Travel time statistical modeling with the Halphen distribution family

ABSTRACT

This article introduces the Halphen distribution family for modeling travel time distributions and their reliability on single road links. This probability family originally used in hydrology has a set of relevant characteristics. It is composed of three probability distribution functions for which the mathematical properties are described here. The article uses a graphical representation, the δ-Moment Ratio Diagram (δ-MRD). This tool allows characterizing travel time reliability as well as selecting best distribution candidates within the fitting processes, by considering empirical data sets. A systematic methodology is developed to take advantage of both aspects. From maximum log-likelihood estimation, it is shown that Halphen distributions are among the best state-of-the-art solutions for the travel time modeling purpose. This global framework is validated using two empirical data sets: an urban data set gathered in Portland, Oregon (USA), and a periurban data set from Lyon (France). The model calibration is eased through the use of the δ-MRD; this property opens new research directions about the mapping between traffic states and statistical modeling. It comes from all these considerations that the Halphen family is suitable to describe accurately the travel time dynamics on single links. Therefore, it could be part of a decision support system for practitioners interested in travel time variability.     

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.     

A novel arterial travel time distribution estimation model and its application to energy/emissions estimation

Arterial travel time information is crucial to advanced traffic management systems and advanced traveler information systems. An effective way to represent this information is the estimation of travel time distribution. In this paper, we develop a modified Gaussian mixture model in order to estimate link travel time distributions along arterial with signalized intersections. The proposed model is applicable to traffic data from either fixed-location sensors or mobile sensors. The model performance is validated using real-world traffic data (more than 1,400 vehicles) collected by the wireless magnetic sensors and digital image recognition in the field. The proposed model shows high potential (i.e., the correction rate are above 0.9) to satisfactorily estimate travel time statistics and classify vehicle stop versus non-stop movements. In addition, the resultant movement classification application can significantly improve the estimation of traffic-related energy and emissions along arterial.     

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...     

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.     

观测路径出行时间下随机网络交通需求估计

道路网络起讫点(OD)需求是城市决策长期交通规划和短期交通管理中的基础参数,准确的交通需求更是实施交通拥堵控制、限行限速、路径诱导等措施的先决条件.综合运用观测的轨迹已知和未知路径出行时间,建立随机网络交通需求估计双层规划模型.上层广义最小二乘模型最小化历史交通需求与待估交通需求、观测路径出行时间与待估路径出行时间之间...     

基于实时交通信息的行程时间估算及路径选择分析

路段行程时间的估计和预测是诱导系统的关键技术之一。由于路网参数不断变化,路段行程时间的估计必须满足实时性的要求。以城市交通控制系统的基本设施为基础,根据我国城市交通目前的发展状况,分析了影响路段行程时间的各种因素和路段行程时间的组成。利用设置在路段上的车辆自动检测装置搜集到的实时交通流信息,并结合随机服务系统的相关理论建立了城市道路路段行程时间的动态计算模型,提出了一种具有真实最短路径意义的实时动态最短路径选择的方法。     

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.     

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。      

Travel time estimation oriented freeway sensor placement problem considering sensor failure

Optimal sensor placement on freeway corridor is of great interest to transportation authorities. However, current traffic sensors are easily subject to various failures. Therefore, it is necessary to incorporate sensor failure into the optimal sensor placement model. In this article, a two-stage stochastic model is proposed for the purpose of travel time estimation on freeway corridor. To balance the effectiveness and reliability, a stochastic conditional value at risk (CVaR) model is also proposed. Since both models are too complicated, a customized genetic algorithm is developed. Numerical experiments show that considering sensor failure makes a significant performance improvement in the sensor placement pattern. Sensitivity analysis is also applied to investigate the impact of a number of allowable sensors and different traffic sensor failure probability.     

A framework for travel time variability analysis using urban traffic incident data

This study aims to develop a framework to estimate travel time variability caused by traffic incidents using integrated traffic, road geometry, incident, and weather data. We develop a series of robust regression models based on the data from a stretch in California's highway system during a two-year period. The models estimate highway clearance time and percent changes in speed for both downstream and upstream sections of the incident bottleneck. The results indicate that highway shoulder and lane width factor adversely impact downstream highway clearance time. Next, travel time variability is estimated based on the proposed speed change models. The results of the split-sample validation show the effectiveness of the proposed models in estimating the travel time variability. Application of the model is examined using a micro-simulation, which demonstrates that equipping travelers with the estimated travel time variability in case of an incident can improve the total travel time by almost 60%. The contribution of this research is to bring several datasets together, which can be advantageous to Traffic Incident Management.     

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.     

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.     

基于行程质量的随机用户平衡分配模型

提出行程质量的概念以描述出行者在不确定环境下的路径选择准则。将行程质量定义为行程时间和行程时间可靠性的线性加权和,综合了影响路径选择的两个不同的重要因素:行程时间和行程时间可靠性。假定在路段通行能力随机变化的情况下出行者以估计行程质量费用最小作为路径选择的标准,建立了基于行程质量的随机用户平衡分配模型。证明了模型解的等价性和唯一性,给出了求解模型的MSA算法。在一个小型测试网络上的计算结果表明:模型能够反映出行者在随机路网中的路径选择行为。     

路径行程时间的组合预测方法研究

立足于历史和实时数据的融合应用,从实际应用角度出发,构筑了一种路径短时行程时间的组合预测模型和相应算法。该组合预测模型包含基于历史数据特征向量的聚类分析子模型和基于路径行程时间序列的自回归子模型,通过贝叶斯概率公式实现子模型的权重分配。并对数据进行滚动式处理,实现权重系数的实时更新。最后选择上海市快速路系统3条典型路径进行实例分析,并与实际牌照自动识别行程时间数据进行对比验证。     

A route guidance system considering travel time unreliability

Under a stochastic roadway, drivers need a route guidance system incorporating travel time variability. To recommend a customized path depending on the trip purpose and the driver’s risk-taking behavior, various path ranking methods have been developed. Unlike those methods, our proposed disutility method can easily incorporate a target arrival time in the ranking process by measuring how late the travel is and by penalizing it depending on the severity of lateness. In addition, the disutility-based route guidance system can properly address travel time unreliability that causes unacceptable disruptions to the driver’s schedule (i.e., unexpected long delay). We compare the disutility-based path ranking method with other ranking methods, the percentile travel time, the mean excess travel time, and the on-time arrival probability. We show that the disutility has stronger discriminating power and requires less solution space to find an optimal path. The most important advantage is that it can estimate a driver’s risk-taking behavior for each trip purpose by using the discrete choice analysis. We construct a simulation framework to acquire the travel time data on a hypothetical roadway. We analyze the data and show how various ranking methods recommend a customized path. Using the data, we show the advantage of the disutiltiy method over the other methods, which is generating a customized path with respect to the target arrival time by properly penalizing the travel time lateness.     

随机交通网络中依赖信息的路径优化问题研究

针对交通网络中路径通行时间具有与时间相关的随机分布特性，将研究在此类交通网络上依赖信息的路径选择问题。在路径选择过程中引入交通信息，在随机交通网络上最优路径选择原则为下一节点的选择将依赖于已实现的路段时间及当前节点的出发时间，通过期望最小值方法，按照路径通行时间期望值最小原则，建立一种通过所获得交通信息来进行路径选择的优化模型，给出了模型的求解算法。并在简单交通网络上对模型进行实现。     

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。     

通行能力约束下的弹性需求交通投影动态演化模型

利用投影动态系统理论建立了具有路段通行能力约束的弹性需求交通网络动态演化模型.通过分析节点路段处交通流量与出行阻抗关系,揭示了出行者在网络局部对出行路线进行调整的决策过程,并分别建立了有通行能力约束的路段流量更新方程和弹性交通需求下的节点最短行程时间估计方程.通过在整个网络上整合上述两类方程,得到最终的交通网络投影动态...