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.     

Analysis of real-time control strategies in a corridor with multiple bus services

Control strategies have been widely used in the literature to counteract the effects of bus bunching in passenger‘s waiting times and its variability. These strategies have only been studied for the case of a single bus line in a corridor. However, in many real cases this assumption does not hold. Indeed, there are many transit corridors with multiple bus lines interacting, and this interaction affects the efficiency of the implemented control mechanism.This work develops an optimization model capable of executing a control scheme based on holding strategy for a corridor with multiple bus lines.We analyzed the benefits in the level of service of the public transport system when considering a central operator who wants to maximize the level of service for users of all the bus lines, versus scenarios where each bus line operates independently. A simulation was carried out considering two medium frequency bus lines that serve a set of stops and where these two bus lines coexist in a given subset of stops. In the simulation we compared the existence of a central operator, using the optimization model we developed, against the independent operation of each line.In the simulations the central operator showed a greater reduction in the overall waiting time of the passengers of 55% compared to a no control scenario. It also provided a balanced load of the buses along the corridor, and a lower variability of the bus headways in the subset of stops where the lines coexist, thus obtaining better reliability for all types of passengers present in the public transport system.     

Bus arrival time calculation model based on smart card data

Bus arrival time is usually estimated using the boarding time of the first passenger at each station. However, boarding time data are not recorded in certain double-ticket smart card systems. As many passengers usually swipe the card much before their alighting, the first or the average alighting time cannot represent the actual bus arrival time, either. This lack of data creates difficulties in correcting bus arrival times. This paper focused on developing a model to calculate bus arrival time that combined the alighting swiping time from smart card data with the actual bus arrival time by the manual survey data. The model was built on the basis of the frequency distribution and the regression analysis. The swiping time distribution, the occupancy and the seating capacity were considered as the key factors in creating a method to calculate bus arrival times. With 1011 groups of smart card data and 360 corresponding records from a manual survey of bus arrival times, the research data were divided into two parts stochastically, a training set and a test set. The training set was used for the parameter determination, and the test set was used to verify the model’s precision. Furthermore, the regularity of the time differences between the bus arrival times and the card swiping times was analyzed using the “trend line” of the last swiping time distribution. Results from the test set achieved mean and standard error rate deviations of 0.6% and 3.8%, respectively. The proposed model established in this study can improve bus arrival time calculations and potentially support state prediction and service level evaluations for bus operations.     

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.     

Control strategies for departure process delays at airport passenger terminals

This paper explores the characteristics of process delays at airport passenger terminals and establishes a queuing model for both passengers and baggage served by different connecting type facilities. The impact of delay propagation on other processes and flights is investigated using an analytical approach. In addition, the extra costs incurred on passengers, process operators, and airlines are examined using the delay cost functions. To reduce the impact of process delays, various delay-controlled strategies are proposed, such as setting scheduled times for completion of a process, increasing the number of service counters, and priority service for emergent flights. Taoyuan International Airport in Taiwan is used as a case study when facing special events. Results showed that the model can effectively and efficiently estimate delay propagation and its costs. In addition, processes that are not consecutive allow more buffer time between different operations, which helps ease propagation of delays caused by previous services.     

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.     

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.     

Evaluating the added-value of online bus arrival prediction schemes

Online predictions of bus arrival times have the potential to reduce the uncertainty associated with bus operations. By better anticipating future conditions, online predictions can reduce perceived and actual passenger travel times as well as facilitate more proactive decision making by service providers. Even though considerable research efforts were devoted to the development of computationally expensive bus arrival prediction schemes, real-world real-time information (RTI) systems are typically based on very simple prediction rules. This paper narrows down the gap between the state-of-the-art and the state-of-the-practice in generating RTI for public transport systems by evaluating the added-value of schemes that integrate instantaneous data and dwell time predictions. The evaluation considers static information and a commonly deployed scheme as a benchmark. The RTI generation algorithms were applied and analyzed for a trunk bus network in Stockholm, Sweden. The schemes are assessed and compared based on their accuracy, reliability, robustness and potential waiting time savings. The impact of RTI on passengers waiting times are compared with those attained by service frequency and regularity improvements. A method which incorporates information on downstream travel conditions outperforms the commonly deployed scheme, leading to a 25% reduction in the mean absolute error. Furthermore, the incorporation of instantaneous travel times improves the prediction accuracy and reliability, and contributes to more robust predictions. The potential waiting time gains associated with the prediction scheme are equivalent to the gains expected when introducing a 60% increase in service frequency, and are not attainable by service regularity improvements.     

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.     

Plan-based flexible bus bridging operation strategy

Bus bridging has been widely used to connect stations affected by metro disruptions such that stranded passengers could resume their journeys. Previous studies generally assumed that a bus operates exclusively on one bridging route with given frequency, which limits the service flexibility and reduce the operational efficiency. We propose a strategy to instruct buses to operate on predefined bridging routes once they are dispatched from depots. Buses are allowed to flexibly serve different bridging routes. Each bus operates based on a bridging plan that lists the stations to serve in sequence instead of route frequencies. A two-stage model is developed to optimize the bridging plans and their assignments to buses with the objectives that balance the operational priorities between minimizing bus bridging time and reducing passenger delay. A Weight Shortest Processing Time first (WSPT) rule based heuristic algorithm is developed to solve the proposed model. The developed model is further incorporated in a rolling horizon framework to handle dynamic passenger arrivals during the disruption period. The effectiveness of the proposed strategy is demonstrated in comparison with alternative strategies in real-world case studies.     

Models of bus boarding and alighting dynamics

Understanding the dynamics of boarding/alighting activities and its impact on bus dwell times is crucial to improving bus service levels. However, research is limited as conventional data collection methods are both time and labour intensive. In this paper, we present the first use of smart card data to study passenger boarding/alighting behaviour and its impact on bus dwell time. Given the nature of these data, we focus on passenger activity time and do not account for the time necessary to open and close doors. We study single decker, double decker and articulated buses and identify the specific effects of floor/entrance type, number of activities and occupancy on both boarding and alighting dynamics. A linear relationship between average boarding and alighting times and their respective standard deviations is also found, whereas the variability of boarding and alighting time decreases with the number of passengers boarding and alighting. After observing the cumulative boarding/alighting processes under different occupancy conditions, we propose a new model to estimate passenger activity time, by introducing critical occupancy – a parameter incorporating the friction between boarding/alighting and on-board passengers. We conduct regression analyses with the proposed and another popular model for simultaneous boarding/alighting processes, finding that the critical occupancy plays a significant role in determining the regime of boarding and alighting processes and the overall activity time. Our results provide potential implications for practice and policy, such as identifying optimal vehicle type for a particular route and modelling transit service reliability.     

Passenger-demands-oriented train scheduling for an urban rail transit network

This paper considers the train scheduling problem for an urban rail transit network. We propose an event-driven model that involves three types of events, i.e., departure events, arrival events, and passenger arrival rates change events. The routing of the arriving passengers at transfer stations is also included in the train scheduling model. Moreover, the passenger transfer behavior (i.e., walking times and transfer times of passengers) is also taken into account in the model formulation. The resulting optimization problem is a real-valued nonlinear nonconvex problem. Nonlinear programming approaches (e.g., sequential quadratic programming) and evolutionary algorithms (e.g., genetic algorithms) can be used to solve this train scheduling problem. The effectiveness of the event-driven model is evaluated through a case study.     

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.     

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.     

快速公交系统站台停靠时间模型研究

快速公交系统停靠站台停车延误是影响快速公交运行车速的关键因素之一,因此构建快速公交系统站台停靠时间模型是提升快速公交服务水平的基础理论研究。本文选取盐城BRT-1号线的起始站、中途站、客流离散站等三类站点为研究对象,综合运用数理统计法与数据挖掘法,构建快速公交系统站台停靠时间模型,并对该模型的合理性进行了检验。研究表明:盐城市BRT-1号线三类站台的快速公交车辆停靠时间与上下车乘客人数呈线性关系,即快速公交车辆停靠时间与上下车乘客人数的检验参数R2均大于0.8。     

A theoretical travel-time model for flexible-route buses

A theoretical model for estimating the expectation and variance of buses' running times under a flexibly-routed mode of service is proposed. The model is based on a probabilistic concept that adequately accommodates the usual randomness in the number and location of passengers served during successive vehicle trips. A few simplifications are embodied in the model but it can serve as a basis for a more refined model such as a computer simulation model that can be used in designing real bus systems.The physical setting assumed in the model is a rectangular grid road network where all houses face the side streets as in some suburban regions. Because it oversimplifies real-life situations, this assumption would need to be relaxed to make the model applicable to more general cases.Both the partially flexible-route service where some passengers are captive to fixed-route service and others are served at their doorsteps, and the fully flexible-route service where all passengers are served at their doorsteps, are studied. In each case, a very simple routing convention that can be conveniently executed by the bus drivers is assumed. The proposed travel time model confirms the intuitively correct phenomenon that when the concentration of passenger trip-ends is very high, the vehicle-route degenerates into a fixed-route in which the buses visit all possible loading points within the service area.     

Stochastic transit equilibrium

We present a transit equilibrium model in which boarding decisions are stochastic. The model incorporates congestion, reflected in higher waiting times at bus stops and increasing in-vehicle travel time. The stochastic behavior of passengers is introduced through a probability for passengers to choose boarding a specific bus of a certain service. The modeling approach generates a stochastic common-lines problem, in which every line has a chance to be chosen by each passenger. The formulation is a generalization of deterministic transit assignment models where passengers are assumed to travel according to shortest hyperpaths. We prove existence of equilibrium in the simplified case of parallel lines (stochastic common-lines problem) and provide a formulation for a more general network problem (stochastic transit equilibrium). The resulting waiting time and network load expressions are validated through simulation. An algorithm to solve the general stochastic transit equilibrium is proposed and applied to a sample network; the algorithm works well and generates consistent results when considering the stochastic nature of the decisions, which motivates the implementation of the methodology on a real-size network case as the next step of this research.     

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.     

Optimally combined headway and timetable reliable public transport system

This paper presents a model-based multiobjective control strategy to reduce bus bunching and hence improve public transport reliability. Our goal is twofold. First, we define a proper model, consisting of multiple static and dynamic components. Bus-following model captures the longitudinal dynamics taking into account the interaction with the surrounding traffic. Furthermore, bus stop operations are modeled to estimate dwell time. Second, a shrinking horizon model predictive controller (MPC) is proposed for solving bus bunching problems. The model is able to predict short time-space behavior of public transport buses enabling constrained, finite horizon, optimal control solution to ensure homogeneity of service both in time and space. In this line, the goal with the selected rolling horizon control scheme is to choose a proper velocity profile for the public transport bus such that it keeps both timetable schedule and a desired headway from the bus in front of it (leading bus). The control strategy predicts the arrival time at a bus stop using a passenger arrival and dwell time model. In this vein, the receding horizon model predictive controller calculates an optimal velocity profile based on its current position and desired arrival time. Four different weighting strategies are proposed to test (i) timetable only, (ii) headway only, (iii) balanced timetable - headway tracking and (iv) adaptive control with varying weights. The controller is tested in a high fidelity traffic simulator with realistic scenarios. The behavior of the system is analyzed by considering extreme disturbances. Finally, the existence of a Pareto front between these two objectives is also demonstrated.     

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.