networks

With the continuous expansion of urban rapid transit networks, disruptive incidents—such as station closures, train delays, and mechanical problems—have become more common, causing such problems as threats to passenger safety, delays in service, and so on. More importantly, these disruptions often have ripple effects that spread to other stations and lines. In order to provide better management and plan for emergencies, it has become important to identify such disruptions and evaluate their influence on travel times and delays. This paper proposes a novel approach to achieve these goals. It employs the tap-in and tap-out data on the distribution of passengers from smart cards collected by automated fare collection (AFC) facilities as well as past disruptions within networks. Three characteristic types of abnormal passenger flow are divided and analyzed, comprising (1) “missed” passengers who have left the system, (2) passengers who took detours, and (3) passengers who were delayed but continued their journeys. In addition, the suggested computing method, serving to estimate total delay times, was used to manage these disruptions. Finally, a real-world case study based on the Beijing metro network with the real tap-in and tap-out passenger data is presented.     

User perspectives in public transport timetable optimisation

The present paper deals with timetable optimisation from the perspective of minimising the waiting time experienced by passengers when transferring either to or from a bus. Due to its inherent complexity, this bi-level minimisation problem is extremely difficult to solve mathematically, since timetable optimisation is a non-linear non-convex mixed integer problem, with passenger flows defined by the route choice model, whereas the route choice model is a non-linear non-continuous mapping of the timetable. Therefore, a heuristic solution approach is developed in this paper, based on the idea of varying and optimising the offset of the bus lines. Varying the offset for a bus line impacts the waiting time passengers experience at any transfer stop on the bus line.In the bi-level timetable optimisation problem, the lower level is a transit assignment calculation yielding passengers’ route choice. This is used as weight when minimising waiting time by applying a Tabu Search algorithm to adapt the offset values for bus lines. The updated timetable then serves as input in the following transit assignment calculation. The process continues until convergence.The heuristic solution approach was applied on the large-scale public transport network in Denmark. The timetable optimisation approach yielded a yearly reduction in weighted waiting time equivalent to approximately 45 million Danish kroner (9 million USD).     

Train boarding and alighting rates at high passenger loads

Line capacity in metro and high‐frequency suburban railways is as much determined by station stop times as by factors such as line speed or train acceleration. This paper applies the method developed by London Underground to estimate the time that trains spend at stations, as a function of the physical characteristics of the situation (e.g. train door width) and the numbers of passengers involved. Analysis was carried out on a number of alternative designs for refurbishment of South West Trains' Class 455 inner‐suburban rolling stock. Whilst there is indeed an interaction between boarding and alighting passengers, this paper demonstrates that the LUL relationship breaks down at the highest passenger loads. Moreover, results indicate that passenger flow is not equal between different parts of the same group of boarders or alighters.     

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.     

基于交通渗流理论的城市轨道交通网络动态服务瓶颈识别

为准确把握轨道交通网络化运营的新态势和新要求,力求轨道交通系统在大客流下做到运输能力和服务水平的供需匹配,需对轨道交通网络的关键瓶颈进行有效识别和疏解。本文借鉴交通渗流理论,提出了限制网络整体服务水平和连通效能的动态服务瓶颈的识别方法,该方法综合考虑了城市轨道交通系统的网络特性、客流特性和服务特性。其中针对区间服务水平状态,该方法提出了定量评定的复合指标模型。以成都地铁线网为案例,基于实际客流运营数据,构建动态网络,识别服务瓶颈,验证了方法的适用性和准确性,对城市轨道交通系统运营管理有实际指导意义。     

An integrated Bayesian approach for passenger flow assignment in metro networks

This paper proposes an integrated Bayesian statistical inference framework to characterize passenger flow assignment model in a complex metro network. In doing so, we combine network cost attribute estimation and passenger route choice modeling using Bayesian inference. We build the posterior density by taking the likelihood of observing passenger travel times provided by smart card data and our prior knowledge about the studied metro network. Given the high-dimensional nature of parameters in this framework, we apply the variable-at-a-time Metropolis sampling algorithm to estimate the mean and Bayesian confidence interval for each parameter in turn. As a numerical example, this integrated approach is applied on the metro network in Singapore. Our result shows that link travel time exhibits a considerable coefficient of variation about 0.17, suggesting that travel time reliability is of high importance to metro operation. The estimation of route choice parameters conforms with previous survey-based studies, showing that the disutility of transfer time is about twice of that of in-vehicle travel time in Singapore metro system.     

Long-term planning for ring-radial urban rail transit networks

Extensive work exists on regular rail network planning. However, few studies exist on the planning and design of ring-radial rail transit systems. With more ring transit lines being planned and built in Asia, Europe and the America's, a detailed study on ring transit lines is timely. An analytical model to find the optimal number of radial lines in a city for any demand distribution is first introduced. Secondly, passenger route choice for different rail networks is analyzed, for a many-to-many Origin-Destination (OD) demand distribution, based on a total travel time cost per passenger basis. The routes considered are: (1) radial lines only; (2) ring line only or radial lines and ring line combined; or (3) direct access to a destination without using the rail system. Mathematica and Matlab are used to code the route choice model. A cost-benefit optimization model to identify the feasibility and optimality of a ring line is proposed. Unlike simulations and agent-based models, this model is shown to be easily transferable to many ring-radial transit networks. The City of Calgary is used as an example to illustrate the applicability of each model. The existing urban rail network and trip distribution are major influencing factors in judging the feasibility and optimal location of the ring line. This study shows the potential net benefit of introducing a ring line by assessing changes in passengers’ costs. The changes in passenger cost parameters, such as ride cost and access cost, are shown to greatly influence the feasibility of a ring line.     

An investigation into passenger preference for express trains during peak hours

Seoul South Korea metro line 9 has a relatively short (27 km) length and dispatches express and local trains alternately with a 3-min headway. Despite a minimal time saving and more crowded conditions with regard to express trains, the passenger dependence on them is growing. The present study investigated the potential reasons for this seemingly irrational phenomenon during peak hours. A multinomial logit model was set up based only on route-specific variables, such as travel times and the proportion of express-train-involved travel time. Furthermore, the influence of trip-related properties, individual-specific characteristics, and latent factors on the preference for express trains was identified by adopting an interaction variable model. As a result, passenger transferrals from, or to, other lines, had a positive influence on the choice of express trains, but those who regularly used line 9 were less dependent on express trains. Passengers with pre-trip plans tended to prefer the use of express trains. Regarding the latent variables, passengers who were well aware of the line 9 system and sensitive to sanitation tended to choose express trains, while those who were sensitive to comfort tended to avoid express trains.     

Train rescheduling model with train delay and passenger impatience time in urban subway network

This paper considers the train rescheduling problem with train delay in urban subway network. With the objective of minimizing the negative effect of train delay to passengers, which is quantified with a weighted combination of travel time cost and the cost of giving up the planned trips, train rescheduling model is proposed to jointly synchronize both train delay operation constraints and passenger behavior choices. Space–time network is proposed to describe passenger schedule‐based path choices and obtain the shortest travel times. Impatience time is defined to describe the intolerance of passengers to train delay. By comparing the increased travel time due to train delay with the passenger impatience time, a binary variable is defined to represent whether the passenger will give up their planned trips or not. The proposed train rescheduling model is implemented using genetic algorithm, and the model effectiveness is further examined through numerical experiments of real‐world urban subway train timetabling test. Duration effects of the train delay to the optimization results are analyzed. Copyright © 2017 John Wiley & Sons, Ltd.     

Demand-driven timetable design for metro services

Timetable design is crucial to the metro service reliability. A straightforward and commonly adopted strategy in daily operation is a peak/off-peak-based schedule. However, such a strategy may fail to meet dynamic temporal passenger demand, resulting in long passenger waiting time at platforms and over-crowding in trains. Thanks to the emergence of smart card-based automated fare collection systems, we can now better quantify spatial–temporal demand on a microscopic level. In this paper, we formulate three optimization models to design demand-sensitive timetables by demonstrating train operation using equivalent time (interval). The first model aims at making the timetable more dynamic; the second model is an extension allowing for capacity constraints. The third model aims at designing a capacitated demand-sensitive peak/off-peak timetable. We assessed the performance of these three models and conducted sensitivity analyzes on different parameters on a metro line in Singapore, finding that dynamical timetable built with capacity constraints is most advantageous. Finally, we conclude our study and discuss the implications of the three models: the capacitated model provides a timetable which shows best performance under fixed capacity constraints, while the uncapacitated model may offer optimal temporal train configuration. Although we imposed capacity constraints when designing the optimal peak/off-peak timetable, its performance is not as good as models with dynamical headways. However, it shows advantages such as being easier to operate and more understandable to the passengers.     

Metro disruption management: Optimal initiation time of substitute bus services under uncertain system recovery time

Determining the initiation time of substitute bus (SB) services is critical for metro disruption management, especially under uncertain recovery time. This study develops a mathematical formulation to determine the optimal initiation time (OIT) of SB services by trading-off their initiation cost and passenger delay cost, thereby minimizing the total system cost. Given the probability distribution of metro disruption duration, we determine the OIT by formulating an optimization problem to minimize the expected total system cost. We then conduct sensitivity analyses of the initiation cost of SB services, passenger value of time, and SB services rate. The results show that SB services ought to be activated only if the metro incident lasts longer than a certain time interval, depending on the factors mentioned earlier, and the OIT should advance with the predicted incident duration. This paper derives analytical results for the case of linear passenger arrival, and determines the results numerically for the case of non-linear passenger arrival when analytical closed-form solutions are not available. The findings will facilitate transit operators to develop response plans in the aftermath of a metro disruption.     

A bi‐level programming approach — Optimal transit fare under line capacity constraints

The fare of a transit line is one of the important decision variables for transit network design. It has been advocated as an efficient means of coordinating the transit passenger flows and of alleviating congestion in the transit network. This paper shows how transit fare can be optimized so as to balance the passenger flow on the transit network and to reduce the overload delays of passengers at transit stops. A bi‐level programming method is developed to optimize the transit fare under line capacity constraints. The upper‐level problem seeks to minimize the total network travel time, while the lower‐level problem is a stochastic user equilibrium transit assignment model with line capacity constraints. A heuristic solution algorithm based on sensitivity analysis is proposed. Numerical example is used to illustrate the application of the proposed model and solution algorithm.     

Energy-efficient metro train rescheduling with uncertain time-variant passenger demands: An approximate dynamic programming approach

In a heavily congested metro line, unexpected disturbances often occur to cause the delay of the traveling passengers, infeasibility of the current timetable and reduction of the operational efficiency. Due to the uncertain and dynamic characteristics of passenger demands, the commonly used method to recover from disturbances in practice is to change the timetable and rolling stock manually based on the experiences and professional judgements. In this paper, we develop a stochastic programming model for metro train rescheduling problem in order to jointly reduce the time delay of affected passengers, their total traveling time and operational costs of trains. To capture the complexity of passenger traveling characteristics, the arriving ratio of passengers at each station is modeled as a non-homogeneous poisson distribution, in which the intensity function is treated as time-varying origin-to-destination passenger demand matrices. By considering the number of on-board passengers, the total energy usage is modeled as the difference between the tractive energy consumption and the regenerative energy. Then, we design an approximate dynamic programming based algorithm to solve the proposed model, which can obtain a high-quality solution in a short time. Finally, numerical examples with real-world data sets are implemented to verify the effectiveness and robustness of the proposed approaches.     

Equity-oriented skip-stopping schedule optimization in an oversaturated urban rail transit network

In this study, we focus on improving system-wide equity performance in an oversaturated urban rail transit network based on multi-commodity flow formulation. From the system perspective, an urban rail transit network is a distributed system, where a set of resources (i.e., train capacity) is shared by a number of users (i.e., passengers), and equitable individuals and groups should receive equal shares of resources. However, when oversaturation occurs in an urban rail transit network during peak hours, passengers waiting at different stations may receive varying shares of train capacity leading to the inequity problem under train all-stopping pattern. Train skip-stopping pattern is an effective operational approach, which holds back some passengers at stations and re-routes their journeys in the time dimension based on the available capacity of each train. In this study, the inequity problem in an oversaturated urban rail transit network is analyzed using a multi-commodity flow modeling framework. In detail, first, discretized states, corresponding to the number of missed trains for passengers, are constructed in a space-time-state three-dimensional network, so that the system-wide equity performance can be viewed as a distribution of all passengers in different states. Different from existing flow-based optimization models, we formulate individual passenger and train stopping pattern as commodity and network structure in the multi-commodity flow-modeling framework, respectively. Then, we aim to find an optimal commodity flow and well-designed network structure through the proposed multi-commodity flow model and simultaneously achieve the equitable distribution of all passengers and the optimal train skip-stopping pattern. To quickly solve the proposed model and find an optimal train skip-stopping pattern with preferable system-wide equity performance, the proposed linear programming model can be effectively decomposed to a least-cost sub-problem with positive arc costs for each individual passenger and a least-cost sub-problem with negative arc costs for each individual train under a Lagrangian relaxation framework. For application and implementation, the proposed train skip-stopping optimization model is applied to a simple case and a real-world case based on Batong Line in the Beijing Subway Network. The simple case demonstrates that our proposed Lagrangian relaxation framework can obtain the approximate optimal solution with a small-gap lower bound and a lot of computing time saved compared with CPLEX solver. The real-world case based on Batong Line in the Beijing Subway Network compares the equity and efficiency indices under the operational approach of train skip-stopping pattern with those under the train all-stopping pattern to state the advantage of the train skip-stopping operational approach.     

Coordination of last train transfers using automated fare collection (AFC) system data

This paper studies last train coordination problem for metro networks, aiming to maximize the total number of passengers who can reach their destinations by metro prior to the end of operation. The concept of last boarding time is defined as the latest time that passengers can board the last trains and reach final destinations. The corresponding method for calculating last boarding time is also put forward. With automatic fare collection system data, an optimization model for coordinating last trains is proposed. The objective function optimizes the number of passengers who can reach their final destinations during the train period using departure times and headways of last trains for each line as decision variables. Afterwards, an adaptive genetic algorithm is put forward to solve this model and is applied to a case study of the Shanghai metro system. Copyright © 2017 John Wiley & Sons, Ltd.     

Isolating high-priority metro and feeder bus transfers using smart card data

Fixed-rail metro (or ‘subway’) infrastructure is generally unable to provide access to all parts of the city grid. Consequently, feeder bus lines are an integral component of urban mass transit systems. While passengers prefer a seamless transfer between these two distinct transportation services, each service’s operations are subject to a different set of factors that contribute to metro-bus transfer delay. Previous attempts to understand transfer delay were limited by the availability of tools to measure the time and cost associated with passengers’ transfer experience. This paper uses data from smart card systems, an emerging technology that automatically collects passenger trip data, to understand transfer delay. The primary objective of this study is to use smart card data to derive a reproducible methodology that isolates high priority transfer points between the metro system and its feeder-bus systems. The paper outlines a methodology to identify transfer transactions in the smart card dataset, estimate bus headways without the aid of geographic location information, estimate three components of the total transfer time (walking time, waiting time, and delay time), and isolate high-priority transfer pairs. The paper uses smart card data from Nanjing, China as a case study. The results isolate eight high priority metro-bus transfer pairs in the Nanjing metro system and finally, offers several targeted measures to improve transfer efficiency.     

Forecasting the short-term metro passenger flow with empirical mode decomposition and neural networks

Short-term passenger flow forecasting is a vital component of transportation systems. The forecasting results can be applied to support transportation system management such as operation planning, and station passenger crowd regulation planning. In this paper, a hybrid EMD-BPN forecasting approach which combines empirical mode decomposition (EMD) and back-propagation neural networks (BPN) is developed to predict the short-term passenger flow in metro systems. There are three stages in the EMD-BPN forecasting approach. The first stage (EMD Stage) decomposes the short-term passenger flow series data into a number of intrinsic mode function (IMF) components. The second stage (Component Identification Stage) identifies the meaningful IMFs as inputs for BPN. The third stage (BPN Stage) applies BPN to perform the passenger flow forecasting. The historical passenger flow data, the extracted EMD components and temporal factors (i.e., the day of the week, the time period of the day, and weekday or weekend) are taken as inputs in the third stage. The experimental results indicate that the proposed hybrid EMD-BPN approach performs well and stably in forecasting the short-term metro passenger flow.     

Multi-objective re-synchronizing of bus timetable: Model,complexity and solution

This work is originally motived by the re-planning of a bus network timetable. The existing timetable with even headways for the network is generated using line by line timetabling approach without considering the interactions between lines. Decision-makers (i.e., schedulers) intend to synchronize vehicle timetable of lines at transfer nodes to facilitate passenger transfers while being concerned with the impacts of re-designed timetable on the regularity of existing timetable and the accustomed trip plans of passengers. Regarding this situation, we investigate a multi-objective re-synchronizing of bus timetable (MSBT) problem, which is characterized by headway-sensitive passenger demand, uneven headways, service regularity, flexible synchronization and involvement of existing bus timetable. A multi-objective optimization model for the MSBT is proposed to make a trade-off between the total number of passengers benefited by smooth transfers and the maximal deviation from the departure times of the existing timetable. By clarifying the mathematical properties and solution space of the model, we prove that the MSBT problem is NP-hard, and its Pareto-optimal front is non-convex. Therefore, we design a non-dominated sorting genetic (NSGA-II) based algorithm to solve this problem. Numerical experiments show that the designed algorithm, compared with enumeration method, can generate high-quality Pareto solutions within reasonable times. We also find that the timetable allowing larger flexibility of headways can obtain more and better Pareto-optimal solutions, which can provide decision-makers more choice.     

Evaluation of an existing bus network using a transit network optimisation model: a case study of the Hiroshima City Bus network

This study evaluates an existing bus network from the perspectives of passengers, operators, and overall system efficiency using the output of a previously developed transportation network optimisation model. This model is formulated as a bi-level optimisation problem with a transit assignment model as the lower problem. The upper problem is also formulated as bi-level optimisation problem to minimise costs for both passengers and operators, making it possible to evaluate the effects of reducing operator cost against passenger cost. A case study based on demand data for Hiroshima City confirms that the current bus network is close to the Pareto front, if the total costs to both passengers and operators are adopted as objective functions. However, the sensitivity analysis with regard to the OD pattern fluctuation indicates that passenger and operator costs in the current network are not always close to the Pareto front. Finally, the results suggests that, regardless of OD pattern fluctuation, reducing operator costs will increase passenger cost and increase inequity in service levels among passengers.