Hybrid model for prediction of bus arrival times at next station

Effective prediction of bus arrival times is important to advanced traveler information systems (ATIS). Here a hybrid model, based on support vector machine (SVM) and Kalman filtering technique, is presented to predict bus arrival times. In the model, the SVM model predicts the baseline travel times on the basic of historical trips occurring data at given time‐of‐day, weather conditions, route segment, the travel times on the current segment, and the latest travel times on the predicted segment; the Kalman filtering‐based dynamic algorithm uses the latest bus arrival information, together with estimated baseline travel times, to predict arrival times at the next point. The predicted bus arrival times are examined by data of bus no. 7 in a satellite town of Dalian in China. Results show that the hybrid model proposed in this paper is feasible and applicable in bus arrival time forecasting area, and generally provides better performance than artificial neural network (ANN)–based methods. Copyright © 2010 John Wiley & Sons, Ltd.     

Modeling schedule recovery processes in transit operations for bus arrival time prediction

Many existing algorithms for bus arrival time prediction assume that buses travel at free‐flow speed in the absence of congestion. As a result, delay incurred at one stop would propagate to downstream stops at the same magnitude. In reality, skilled bus operators often constantly adjust their speeds to keep their bus on schedule. This paper formulates a Markov chain model for bus arrival time prediction that explicitly captures the behavior of bus operators in actively pursuing schedule recovery. The model exhibits some desirable properties in capturing the schedule recovery process. It guarantees provision of the schedule information if the probability of recovering from the current schedule deviation is sufficiently high. The proposed model can be embedded into a transit arrival time estimation model for transit information systems that use both real‐time and schedule information. It also has the potential to be used as a decision support tool to determine when dynamic or static information should be used.     

Estimation of bus dwell time using univariate time series models

A significant proportion of bus travel time is contributed by dwell time for passenger boarding and alighting. More accurate estimation of bus dwell time (BDT) can enhance efficiency and reliability of public transportation system. Regression and probabilistic models are commonly used in literatures where a set of independent variables are used to define the statistical relationship between BDT and its contributing factors. However, due to technical and monetary constraints, it is not always feasible to collect all the data required for the models to work. More importantly, the contributing factors may vary from one bus route to another. Time series based methods can be of great interest as they require only historical time series data, which can be collected using a facility known as automatic vehicle location (AVL) system. This paper assesses four different time series based methods namely random walk, exponential smoothing, moving average (MA), and autoregressive integrated moving average to model and estimate BDT based on AVL data collected from Auckland. The performances of the proposed methods are ranked based on three important factors namely prediction accuracy, simplicity, and robustness. The models showed promising results and performed differently for central business district (CBD) and non‐CBD bus stops. For CBD bus stops, MA model performed the best, whereas for non‐CBD bus stops, ARIMA model performed the best compared with other time series based models. Copyright © 2014 John Wiley & Sons, Ltd.     

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.     

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.     

Time control point strategy coupled with transfer coordination in bus schedule design

A schedule consisting of an appropriate arrival time at each time control point can ensure reliable transport services. This paper develops a novel time control point strategy coupled with transfer coordination for solving a multi‐objective schedule design problem to improve schedule adherence and reduce intermodal transfer disutility. The problem is formulated using a robust mixed‐integer nonlinear programming model. The mixed‐integer nonlinear programming model is equivalently transformed into a robust mixed‐integer linear programming model, which is then approximated by a deterministic mixed‐integer linear programming model through Monte Carlo simulation. Thus, the optimal scheduled arrival time at each time control point can be precisely obtained using cplex . Numerical experiments based on three bus lines and the mass rapid transit system in Singapore are presented, and the results show that the schedule determined using the developed model is able to provide not only reliable bus service but also a smooth transfer experience for passengers. Copyright © 2016 John Wiley & Sons, Ltd.     

A genetic algorithm-based method for improving quality of travel time prediction intervals

The transportation literature is rich in the application of neural networks for travel time prediction. The uncertainty prevailing in operation of transportation systems, however, highly degrades prediction performance of neural networks. Prediction intervals for neural network outcomes can properly represent the uncertainty associated with the predictions. This paper studies an application of the delta technique for the construction of prediction intervals for bus and freeway travel times. The quality of these intervals strongly depends on the neural network structure and a training hyperparameter. A genetic algorithm–based method is developed that automates the neural network model selection and adjustment of the hyperparameter. Model selection and parameter adjustment is carried out through minimization of a prediction interval-based cost function, which depends on the width and coverage probability of constructed prediction intervals. Experiments conducted using the bus and freeway travel time datasets demonstrate the suitability of the proposed method for improving the quality of constructed prediction intervals in terms of their length and coverage probability.     

Improving transportation service quality based on information fusion

How to improve transportation service quality and thus attract more passengers to use public transportation systems is an important concern for city governments around the world. In this study, we propose a novel information fusion model that addresses the dependent relationships among the various criteria for a method of non-additive weighted gap analysis aimed at evaluating and improving the service quality of transport systems. The hybrid model remedies prior shortcomings and should be more applicable to real-world situations. The proposed model is applied to a real case study of Taipei city bus companies to demonstrate its usefulness. The resulting analysis and the managerial applications for improving the bus service quality are also discussed with regards to the current policies of Taipei city.     

Real-time bus route state forecasting using particle filter and mesoscopic modeling

In the absence of system control strategies, it is common to observe bus bunching in transit operations. A transit operator would benefit from an accurate forecast of bus operations in order to control the system before it becomes too disrupted to be restored to a stable condition. To accomplish this, we present a general bus prediction framework. This framework relies on a stochastic and event-based bus operation model that provides sets of possible bus trajectories based on the observation of current bus positions, available via global positioning system (GPS) data. The median of the set of possible trajectories, called a particle, is used as the prediction. In particular, this enables the anticipation of irregularities between buses. Several bus models are proposed depending on the dwell and inter-stop running time representations. These models are calibrated and applied to a real case study thanks to the high quality data provided by TriMet (the Portland, Oregon, USA transit district). Predictions are finally evaluated by an a posteriori comparison with the real trajectories. The results highlight that only bus models accounting for the bus load can provide valid forecasts of a bus route over a large prediction horizon, especially for headway variations. Accounting for traffic signal timings and actual traffic flows does not significantly improves the prediction. Such a framework paves the way for further development of refined dynamic control strategies for bus operations.     

International experience with speed limits during and prior to the energy crisis of 1973–4

This paper presents an artificial neural network (ANN) based method for estimating route travel times between individual locations in an urban traffic network. Fast and accurate estimation of route travel times is required by the vehicle routing and scheduling process involved in many fleet vehicle operation systems such as dial‐a‐ride paratransit, school bus, and private delivery services. The methodology developed in this paper assumes that route travel times are time‐dependent and stochastic and their means and standard deviations need to be estimated. Three feed‐forward neural networks are developed to model the travel time behaviour during different time periods of the day‐the AM peak, the PM peak, and the off‐peak. These models are subsequently trained and tested using data simulated on the road network for the City of Edmonton, Alberta. A comparison of the ANN model with a traditional distance‐based model and a shortest path algorithm is then presented. The practical implication of the ANN method is subsequently demonstrated within a dial‐a‐ride paratransit vehicle routing and scheduling problem. The computational results show that the ANN‐based route travel time estimation model is appropriate, with respect to accuracy and speed, for use in real applications.     

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.     

Welfare maximization for bus transit systems with timed transfers and financial constraints

Conventional and flexible bus services may be combined to better serve regions with a wide range of characteristics. If demand densities and resulting service frequencies are low, the coordination of bus arrivals at transfer stations may significantly reduce passenger transfer times. A method is proposed for integrating, coordinating, and optimizing bus services while considering many‐to‐many travel patterns, demand elasticity, financial constraints, and appropriate service type for various regions. The objective is to maximize welfare, that is, the sum of producer and consumer surplus. The problem is solved with a hybrid optimization method, in which a genetic algorithm with bounded integer variables is selected for solving one of the subproblems. The service types, fares, headways, and service zone sizes are jointly optimized. Sensitivity analyses explore how the choice among conventional and flexible busses depends on the demand, subsidy, and demand elasticity parameters. The results also show that welfare can increase due to coordination, and these increases are found to be higher in cases with high demand or low subsidy. Copyright © 2015 John Wiley & Sons, Ltd.     

Crowding in public transport systems: Effects on users,operation and implications for the estimation of demand

The effects of high passenger density at bus stops, at rail stations, inside buses and trains are diverse. This paper examines the multiple dimensions of passenger crowding related to public transport demand, supply and operations, including effects on operating speed, waiting time, travel time reliability, passengers’ wellbeing, valuation of waiting and in-vehicle time savings, route and bus choice, and optimal levels of frequency, vehicle size and fare. Secondly, crowding externalities are estimated for rail and bus services in Sydney, in order to show the impact of crowding on the estimated value of in-vehicle time savings and demand prediction. Using Multinomial Logit (MNL) and Error Components (EC) models, we show that alternative assumptions concerning the threshold load factor that triggers a crowding externality effect do have an influence on the value of travel time (VTTS) for low occupancy levels (all passengers sitting); however, for high occupancy levels, alternative crowding models estimate similar VTTS. Importantly, if demand for a public transport service is estimated without explicit consideration of crowding as a source of disutility for passengers, demand will be overestimated if the service is designed to have a number of standees beyond a threshold, as analytically shown using a MNL choice model. More research is needed to explore if these findings hold with more complex choice models and in other contexts.     

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 network‐based dynamic air traffic flow model for short‐term en route traffic prediction

This paper presents a dynamic network‐based approach for short‐term air traffic flow prediction in en route airspace. A dynamic network characterizing both the topological structure of airspace and the dynamics of air traffic flow is developed, based on which the continuity equation in fluid mechanics is adopted to describe the continuous behaviour of the en route traffic. Building on the network‐based continuity equation, the space division concept in cell transmission model is introduced to discretize the proposed model both in space and time. The model parameters are sequentially updated based on the statistical properties of the recent radar data and the new predicting results. The proposed method is applied to a real data set from Shanghai Area Control Center for the short‐term air traffic flow prediction both at flight path and en route sector level. The analysis of the case study shows that the developed method can characterize well the dynamics of the en route traffic flow, thereby providing satisfactory prediction results with appropriate uncertainty limits. The mean relative prediction errors are less than 0.10 and 0.14, and the absolute errors fall in the range of 0 to 1 and 0 to 3 in more than 95% time intervals respectively, for the flight path and en route sector level. Copyright © 2017 John Wiley & Sons, Ltd.     

Investigating the impact of stochastic vehicle arrivals to optimal stop spacing and headway for a feeder bus route

Stop spacing and service frequency (i.e., the inverse of headway) are key elements in transit service planning. The trade‐offs between increasing accessibility and reducing travel time, which affect transit system performance, need to be carefully evaluated. The objective of this study is to optimize stop spacing and headway for a feeder bus route, considering the relationship between the variance of inter‐arrival time (VIAT), which yields the minimum total cost (including user and operator costs). A solution algorithm, called successive substitution, is adapted to efficiently search for the optimal solutions. In a numerical example, the developed model is applied to planning a feeder bus route in Newark, New Jersey. The results indicate that the optimal stop spacing should be longer that those suggested by previous studies where the impact of VIAT was ignored. Reducing VIAT via certain operational control strategies (i.e., holding/stop‐skipping, transit signal priority) may shorten stop spacing and improve accessibility. Copyright © 2014 John Wiley & Sons, Ltd.     

Optimal design of a short‐turning strategy considering seat availability

We develop a methodology to optimize the schedule coordination of a full‐stop service pattern and a short‐turning service pattern on a bus route. To capture the influence of bus crowding and seat availability on passengers' riding experience, we develop a Markov model to describe the seat‐searching process of a passenger and an approach to estimate the transition probabilities of the Markov model. An optimization model that incorporates the Markov model is proposed to design the short‐turning strategy. The proposed model minimizes the total cost, which includes operational cost, passengers' waiting time cost and passengers' in‐vehicle travel time cost. Algorithm is developed to produce optimal values of the decision variables. The proposed methodology is evaluated in a case study. Compared with methodologies that ignore the effect of bus crowding, the proposed methodology could better balance bus load along the route and between two service patterns, provide passengers with better riding experience and reduce the total cost. In addition, it is shown that the optimal design of the short‐turning strategy is sensitive to seat capacity. Copyright © 2016 John Wiley & Sons, Ltd.     

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。     

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.     

A case study of Beijing bus crew scheduling: a variable neighborhood‐based approach

Crew scheduling for bus drivers in large bus agencies is known to be a time‐consuming and cumbersome problem in transit operations planning. This paper investigates a new meta‐heuristics approach for solving real‐world bus‐driver scheduling problems. The drivers' work is represented as a series of successive pieces of work with time windows, and a variable neighborhood search (VNS) algorithm is employed to solve the problem of driver scheduling. Examination of the modeling procedure developed is performed by a case study of two depots of the Beijing Public Transport Group, one of the largest transit companies in the world. The results show that a VNS‐based algorithm can reduce total driver costs by up to 18.1%, implying that the VNS algorithm may be regarded as a good optimization technique to solve the bus‐driver scheduling problem. Copyright © 2015 John Wiley & Sons, Ltd.