Measuring vulnerability of urban metro network from line operation perspective

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

Optimal slack time for timed transfers at a transit terminal

At transit terminals where two routes interchange passengers, total system costs may be reduced by allowing some “slack” time in the vehicle schedules to decrease the probability of missed connections. Transfer cost functions are formulated and used to determine optimal slack time for simple systems with transfers between one bus route and one rail line. Some analytic results are derived for empirical discrete and Gumbel distributions of bus arrival times. Relations between the optimal slack times and headways, transfer volumes, passenger time values, bus operating costs, and standard deviations of bus and train arrivals are also developed numerically using normally distributed arrivals. However, the proposed numerical approach can optimize slack times for any observed arrival distributions. The results provide some guidelines on desirable slack times and show that schedule coordination between the two routes is not worth attempting when standard deviations of arrivals exceed certain levels. Possible extensions of this work are suggested in the last section.     

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.     

An application-oriented model of passenger waiting time based on bus departure time intervals

This paper develops an application-oriented model to estimate waiting times as a function of bus departure time intervals. Bus stops are classified into Type A and B depending on whether they are connected with urban rail transit systems. Distributions of passenger arrival rates are analyzed based on field data for Beijing. The results indicate that the best fits for the distribution of passenger arrival rates for Type A and B bus stops are the lognormal distribution and gamma distribution, respectively. By analyzing relationships between passenger arrival rates and bus departure time intervals, it is demonstrated that parameters of the passenger arrival rate distribution can be expressed by the average and coefficient of variation of bus departure time intervals in functional relationships. The validation shows that the model provides a reliable estimation of the average passenger waiting time based on readily available bus departure time intervals.     

Optimizing coordinated transfer with probabilistic vehicle arrivals and passengers' walking time

Supporting efficient connections by synchronizing vehicle arrival time and passengers' walking time at a transfer hub may significantly improve service quality, stimulate demand, and increase productivity. However, vehicle travel times and walking times in urban settings often varies spatially and temporally due to a variety of factors. Nevertheless, the reservation of slack time and/or the justification of vehicle arrival time at the hub may substantially increase the success of transfer coordination. To this end, this paper develops a model that considers probabilistic vehicle arrivals and passengers walking speeds so that the slack time and the scheduled bus arrival time can be optimized by minimizing the total system cost. A case study is conducted in which the developed model is applied to optimize the coordination of multiple bus routes connecting at a transfer station in Xi'an, China. The relationship between decision variables and model parameters, including the mean and the standard deviation of walking time, is explored. It was found that the joint impact of probabilistic vehicle arrivals and passengers' walking time significantly affects the efficiency of coordinated transfer. The established methodology can essentially be applied to any distribution of bus arrival and passenger walking time. Copyright © 2017 John Wiley & Sons, Ltd.     

A model of bus bunching under reliability-based passenger arrival patterns

If bus service departure times are not completely unknown to the passengers, non-uniform passenger arrival patterns can be expected. We propose that passengers decide their arrival time at stops based on a continuous logit model that considers the risk of missing services. Expected passenger waiting times are derived in a bus system that allows also for overtaking between bus services. We then propose an algorithm to derive the dwell time of subsequent buses serving a stop in order to illustrate when bus bunching might occur. We show that non-uniform arrival patterns can significantly influence the bus bunching process. With case studies we find that, even without exogenous delay, bunching can arise when the boarding rate is insufficient given the level of overall demand. Further, in case of exogenous delay, non-uniform arrivals can either worsen or improve the bunching conditions, depending on the level of delay. We conclude that therefore such effects should be considered when service control measures are discussed.     

A bi-level model for single-line rail timetable design with consideration of demand and capacity

This paper proposes a bi-level model to solve the timetable design problem for an urban rail line. The upper level model aims at determining the headways between trains to minimize total passenger cost, which includes not only the usual perceived travel time cost, but also penalties during travel. With the headways given by the upper level model, passengers’ arrival times at their origin stops are determined by the lower level model, in which the cost-minimizing behavior of each passenger is taken into account. To make the model more realistic, explicit capacity constraints of individual trains are considered. With these constraints, passengers cannot board a full train, but wait in queues for the next coming train. A two-stage genetic algorithm incorporating the method of successive averages is introduced to solve the bi-level model. Two hypothetical examples and a real world case are employed to evaluate the effectiveness of the proposed bi-level model and algorithm. Results show that the bi-level model performs well in reducing total passenger cost, especially in reducing waiting time cost and penalties. And the section loading-rates of trains in the optimized timetable are more balanced than the even-headway timetable. The sensitivity analyses show that passenger’s desired arrival time interval at destination and crowding penalty factor have a high influence on the optimal solution. And with the dispersing of passengers' desired arrival time intervals or the increase of crowding penalty factor, the section loading-rates of trains become more balanced.     

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.

     

Development of a probabilistic model to optimize disseminated real‐time bus arrival information for pre‐trip passengers

In the advent of Advanced Traveler Information Systems (ATIS), the total wait time of passengers for buses may be reduced by disseminating real‐time bus arrival times for the next or series of buses to pre‐trip passengers through various media (e.g., internet, mobile phones, and personal digital assistants). A probabilistic model is desirable and developed in this study, while realistic distributions of bus and passenger arrivals are considered. The disseminated bus arrival time is optimized by minimizing the total wait time incurred by pre‐trip passengers, and its impact to the total wait time under both late and early bus arrival conditions is studied. Relations between the optimal disseminated bus arrival time and major model parameters, such as the mean and standard deviation of arrival times for buses and pre‐trip passengers, are investigated. Analytical results are presented based on Normal and Lognormal distributions of bus arrivals and Gumbel distribution of pre‐trip passenger arrivals at a designated stop. The developed methodology can be practically applied to any arrival distributions of buses and passengers.     

Optimal assignment for check-in counters based on passenger arrival behaviour at an airport

Establishing how to utilize check-in counters at airport passenger terminals efficiently is a major concern facing airport operators and airlines. Inadequate terminal capacity and the inefficient utilization of facilities such as check-in counters are major factors causing congestion and delays at airport passenger terminals. However, such delays and congestion can be reduced by increasing the efficiency of check-in counter operations, based on an understanding of passengers' airport access behaviour. This paper presents an assignment model for check-in counter operations, based on passengers' airport arrival patterns. In setting up the model, passenger surveys are used to determine when passengers arrive at the airport terminals relative to their flight departure times. The model then uses passenger arrival distribution patterns to calculate the most appropriate number of check-in counters and the duration of time that each counter should be operated. This assignment model has been applied at the Seoul Gimpo International Airport in Korea. The model provides not only a practical system for the efficient operations of time-to-time check-in counter assignments, but also a valuable means of developing effective longer-term solutions to the problem of passenger terminal congestion and delays. It also offers airlines a means of operating check-in counters with greater cost effectiveness, thus leading to enhanced customer service.     

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.     

Passenger arrival and waiting time distributions dependent on train service frequency and station characteristics: A smart card data analysis

Waiting time at public transport stops is perceived by passengers to be more onerous than in-vehicle time, hence it strongly influences the attractiveness and use of public transport. Transport models traditionally assume that average waiting times are half the service headway by assuming random passenger arrivals. However, research agree that two distinct passenger behaviour types exist: one group arrives randomly, whereas another group actively tries to minimise their waiting time by arriving in a timely manner at the scheduled departure time. This study proposes a general framework for estimating passenger waiting times which incorporates the arrival patterns of these two groups explicitly, namely by using a mixture distribution consisting of a uniform and a beta distribution. The framework is empirically validated using a large-scale automatic fare collection system from the Greater Copenhagen Area covering metro, suburban, and regional rail stations thereby giving a range of service headways from 2 to 60 min. It was shown that the proposed mixture distribution is superior to other distributions proposed in the literature. This can improve waiting time estimations in public transport models. The results show that even at 5-min headways 43% of passengers arrive in a timely manner to stations when timetables are available. The results bear important policy implications in terms of providing actual timetables, even at high service frequencies, in order for passengers to be able to minimise their waiting times.     

Travel time variability and airport accessibility

We analyze the cost of access travel time variability for air travelers. Reliable access to airports is important since the cost of missing a flight is likely to be high. First, the determinants of the preferred arrival times at airports are analyzed. Second, the willingness to pay (WTP) for reductions in access travel time, early and late arrival time at the airport, and the probability to miss a flight are estimated, using a stated choice experiment. The results indicate that the WTPs are relatively high. Third, a model is developed to calculate the cost of variable travel times for representative air travelers going by car, taking into account travel time cost, scheduling cost and the cost of missing a flight using empirical travel time data. In this model, the value of reliability for air travelers is derived taking “anticipating departure time choice” into account, meaning that travelers determine their departure time from home optimally. Results of the numerical exercise show that the cost of access travel time variability for business travelers are between 0% and 30% of total access travel cost, and for non-business travelers between 0% and 25%. These numbers depend strongly on the time of the day.     

Modelling waiting time for passengers transferring from rail to buses

This paper develops a mathematical model to calculate the average waiting time for passengers transferring from rail transit to buses based on the statistical analysis of primary data collected in Beijing. An important part of the average waiting time modelling is to analyse the distributions of passenger arrival rates. It is shown that the lognormal and gamma distributions have the best fit for direct transfer and non-direct transfer passengers, respectively. Subsequently, an average waiting time model for transferring passengers is developed based on passenger arrival rate distributions. Furthermore, case studies are conducted for two scenarios with real and estimated data, resulting in relative errors of ?3.69% and ?3.77%, respectively. Finally, the paper analyses the impacts of bus headway, the headway of rail cars, and the proportion of direct transfer passengers on average waiting time.     

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.     

Unified estimator for excess journey time under heterogeneous passenger incidence behavior using smartcard data

Excess journey time (EJT), the difference between actual passenger journey times and journey times implied by the published timetable, strikes a useful balance between the passenger’s and operator’s perspectives of public transport service quality. Using smartcard data, this paper tried to characterize transit service quality with EJT under heterogeneous incidence behavior (arrival at boarding stations). A rigorous framework was established for analyzing EJT, in particular for reasoning about passenger’ journey time standards as implied by varying incidence behavior. It was found that although the wrong assumption about passenger incidence behavior and journey time standards could result in a biased estimate of EJT for individual passenger journeys, the unified estimator of EJT proposed in this paper is unbiased at the aggregate level regardless of the passenger incidence behavior (random incidence, scheduled incidence, or a mixture of both). A case study based on the London Overground network (with a tap-in-and-tap-out smartcard system) was conducted to demonstrate the applicability of the proposed method. EJT was estimated using the smartcard (Oyster) data at various levels of spatial and temporal aggregation in order to measure and evaluate the service quality. Aggregate EJT was found to vary substantially across the different London Overground lines and across time periods of weekday service.     

Optimal timetable development for community shuttle network with metro stations

This paper investigates an issue for optimizing synchronized timetable for community shuttles linked with metro service. Considering a passenger arrival distribution, the problem is formulated to optimize timetables for multiple community shuttle routes, with the objective of minimizing passenger’s schedule delay cost and transfer cost. Two constraints, i.e., vehicle capacity and fleet size, are modeled in this paper. The first constraint is treated as soft, and the latter one is handled by a proposed timetable generating method. Two algorithms are employed to solve the problem, i.e., a genetic algorithm (GA) and a Frank–Wolfe algorithm combined with a heuristic algorithm of shifting departure times (FW-SDT). FW-SDT is an algorithm specially designed for this problem. The simulated and real-life examples confirm the feasibility of the two algorithms, and demonstrate that FW-SDT outperforms GA in both accuracy and effectiveness.     

Analysis of performance and equity in ground delay programs

The discrepancy between the projected demand for arrival slots at an airport and the projected available arrival slots on a given day is resolved by the Ground Delay Program (GDP). The current GDP rationing rule, Ration-by-Schedule, allocates the available arrival slots at the affected airport by scheduled arrival time of the flights with some adjustments to balance the equity between airlines. This rule does not take into account passenger flow and fuel flow performance in the rationing assignment tradeoff.This paper examines the trade-off between passenger delays and excess surface fuel burn as well as airline equity and passenger equity in GDP slot allocation using different rationing rules. A GDP Rationing Rule Simulator (GDP-RRS) is developed to calculate performance and equity metrics for all stakeholders using six alternate rules. The results show that there is a trade-off between GDP performance and GDP equity. Ration-by-Passengers (a rule which maximizes the passenger throughput) decreased total passenger delay by 22% and decreased total excess fuel burn by 57% with no change in total flight delay compared to the traditional Ration-by-Schedule. However, when the airline and passenger equity are primary concerns, the Ration-by-Schedule is preferred.     

Establishing value of time for the inter-island passenger transport of the Western Visayas region,Philippines

Transportation infrastructure planning process requires cost–benefit analysis in the evaluation of project proposals. Value of time (VOT) facilitates the conversion of travel time savings, which is a significant proportion of benefits in monetary terms. In cases where VOT has not been established, planners resort to crude estimates that often results in erroneous or biased measurements of benefits. This is the case of the Western Visayas region in the Philippines where transportation studies are rare. Secondary cities and its peripheral regions have often been overlooked subjects of transportation studies. In this study, multinomial logit models using revealed preference data were estimated to facilitate the calculation of the VOT. The total cost, square of the total cost, and total time were identified as significant explanatory variables affecting mode choice. The square of the total cost term was introduced in the models in order to account for income effect. Results indicate that VOT estimates for the inter-island passenger transportation between Iloilo and Negros Occidental generally range from 78.15PHP to 179.15PHP (1.91USD to 4.37USD) depending on trip and traveller characteristics.     

Train scheduling for minimizing passenger waiting time with time-dependent demand and skip-stop patterns: Nonlinear integer programming models with linear constraints

This paper focuses on how to minimize the total passenger waiting time at stations by computing and adjusting train timetables for a rail corridor with given time-varying origin-to-destination passenger demand matrices. Given predetermined train skip-stop patterns, a unified quadratic integer programming model with linear constraints is developed to jointly synchronize effective passenger loading time windows and train arrival and departure times at each station. A set of quadratic and quasi-quadratic objective functions are proposed to precisely formulate the total waiting time under both minute-dependent demand and hour-dependent demand volumes from different origin–destination pairs. We construct mathematically rigorous and algorithmically tractable nonlinear mixed integer programming models for both real-time scheduling and medium-term planning applications. The proposed models are implemented using general purpose high-level optimization solvers, and the model effectiveness is further examined through numerical experiments of real-world rail train timetabling test cases.