The Aw–Rascle and Zhang’s model: Vacuum problems,existence and regularity of the solutions of the Riemann problem

In this paper we will discuss some aspects of the recent macroscopic models of the second-order proposed by [Aw, A., Rascle, M., 2000. Resurrection of second order models of traffic flow. SIAM Journal of Applied Mathematics 60 (3), 916–938] and [Zhang, H.M., 2002. A non-equilibrium traffic model devoid of gas-like behavior. Transportation Research Part B 36, 275–290]. These models were suggested after the publication of an article written by [Daganzo, C.F., 1995. Requiem for second-order fluid approximations of traffic flow. Transportation Research Part B 29, 277–286] showing that some classical second-order models can exhibit non-physical solutions. It is shown in this note that the ARZ (Aw–Rascle–Zhang) model respects the anisotropic character of traffic flow, that it yields physical solutions, and that vacuum problems can be solved satisfactorily, provided that the fundamental diagram (equilibrium speed–density relationship) is extended in a suitable fashion. It follows that the Riemann problem for the ARZ model with extended fundamental diagram always admits a solution, and that this solution depends continuously on the initial conditions.     

Comparing traffic state estimators for mixed human and automated traffic flows

This article addresses the problem of modeling and estimating traffic streams with mixed human operated and automated vehicles. A connection between the generalized Aw Rascle Zhang model and two class traffic flow motivates the choice to model mixed traffic streams with a second order traffic flow model. The traffic state is estimated via a fully nonlinear particle filtering approach, and results are compared to estimates obtained from a particle filter applied to a scalar conservation law. Numerical studies are conducted using the Aimsun micro simulation software to generate the true state to be estimated. The experiments indicate that when the penetration rate of automated vehicles in the traffic stream is variable, the second order model based estimator offers improved accuracy compared to a scalar modeling abstraction. When the variability of the penetration rate decreases, the first order model based filters offer similar performance.     

A variational formulation for higher order macroscopic traffic flow models of the GSOM family

The GSOM (Generic second order modelling) family of traffic flow models combines the LWR model with dynamics of driver-specific attributes and can be expressed as a system of conservation laws. The object of the paper is to show that a proper Lagrangian formulation of the GSOM model can be recast as a Hamilton–Jacobi equation, the solution of which can be expressed as the value function of an optimal control problem. This value function is interpreted as the position of vehicles, and the optimal trajectories of the optimal control formulation can be identified with the characteristics. Further the paper analyzes the initial and boundary conditions, proposes a generalization of the inf-morphism and the Lax–Hopf formulas to the GSOM model, and considers numerical aspects.     

A study of the influence of severe environmental conditions on common traffic congestion features

On the basis of real traffic and environmental data measured on German freeways, we studied common features of traffic congestion under the influence of severe weather conditions. We have found that traffic features [J] and [S] defining traffic phases “wide moving jam” (J) and “synchronized flow” (S) in Kerner's three‐phase theory are indeed common spatiotemporal traffic features. The quantitative parameters for both traffic phases [S] and [J] were investigated in a comparison of “ideal” weather conditions (good visibility and no precipitation) and severe weather situations (icy road, wind, precipitation, etc.). We showed spatiotemporal congested patterns in several space–time diagrams based on the Automatic Tracking of Moving Jams/Forecasting of Traffic Objects (ASDA/FOTO) model reconstruction for roadside detectors. A statistical study of traffic phase [J] parameters was presented, showing the average values and standard deviation of the quantities. Similarities and differences were analyzed, and some consequences for vehicular applications were discussed to cope with severe weather conditions. Copyright © 2013 John Wiley & Sons, Ltd.     

Modeling traffic's flow-density relation: Accommodation of multiple flow regimes and traveler types

This research investigates freeway-flow impacts of different traveler types by specifying and applying a latent-segmentation model of congested and uncongested driving behaviors. Drivers in uncongested conditions are assumed to drive at self-chosen speeds, while drivers in congested conditions are assumed to take speed as given and choose a spacing (between their vehicle and the previous vehicle). Several classes of driver-vehicle combinations are distinguished in a data set based on double-loop-detector pulses and a household travel survey. These classifications are made on the basis of vehicle type and gender, leading to class estimates of speeds and spacings. The segmentation model is specified as a logit function of density, weather, and vehicle type, leading to estimates of congested-condition probabilities. Unobserved heterogeneity is incorporated in all models via common error assumptions.Results indicate that segmentation models are promising tools for traffic data analysis and that information on travelers, their vehicles, and weather conditions explains significant variation in flow data. By clarifying a greater understanding of traffic conditions and traveler behavior explains much scatter in the fundamental relation between flow, speed, and density, can assist regions in their traffic-management efforts and engineers in their design of roadway facilities. Ultimately, such improvements to travel networks should enhance quality of life.     

Identifying the onset of congestion rapidly with existing traffic detectors

From an operations standpoint the most important function of a traffic surveillance system is determining reliably whether the facility is free flowing or congested. The second most important function is responding rapidly when the facility becomes congested. These functions are complicated by the fact that conventional vehicle detectors are only capable of monitoring discrete points along the roadway while incidents may occur at any location on the facility. The point detectors are typically placed at least one-third of a mile apart and conditions between the detectors must be inferred from the local measurements.This paper presents a new approach for traffic surveillance that addresses these issues. It uses existing dual loop detector stations to match vehicle measurements between stations and monitor the entire roadway. Rather than expending a considerable effort to detect congested conditions, the research employs a relatively simple strategy to look for free flow traffic. Whenever a unique vehicle passes the downstream station, the algorithm looks to see if a similar vehicle passed the upstream station within a time window that is bounded by feasible travel times. The approach provides vehicle reidentification and travel time measurement on freeways during free flow and through the onset of congestion. If desired, other algorithms can be used with the same detectors to provide similar measurements during congested conditions. The work should prove beneficial for traffic management and traveler information applications, while promising to be deployable in the short term.     

Microscopic modeling of large‐scale pedestrian–vehicle conflicts in the city of Madinah,Saudi Arabia

This paper presents a micro‐simulation modeling framework for evaluating pedestrian–vehicle conflicts in crowded crossing areas. The framework adopts a simulation approach that models vehicles and pedestrians at the microscopic level while satisfying two sets of constraints: (1) flow constraints and (2) non‐collision constraints. Pedestrians move across two‐directional cells as opposed to one‐dimensional lanes as in the case of vehicles; therefore, extra caution is considered when modeling the shared space between vehicles and pedestrians. The framework is used to assess large‐scale pedestrian–vehicle conflicts in a highly congested ring road in the City of Madinah that carries 20 000 vehicles/hour and crossed by 140 000 pedestrians/hour after a major congregational prayer. The quantitative and visual results of the simulation exhibits serious conflicts between pedestrians and vehicles, resulting in considerable delays for pedestrians crossing the road (9 minutes average delay) and slow traffic conditions (average speed <10 km/hour). The model is then used to evaluate the following three mitigating strategies: (1) pedestrian‐only phase; (2) grade separation; and (3) pedestrian mall. A matrix of operational measures of effectiveness for network‐wide performance (e.g., average travel time, average speed) and for pedestrian‐specific performance (e.g., mean speed, mean density, mean delay, mean moving time) is used to assess the effectiveness of the proposed strategies. Copyright © 2012 John Wiley & Sons, Ltd.     

Revisiting Jiang’s dynamic continuum model for urban cities

Jiang et al. (Jiang, Y.Q., Wong, S.C., Ho, H.W., Zhang, P., Liu, R.X., Sumalee, A., 2011. A dynamic traffic assignment model for a continuum transportation system. Transportation Research Part B 45 (2), 343–363) proposed a predictive continuum dynamic user-optimaDUO-l to investigate the dynamic characteristics of traffic flow and the corresponding route-choice behavior of travelers. Their modeled region is a dense urban city that is arbitrary in shape and has a single central business district (CBD). However, we argue that the model is not well posed due to an inconsistency in the route-choice strategy under certain conditions. To overcome this inconsistency, we revisit the PDUO-C problem, and construct an improved path-choice strategy. The improved model consists of a conservation law to govern the density, in which the flow direction is determined by the improved path-choice strategy, and a Hamilton–Jacobi equation to compute the total travel cost. The simultaneous satisfaction of both equations can be treated as a fixed-point problem. A self-adaptive method of successive averages (MSA) is proposed to solve this fixed-point problem. This method can automatically determine the optimal MSA step size using the least squares approach. Numerical examples are used to demonstrate the effectiveness of the model and the solution algorithm.     

Book reviews

Road haulage licensing and EC Transport Policy. By K. J. Button. (Aldershot: Gower Publishing Co., 1984.) [Pp.127.] £14.50.

Bicycles and Public Transportation: New Links to Suburban Transit Markets. By Michael A. Replogle. (Bicycle Federation, Washington DC, 1983.) [Pp. 171.] US$15.95.

Urban Transport in ASEAN. By V. Setty Pendakur. (Institute of Southeast Asian Studies — Research Notes and Discussions Papers Series No. 43, 1984.) [Pp. 65] $4.50 ISBN 9971–902–67–2.

The World Railway System. By Bernard de Fontgalland (Cambridge Univerisity Press, 1984.) [Pp. 209.] £16.00.     

Personalized real-time traffic information provision: Agent-based optimization model and solution framework

The advancement of information and communication technology allows the use of more sophisticated information provision strategies for real-time congested traffic management in a congested network. This paper proposes an agent-based optimization modeling framework to provide personalized traffic information for heterogeneous travelers. Based on a space–time network, a time-dependent link flow based integer programming model is first formulated to optimize various information strategies, including elements of where and when to provide the information, to whom the information is given, and what alternative route information should be suggested. The analytical model can be solved efficiently using off-the-shelf commercial solvers for small-scale network. A Lagrangian Relaxation-based heuristic solution approach is developed for medium to large networks via the use of a mesoscopic dynamic traffic simulator.     

Phase transition model of non-stationary traffic flow: Definition,properties and solution method

We consider the problem of modeling traffic phenomena at a macroscopic level. Increasing availability of streaming probe data allowing the observation of non-stationary traffic motivates the development of models capable of leveraging this information. We propose a phase transition model of non-stationary traffic in conservation form, capable of propagating joint measurements from fixed and mobile sensors, to model complex traffic phenomena such as hysteresis and phantom jams, and to account for forward propagation of information in congested traffic. The model is shown to reduce to the Lighthill–Whitham–Richards model within each traffic phase for the case of stationary states, and to have a physical mesoscopic interpretation in terms of drivers’ behavior. A corresponding discrete formulation appropriate for practical implementation is shown to provide accurate numerical solution to the proposed model. The performance of the model introduced is assessed on benchmark cases and on experimental vehicle trajectories from the NGSIM datasets.     

Real-time queue length estimation for congested signalized intersections

How to estimate queue length in real-time at signalized intersection is a long-standing problem. The problem gets even more difficult when signal links are congested. The traditional input–output approach for queue length estimation can only handle queues that are shorter than the distance between vehicle detector and intersection stop line, because cumulative vehicle count for arrival traffic is not available once the detector is occupied by the queue. In this paper, instead of counting arrival traffic flow in the current signal cycle, we solve the problem of measuring intersection queue length by exploiting the queue discharge process in the immediate past cycle. Using high-resolution “event-based” traffic signal data, and applying Lighthill–Whitham–Richards (LWR) shockwave theory, we are able to identify traffic state changes that distinguish queue discharge flow from upstream arrival traffic. Therefore, our approach can estimate time-dependent queue length even when the signal links are congested with long queues. Variations of the queue length estimation model are also presented when “event-based” data is not available. Our models are evaluated by comparing the estimated maximum queue length with the ground truth data observed from the field. Evaluation results demonstrate that the proposed models can estimate long queues with satisfactory accuracy. Limitations of the proposed model are also discussed in the paper.     

Average time gaps in congested freeway flow

Characteristics of time gaps (that is, the time separation between the rear of the lead vehicle and the front of the following vehicle) in congested freeway flow provide an important link between microscopic and macroscopic traffic flow. Although individual time gaps are a microscopic phenomenon, average time gaps can easily be determined from commonly collected macroscopic traffic flow data. Data from San Diego freeways and the Queen Elizabeth Way in Ontario, Canada are analyzed to show that average time gaps in congested flow are essentially constant with respect to speed; that they vary considerably between lanes at a single location and, for the same lane, from site to site; that they display considerable scatter; and that at some sites there is a distinct increase in average time gaps in the median lane in the transition to congested flow but at others there is no change or a slight reduction. The variability of average time gaps is not easily explained, although differences in driver populations may partly explain differences among different sites. Hysteresis due to acceleration and deceleration does not appear to be an explanation for the high degree of scatter in average time gaps, since no positive correlation was found between speed changes and average time gaps.     

Including heavy vehicles in a car‐following model: modelling,calibrating and validating

Heavy vehicles influence general traffic in many different ways compared with passenger vehicles, and this may result in different levels of traffic instability. Increases in the number and proportion of heavy vehicles in the traffic stream will therefore result in different traffic flow conditions. This research initially outlines the different car‐following behaviour of drivers in congested heterogeneous traffic conditions indicating the necessity for developing a car‐following model, which includes these differences. A psychophysical car‐following model, similar in form to Weideman's car‐following model, was developed. Due to the complexity of the developed model, the calibration of the model was undertaken using a particle swarm optimisation algorithm with the data recorded under congested traffic conditions. This was then incorporated into a traffic microsimulation model. The results showed that the car‐following perceptual thresholds and thus action points of drivers differ based on their vehicle and the lead vehicle types. The inclusion of the heavy vehicles in the model showed significant impacts on the traffic dynamic and interactions amongst different vehicles. Copyright © 2016 John Wiley & Sons, Ltd.     

The identification and empirical characterization of vehicular (Lagrangian) fundamental diagrams in multilane traffic flow

Traditional macroscopic traffic flow modeling framework adopts the spatial–temporal coordinate system to analyze traffic flow dynamics. With such modeling and analysis paradigm, complications arise for traffic flow data collected from mobile sensors such as probe vehicles equipped with mobile phones, Bluetooth, and Global Positioning System devices. The vehicle‐based measurement technologies call for new modeling thoughts that address the unique features of moving measurements and explore their full potential. In this paper, we look into the concept of vehicular fundamental diagram (VFD) and discuss its engineering implications. VFD corresponds to a conventional fundamental diagram (FD) in the kinematic wave (KW) theory that adopts space–time coordinates. Similar to the regular FD in the KW theory, VFD encapsulates all traffic flow dynamics. In this paper, to demonstrate the full potential of VFD in interpreting multilane traffic flow dynamics, we generalize the classical Edie's formula and propose a direct approach of reconstructing VFD from traffic measurements in the vehicular coordinates. A smoothing algorithm is proposed to effectively reduce the nonphysical fluctuation of traffic states calculated from multilane vehicle trajectories. As an example, we apply the proposed methodology to explore the next‐generation simulation datasets and identify the existence and forms of shock waves in different coordinate systems. Our findings provide empirical justifications and further insight for the Lagrangian traffic flow theory and models when applied in practice. Copyright © 2015 John Wiley & Sons, Ltd.     

Observing freeway ramp merging phenomena in congested traffic

This work conducts a comprehensive investigation of traffic behavior and characteristics during freeway ramp merging under congested traffic conditions. On the Tokyo Metropolitan Expressway, traffic congestion frequently occurs at merging bottleneck sections, especially during heavy traffic demand. The Tokyo Metropolitan Expressway public corporation, generally applies different empirical strategies to increase the flow rate and decrease the accident rate at the merging sections. However, these strategies do not rely either on any behavioral characteristics of the merging traffic or on the geometric design of the merging segments. There have been only a few research publications concerned with traffic behavior and characteristics in these situations. Therefore, a three‐year study is undertaken to investigate traffic behavior and characteristics during the merging process under congested situations. Extensive traffic data capturing a wide range of traffic and geometric information were collected using detectors, videotaping, and surveys at eight interchanges in Tokyo Metropolitan Expressway. Maximum discharged flow rate from the head of the queue at merging sections in conjunction with traffic and geometric characteristics were analyzed. In addition, lane changing maneuver with respect to the freeway and ramp traffic behaviors were examined. It is believed that this study provides a thorough understanding of the freeway ramp merging dynamics. In addition, it forms a comprehensive database for the development and implementation of congestion management techniques at merging sections utilizing Intelligent Transportation System.     

Empirical analysis of heterogeneous traffic flow and calibration of porous flow model

Heterogeneous traffic flow, characterized by a free inter-lane exchange, has become an important issue in addressing congestion in urban areas. It is of particular interest in many developing countries, that experience a strong increase in motorcycle use. New approaches to the heterogeneous non-lane-based flow have been proposed. However insufficient empirical verification has been made to estimate vehicle interaction, that is necessary for an accurate representation of mixed-flow conditions. In this paper, we focus on the porous flow approach to capture the complex interactions. The parameters from this approach are estimated from empirical observations. Video data was recorded and processed to capture vehicle interactions at a number of road sections in Surabaya City, Indonesia. The specific behavior of each vehicle in the traffic flow was captured by developing the pore size–density distributions, analyzing the class-specific critical pore sizes, and producing the class specific speed–density and flow–density diagrams. The results reveal how critical pore sizes are based on pore size–density distributions, the flow diagram for each vehicle class, and how traffic flow relationships for motorcyclists and the other vehicles exhibit significant differences. It is concluded that the proposed approach can represent the specific behavior of the motorcyclist in heterogeneous traffic flow, in both the situations of with- and without an exclusive lane for motorcycles, can clarify motorcyclist’s behavior in terms of passenger car unit of motorcycle, and can therefore support policy making on the improvement of urban transport.     

Improving fuel consumption and CO2 emissions calculations in urban areas by coupling a dynamic micro traffic model with an instantaneous emissions model

Τhis study demonstrates the combination of a microscopic traffic simulator (AIMSUN) with an instantaneous emissions model (AVL CRUISE) to investigate the impact of traffic congestion on fuel consumption on an urban arterial road. The micro traffic model was enhanced by an improved car-following law according to Morello et al. (2014) and was calibrated to replicate measured driving patterns over an urban corridor in Turin, Italy, operating under adaptive urban traffic control (UTC). The method was implemented to study the impact of congestion on fuel consumption for the category of Euro 5 diesel <1.4 l passenger cars. Free flow and congested conditions led to respective consumption differences of −25.8% and 20.9% over normal traffic. COPERT 5 rather well predicted the impact of congestion but resulted to a much lower relative reduction in free flow conditions. Start and stop system was estimated to reduce consumption by 6% and 11.9% under normal and congested conditions, respectively. Using the same modelling approach, UTC was found to have a positive impact on CO₂ emissions of 8.1% and 4.5% for normal and congested conditions, respectively, considering the Turin vehicle fleet mix for the year 2013. Overall, the study demonstrates that the combination of detailed and validated micro traffic and emissions models offers a powerful combination to study traffic and powertrain impacts on greenhouse gas and fuel consumption of on road vehicles over a city network.     

Recognition and tracking of spatial–temporal congested traffic patterns on freeways

The two models FOTO (Forecasting of Traffic Objects) and ASDA (Automatische Staudynamikanalyse: Automatic Tracking of Moving Traffic Jams) for the automatic recognition and tracking of congested spatial–temporal traffic flow patterns on freeways are presented. The models are based on a spatial–temporal traffic phase classification made in the three-phase traffic theory by Kerner. In this traffic theory, in congested traffic two different phases are distinguished: “wide moving jam” and “synchronized flow”. The model FOTO is devoted to the identification of traffic phases and to the tracking of synchronized flow. The model ASDA is devoted to the tracking of the propagation of moving jams. The general approach and the different extensions of the models FOTO and ASDA are explained in detail. It is stressed that the models FOTO and ASDA perform without any validation of model parameters in different environmental and traffic conditions. Results of the online application of the models FOTO and ASDA at the TCC (Traffic Control Center) of Hessen near Frankfurt (Germany) are presented and evaluated.     

Accounting for traffic speed dynamics when calculating COPERT and PHEM pollutant emissions at the urban scale

Coupling a traffic microsimulation with an emission model is a means of assessing fuel consumptions and pollutant emissions at the urban scale. Dealing with congested states requires the efficient capture of traffic dynamics and their conditioning for the emission model. Two emission models are investigated here: COPERT IV and PHEM v11. Emission calculations were performed at road segments over 6 min periods for an area of Paris covering 3 km². The resulting network fuel consumption (FC) and nitrogen oxide (NOx) emissions are then compared. This article investigates: (i) the sensitivity of COPERT to the mean speed definition, and (ii) how COPERT emission functions can be adapted to cope with vehicle dynamics related to congestion. In addition, emissions are evaluated using detailed traffic output (vehicle trajectories) paired with the instantaneous emission model, PHEM.COPERT emissions are very sensitive to mean speed definition. Using a degraded speed definition leads to an underestimation ranging from −13% to −25% for fuel consumption during congested periods (from −17% to −36% respectively for NOx emissions). Including speed distribution with COPERT leads to higher emissions, especially under congested conditions (+13% for FC and +16% for NOx). Finally, both these implementations are compared to the instantaneous modeling chain results. Performance indicators are introduced to quantify the sensitivity of the coupling to traffic dynamics. Using speed distributions, performance indicators are more or less doubled compared to traditional implementation, but remain lower than when relying on trajectories paired with the PHEM emission model.