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.     

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.     

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.     

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.     

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的偏差,约束为交通需求、路段流量、路段出行时间与路径出行时间之间的传播关系,通过高斯混合模型（GMM）对其中轨迹未知的观测出行时间依概率聚类。下层为随机网络交通出行均衡模型,分别运用出行时间预算和随机用户均衡处理路网不确定性和出行者感知误差。上、下层之间通过交通需求和OD-路段关联比例进行信息传递。设计迭代算法框架求解双层规划模型,迭代算法包含求解上层模型的最速下降法、求解下层模型的相继平均算法和求解GMM模型的最大期望（EM）算法。通过算例表明轨迹未知的路径出行信息的加入在提升需求估计精度的同时也增大了估计值的方差;设计的迭代算法能够稳定收敛到10^-5的精度;GMM软聚类方法估计的交通需求显著优于硬聚类方法估计的需求值;交通需求值对观测路径出行时间的扰动更加敏感。研究考虑出行者风险态度,通过轨迹信息的重新构建揭示城市交通需求演化规律。     

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.     

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.     

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.     

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。     

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.     

基于交通流理论的公交站点间行程时间预测

分析了公交站点间车辆运行过程,将行程预测时间划分为交叉口排队等待时间、路段行驶时间和停站时间3个部分,利用交通波理论和延误三角形,分别建立了无公交专用车道和有公交专用车道2种情况下排队等待时间的动态预测模型;根据乘客到站规律和上下车规律,提出了公交车进站停靠时间模型;针对无公交专用车道条件下的时间预测方法进行了实例演算.实验数据表明,基于交通波行程时间预测方法具有较高的精度,可以满足站点间行程时间预报要求.     

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.     

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.     

动态输入下路段行程时间研究

以元胞传输模型(LWR模型的离散形式)作为分析工具,以行程时间为研究对象,研究了单车道路段没有出入口的基本路段受交通信号控制影响下的动态行程时间.考虑到路段上车辆密度对车辆速度的影响,文章定义了路段加权密度来表征车辆进入路段时路段的状态.分析结果表明,动态行程时间和车辆进入路段时的流量基本上没有关系;当车辆进入路段时刻一定时,路段加权密度和车辆的动态行程时间成线性关系.     

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.     

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.     

供需不确定条件下的预算-超额用户平衡模型

为更加全面、准确反映随机路网中出行者规避风险的择路行为,以预算-超额行程时间作为出行者选择路径的依据,提出了一种供应及需求不确定条件下同时考虑可靠性和不可靠性的交通分配模型——预算-超额用户平衡模型,推导了需求服从Gamma分布、路段通行能力服从均匀分布条件下预算-超额行程时间的解析表达式,并以此为基础建立起用等价变分不等式表示的平衡模型。利用一个小型测试网络比较了用户平衡模型、基于可靠性的用户平衡模型以及预算-超额用户平衡模型的性能。研究结果表明：提出的模型是有效、可行的;其平衡流量模式不同于用户平衡模型和基于可靠性的用户平衡模型;随着需求水平、可靠度以及路段通行能力退化程度的增加,预算-超额行程时间随之增加。     

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。     

Robust traffic assignment model: Formulation,solution algorithms and empirical application

ABSTRACT

The deterministic traffic assignment problem based on Wardrop's first criterion of traffic network utilization has been widely studied in the literature. However, the assumption of deterministic travel times in these models is restrictive, given the large degree of uncertainty prevalent in urban transportation networks. In this context, this paper proposes a robust traffic assignment model that generalizes Wardrop's principle of traffic network equilibrium to networks with stochastic and correlated link travel times and incorporates the aversion of commuters to unreliable routes.

The user response to travel time uncertainty is modeled using the robust cost (RC) measure (defined as a weighted combination of the mean and standard deviation of path travel time) and the corresponding robust user equilibrium (UE) conditions are defined. The robust traffic assignment problem (RTAP) is subsequently formulated as a Variational Inequality problem. To solve the RTAP, a Gradient Projection algorithm is proposed, which involves solving a series of minimum RC path sub-problems that are theoretically and practically harder than deterministic shortest path problems. In addition, an origin-based heuristic is proposed to enhance computational performance on large networks. Numerical experiments examine the computational performance and convergence characteristics of the exact algorithm and establish the accuracy and efficiency of the origin-based heuristic on various real-world networks. Finally, the proposed RTA model is applied to the Chennai road network using empirical data, and its benefits as a normative benchmark are quantified through comparisons against the standard UE and System Optimum (SO) models.     

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。