Bus travel time modelling using GPS probe and smart card data: A probabilistic approach considering link travel time and station dwell time

Abstract

Path travel time estimation for buses is critical to public transit operation and passenger information system. State-of-the-art methods for estimating path travel time are usually focused on single vehicle with a limited number of road segments, thereby neglecting the interaction among multiple buses, boarding behavior, and traffic flow. This study models path travel time for buses considering link travel time and station dwell time. First, we fit link travel time to shifted lognormal distributions as in previous studies. Then, we propose a probabilistic model to capture interactions among buses in the bus bay as a first-in-first-out queue, with every bus sharing the same set of behaviors: queuing to enter the bus bay, loading/unloading passengers, and merging into traffic flow on the main road. Finally, path travel time distribution is estimated by statistically summarizing link travel time distributions and station dwell time distributions. The path travel time of a bus line in Hangzhou is analyzed to validate the effectiveness of the proposed model. Results show that the model-based estimated path travel time distribution resembles the observed distribution well. Based on the calculation of path travel time, link travel time reliability is identified as the main factor affecting path travel time reliability.     

Urban travel time reliability at different traffic conditions

The decision making of travelers for route choice and departure time choice depends on the expected travel time and its reliability. A common understanding of reliability is that it is related to several statistical properties of the travel time distribution, especially to the standard deviation of the travel time and also to the skewness. For an important corridor in Changsha (P.R. China) the travel time reliability has been evaluated and a linear model is proposed for the relationship between travel time, standard deviation, skewness, and some other traffic characteristics. Statistical analysis is done for both simulation data from a delay distribution model and for real life data from automated number plate recognition (ANPR) cameras. ANPR data give unbiased travel time data, which is more representative than probe vehicles. The relationship between the mean travel time and its standard deviation is verified with an analytical model for travel time distributions as well as with the ANPR travel times. Average travel time and the standard deviation are linearly correlated for single links as well as corridors. Other influence factors are related to skewness and travel time standard deviations, such as vehicle density and degree of saturation. Skewness appears to be less well to explain from traffic characteristics than the standard deviation is.     

Estimation of delay variability at signalized intersections for urban arterial performance evaluation

Urban arterial performance evaluation has been broadly studied, with the major focus on average travel time estimation. However, in view of the stochastic nature of interrupted flow, the ability to capture the characteristics of travel time variability has become a critical step in determining arterial level of service (LOS). This article first presents a stochastic approach that integrates classic cumulative curves and probability theories in order to investigate delay variability at signalized intersections, as a dominant part of the link travel time variability. This serves as a basis for arterial travel time estimation, which can be obtained through a convolution of individual link travel time distributions. The proposed approach is then applied in the estimation of travel time along one arterial in Shanghai, China, with abundant automatic vehicle identification (AVI) data sources. The travel time variability is evaluated thoroughly at 30-min intervals, with promising results achieved in comparison to the field measurements. In addition, the estimated travel time distributions are utilized to illustrate the probability of multiple LOS ranges, namely, reliability LOS. The results provide insights into how we might achieve a more reliable and informative understanding of arterial performance.     

The impact of route guidance,departure time advice and alternative routes on door-to-door travel time reliability: Two data-driven assessment methods

ABSTRACT

Conventional travel time reliability assessment has evolved from road segments to the route level. However, a connection between origin and destination usually consists of multiple routes, thereby providing the option to choose. Having alternatives can compensate for the deterioration of a single route; therefore, this study assesses the reliability and quality of the aggregate of the route set of an origin-destination (OD) pair. This paper proposes two aggregation methods for analyzing the reliability of travel times on the OD level: 1) an adapted Logsum method and 2) a route choice model. The first method analyzes reliability from a network perspective and the second method is based on the reliability as perceived by a traveler choosing his route from the available alternatives. A case study using detailed data on actual travel times illustrates both methods and shows the impact of having variable departure times and the impact of information strategies on travel time reliability.     

Analyzing travel time reliability and its influential factors of emergency vehicles with generalized extreme value theory

Travel time reliability is very critical for emergency vehicle (EV) service and operation. The travel time characteristics of EVs are quite different from those of ordinary vehicles (OVs). Although EVs own highest road privilege, they may still experience unexpected delay that results in massive loss to the society. In this study, we employ the generalized extreme value (GEV) theory to measure extremely prolonged travel time and analyze the potential influential factors. First, among three GEV distributions, Weibull distributions are found to be the best distribution model according to several goodness-of-fit tests; a new reliability index is derived to measure travel time reliability. Numerical examples demonstrate the advantages of GEV-based reliability index over variance and percentile value in the applications of EV. This index will be of great practicability in the EV operation performance and reliable route choices. Second, we further investigate the potentially influential factors of EV travel time reliability. Results show that link length and left-turn traffic volume may have an adverse impact on the link reliability while more left-turn lanes may increase the travel time reliability. The influential factor study will help us understand the causes of the EV travel time delay and the differences of travel time reliability between OVs and EVs.     

Quantifying travel time variability at a single bottleneck based on stochastic capacity and demand distributions

Travel time reliability, an essential factor in traveler route and departure time decisions, serves as an important quality of service measure for dynamic transportation systems. This article investigates a fundamental problem of quantifying travel time variability from its root sources: stochastic capacity and demand variations that follow commonly used log-normal distributions. A volume-to-capacity ratio-based travel time function and a point queue model are used to demonstrate how day-to-day travel time variability can be explained from the underlying demand and capacity variations. One important finding is that closed-form solutions can be derived to formulate travel time variations as a function of random demand/capacity distributions, but there are certain cases in which a closed-form expression does not exist and numerical approximation methods are required. This article also uses probabilistic capacity reduction information to estimate time-dependent travel time variability distributions under conditions of non-recurring traffic congestion. The proposed models provide theoretically rigorous and practically useful tools for understanding the causes of travel time unreliability and evaluating the system-wide benefit of reducing demand and capacity variability.     

基于蒙特卡罗模拟方法的快速路运行时间可靠度研究

运行时间可靠度作为一个非常重要的概率测度参数能有效地评价交通网络的动态特性。在对运行时间可靠度的概念界定的基础上，分析了快速路运行时间可靠度的影响因素。提出了运用蒙特卡罗模拟方法计算运行时间可靠度，即采用蒙特卡罗模拟方法随机的对快速路入口的交通需求变量进行抽样，根据得到的样本值确定路径出行时间，然后对此出行时间进行检查，如果超过了规定的阚值，则认为不可靠，否则可靠。并通过一个算例对该模型进行了验证。最后指出了运行时间可靠度这一概率参数的应用前景。     

Bi-objective routing problem with asymmetrical travel time distributions

Recent studies have confirmed that travelers consider travel time reliability in addition to average travel time when making route choice decisions. In this study, we develop a bi-objective routing model that seeks to simultaneously optimize the average travel time and travel time reliability. The semi-standard deviation (SSD) is chosen as the reliability measure because it reflects travelers' concerns over longer travel time better than the commonly used standard deviation. The Pareto-optimal solutions to the bi-objective model are found by using an improved strength Pareto evolutionary algorithm. Tests on a real-world urban network with field measured travel time data have demonstrated good performance of the algorithm in the aspects, such as computational efficiency, quick convergence, and closeness to the global Pareto-optimal. Overall, the bi-objective routing model generates reasonable path recommendations. The SSD-based model is sensitive to the asymmetry of travel time distribution and tends to avoid paths with excessively long delays. This would be particularly helpful to those users placing high values on travel time reliability.     

Freeway path travel time prediction based on heterogeneous traffic data through nonparametric model

Providing reliable travel time prediction is very much needed for commuters for their upcoming trips to reduce travel time and relieve traffic congestion. This article proposes an integrated model for path and multi-step-ahead travel time prediction on freeways using both historical and real-time heterogeneous traffic and weather data. The model's performance is investigated in a case study under various traffic scenarios. Results indicate that the proposed model provides satisfactory prediction results in various performance tests. For practical purposes, general guidelines for selecting the model's parameter sets as well as the efficient size of historical data are also presented.     

Effectiveness of travel time reliability indicators in the light of the assessment of dynamic managed lane strategy

ABSTRACT

The aim of traffic management is to ensure a high quality of service for a maximum number of users by decreasing congestion and increasing safety. Uncertainty of travel times decreases the quality of service and leads end users to modify their plans regardless of the average travel time. Indicators describing travel time reliability are being developed and should be used in the future both for the optimization and for the assessment of active traffic management operations. This article discusses the efficiency of certain reliability indicators in an ex-post assessment of a traffic management strategy. Ex-post assessment is based on an observational before–after study. As some factors other than the studied management strategy may intervene between the two periods, and as most reliability indicators require knowledge of the full travel time distribution and not only its average, a methodology is developed for the identification of the impact of these exogenous factors on the whole distribution. Many reliability indicators are split into different parts allowing the identification of the part due to the management strategy impact. The methodology is tested numerically on a managed lane operation consisting of Hard Shoulder Running (HSR) at rush hour on a section of a French motorway. The variation of some reliability indicators appears misleading, whereas the splitting of the indicators increases our understanding of the strategy and highlights its impact. The paper gives the reliability assessment of the HSR field test and discusses different reliability indicators to identify their potential performances and shortcomings.     

基于L-偏度和L-峰度的行程时间可变性表征方法

为了定量化测度行程时间可变性右偏且长尾的实证特征,考虑实际观测中可能存在的数据样本量不足和离群值干扰问题,提出基于线性矩的L-偏度和L-峰度用于精确表征行程时间可变性。考虑到线性矩是顺序统计量期望的线性组合,给出了避免遍历所有子样本的线性矩估计方法。根据线性矩概念,探究了L-偏度和L-峰度的数学含义和其表征行程时间可变性的有效性,以及样本L-偏度和L-峰度的计算方法。理论研究发现,在表征范围和样本估计质量方面,相较于传统偏度和峰度,L-偏度和L-峰度对行程时间可变性具有更加优越的表征能力。采用深圳市车牌照识别系统的行程时间数据集进行案例分析,从无偏性、鲁棒性和有效性3个维度证明了L-偏度和L-峰度相较于传统偏度和峰度的优越性。分析结果如下：样本L-偏度和L-峰度在样本量不足时仍然是总体近似的无偏估计,而传统偏度和峰度的系统性误差较大;L-偏度和L-峰度对离群值具有鲁棒性,而传统偏度和峰度对离群值过于敏感;样本L-偏度和L-峰度对总体的估计波动小且精度高,具有良好的估计有效性;L-偏度和L-峰度分别与传统偏度和峰度有较高相关性,但又能够辨识出不同时空下行程时间可变性分布的差异。基于L-偏...     

Travel mode identification using bluetooth technology

Bluetooth technology has been widely used in transportation studies to collect traffic data. Bluetooth media access control (MAC) readers can be installed along roadways to collect Bluetooth-based data. This data is commonly used to measure traffic performance. One of the advantages of using Bluetooth technology to measure traffic performance is that travel time can be measured directly with a certain level of error instead of by estimation. However, travel time outliers can commonly be observed due to different travel mode on arterials. Since travel mode information cannot be directly obtained from the raw Bluetooth-based data, a mathematical methodology is in need to identify travel mode. In this study, a genetic algorithm and neural network (GANN)-based model was developed to identify travel mode. GPS-enabled devices were used to collect ground truth travel time. In order to additionally compare the model performance, K nearest neighbor (KNN) and support vector machine (SVM) were also implemented. N-fold cross validation was applied to statistically assess the models’ results. Since the model performances depend on the model inputs, seven collections of model inputs were tested in order to achieve the best travel mode identification performance. An arterial segment with four consecutive links and three intersections was selected to be the study segment. The results suggested that correctly identifying the three travel modes successfully every time was not possible, although the GANN based model had low misidentification rates. In our study, 6.12% of autos were misidentified as bikes and 10.53% of bikes were misidentified as autos using three links.     

基于探测车数据的路段行程时间估计

利用探测车数据进行路段行程时间估计面临着两类误差：采样误差和非采样误差,从而导致估计结果精度不高和可靠性差。在回顾已有估计方法的基础上,有针对性地引入了自适应式卡尔曼滤波,建立了相应的状态方程和观测方程,利用相似时间特征的历史数据标定了状态转移系数,并对滤波进行了求解。以实际数据对估计方法进行了验证,平均相对误差为13.13%。研究表明,自适应式卡尔曼滤波能够应用到基于探测车数据的路段行程时间估计中来,并具有估计精度高、收敛速度快、参数少、对初值不敏感等优点。     

Plate scanning tools to obtain travel times in traffic networks

The management of vehicle travel times has been shown to be fundamental to traffic network analysis. To collect travel time measurement, some methods focus solely on isolated links or highway segments, and where two measurement points, at the beginning and at the end of a section, are deemed sufficient to evaluate users' travel time. However, in many cases, transport studies involve networks in which the problem is more complex. This article takes advantage of the plate scanning technique to propose an algorithm that minimizes the required number of registering devices and their location in order to identify vehicles candidates to compute the travel times of a given set of routes (or subroutes). The merits of the proposed method are explained using simple examples and are illustrated by its application to the real network of Ciudad Real.     

基于元胞自动机的动态路段走行时间计算模型

为建立合理的动态交通网络中路段走行时间模型,分析了动态路段走行时间函数的一般形式,对比国内外常用的几种离散型动态路段走行时间函数,基于元胞自动机交通流模型,建立了动态路段走行时间模型。模型可以根据实际路段驶入率、驶出率,推算出任意时刻进入路段车辆的走行时间,并利用M atlab对模型进行求解和数值分析。结果表明,车辆进入路段后的交通状态是动态路段走行时间的主要影响因素;根据累积驶入驶出车辆数曲线可以直接求出动态路段走行时间,能够为动态交通网络中路径走行时间求解奠定基础。      

Measuring Truck Travel Time Reliability Using Truck Probe GPS Data

Truck probe data collected by global positioning system (GPS) devices has gained increased attention as a source of truck mobility data, including measuring truck travel time reliability. Most reliability studies that apply GPS data are based on travel time observations retrieved from GPS data. The major challenges to using GPS data are small, nonrandom observation sets and low reading frequency. In contrast, using GPS spot speed (instantaneous speed recorded by GPS devices) directly can address these concerns. However, a recently introduced GPS spot-speed-based reliability metric that uses speed distribution does not provide a numerical value that would allow for a quantitative evaluation. In light of this, the research described in this article improves the current GPS spot speed distribution-based reliability approach by calculating the speed distribution coefficient of variation. An empirical investigation of truck travel time reliability on Interstate 5 in Seattle, WA, is performed. In addition, correlations are provided between the improved approach and a number of commonly used reliability measures. The reliability measures are not highly correlated, demonstrating that different measures provide different conclusions for the same underlying data and traffic conditions. The advantages and disadvantages of each measure are discussed and recommendations of the appropriate measures for different applications are presented.     

Developing travel time estimation methods using sparse GPS data

Existing methods of estimating travel time from GPS data are not able to simultaneously take account of the issues related to uncertainties associated with GPS and spatial road network data. Moreover, they typically depend upon high-frequency data sources from specialist data providers, which can be expensive and are not always readily available. The study reported here therefore sought to better estimate travel time using “readily available” vehicle trajectory data from moving sensors such as buses, taxis, and logistical vehicles equipped with GPS in “near” real time. To do this, accurate locations of vehicles on a link were first map-matched to reduce the positioning errors associated with GPS and digital road maps. Two mathematical methods were then developed to estimate link travel times from map-matched GPS fixes, vehicle speeds, and network connectivity information with a special focus on sampling frequencies, vehicle penetration rates, and time window lengths. Global positioning system (GPS) data from Interstate I-880 (California) for a total of 73 vehicles over 6 h were obtained from the University of California Berkeley's Mobile Century Project, and these were used to evaluate several travel time estimation methods, the results of which were then validated against reference travel time data collected from high resolution video cameras. The results indicate that vehicle penetration rates, data sampling frequencies, vehicle coverage on the links, and time window lengths all influence the accuracy of link travel time estimation. The performance was found to be best in the 5-min time window length and for a GPS sampling frequency of 60 s.     

运行时间可靠度在单向交通组织中的应用

运用网络可靠性计算的串并联理论,提出了道路网络中节点OD（Origin-Destination）对之间的路径运行时间可靠度计算方法,建立了基于节点OD需求的路网运行时间可靠度计算模型。在节点OD需求已知的情况下,根据交通组织状况,采用动态交通分配和交通仿真方法获得模型参数,计算节点OD对之间分别在双向和单向交通组织条件下的运行时间可靠度,并建立交通组织方案的临界判别条件,作为单向交通组织方案评价和决策的量化指标。     

Modeling arterial travel time distribution by accounting for link correlations: a copula-based approach

The estimation of urban arterial travel time distribution (TTD) is critical to help implement Intelligent Transportation Systems (ITS) and provide travelers with timely and reliable route guidance. The state-of-practice procedure for arterial TTD estimation commonly assumes that the path travel time follows a certain distribution without considering link correlations. However, this approach appears inappropriate since travel times on successive links are essentially dependent along signalized arterials. In this study, a copula-based approach is proposed to model arterial TTD by accounting for spatial link correlations. First, TTDs on consecutive links along one arterial in Hangzhou, China are investigated. Link TTDs are estimated through the nonparametric kernel smoothing method. Link correlations are analyzed in both unfavorable and favorable coordination cases. Then, Gaussian copula models are introduced to model the dependent structure between link TTDs. The parameters of Gaussian copula are obtained by Maximum-Likelihood Estimation (MLE). Next, path TTDs covering consecutive links are estimated based on the estimated copula models. The results demonstrate the advantage of the proposed copula-based approach, compared with the convolution without capturing link correlations and the empirical distribution fitting methods in both unfavorable and favorable coordination cases.     

基于RFID电子车牌数据的公交行程时间预测方法

为了给公交优先信号配时系统提供足够的"思考"时间和准确的控制依据,基于重庆市RFID电子车牌数据提出了一种采用自适应渐消卡尔曼滤波和小波神经网络组合模型动态预测公交行程时间的方法。综合分析公交行程时间的动态和静态影响因素,选取的模型输入参量为标准车流量、路段车辆平均行程时间、平均车速离散性和前班次公交行程时间。利用RFID电子车牌系统采集重庆市鹅公岩大桥路段车辆行驶数据,选取3 000组实际运行数据完成公交行程时间预测模型的训练,另筛选50组数据验证模型的有效性和准确性。研究结果表明：组合模型可动态自适应预测公交行程时间,预测值平均相对误差为3.23%,绝对误差集中在8 s左右,明显优于2种单一模型和基于传统GPS数据的公交行程时间预测模型,可认为选择RFID电子车牌数据作为组合模型的输入,能够明显改善模型预测精度;组合模型预测值的残差分布更为集中、鲁棒性较好,泛化能力强。选择平均绝对误差值、均方根误差值和平均绝对百分比误差作为模型评价指标,结果进一步表明,组合模型的综合预测效果明显优于单一的自适应渐消卡尔曼滤波和小波神经网络。研究方案可为先进公交信息化系统提供良好的技术支撑。