Platoon-based traffic flow model for estimating breakdown probability at single-lane expressway bottlenecks

This study investigates the mechanism of traffic breakdown and establishes a traffic flow model that precisely simulates the stochastic and dynamic processes of traffic flow at a bottleneck. The proposed model contains two models of stochastic processes associated with traffic flow dynamics: a model of platoon formation behind a bottleneck and a model of speed transitions within a platoon. After these proposed models are validated, they are applied to a simple one-way, one-lane expressway section containing a bottleneck, and the stochastic nature of traffic breakdown is demonstrated through theoretical exercises.     

Nonlinear multivariate time–space threshold vector error correction model for short term traffic state prediction

We propose Time–Space Threshold Vector Error Correction (TS-TVEC) model for short term (hourly) traffic state prediction. The theory and method of cointegration with error correction mechanism is employed in the general design of the new statistical model TS-TVEC. An inherent connection between mathematical form of error correction model and traffic flow theory is revealed through the transformation of the well-known Fundamental Traffic Diagrams. A threshold regime switching framework is implemented to overcome any unknown structural changes in traffic time series. Spatial cross correlated information is incorporated with a piecewise linear vector error correction model. A Neural Network model is also constructed in parallel to comparatively test the effectiveness and robustness of the new statistical model. Our empirical study shows that the TS-TVEC model is an effective tool that is capable of modeling the complexity of stochastic traffic flow processes and potentially applicable to real time traffic state prediction.     

A stochastic model of traffic flow: Theoretical foundations

In a variety of applications of traffic flow, including traffic simulation, real-time estimation and prediction, one requires a probabilistic model of traffic flow. The usual approach to constructing such models involves the addition of random noise terms to deterministic equations, which could lead to negative traffic densities and mean dynamics that are inconsistent with the original deterministic dynamics. This paper offers a new stochastic model of traffic flow that addresses these issues. The source of randomness in the proposed model is the uncertainty inherent in driver gap choice, which is represented by random state dependent vehicle time headways. A wide range of time headway distributions is allowed. From the random time headways, counting processes are defined, which represent cumulative flows across cell boundaries in a discrete space and continuous time conservation framework. We show that our construction implicitly ensures non-negativity of traffic densities and that the fluid limit of the stochastic model is consistent with cell transmission model (CTM) based deterministic dynamics.     

Microscopic driving theory with oscillatory congested states: Model and empirical verification

The essential distinction between the Fundamental Diagram Approach (FDA) and Kerner’s three-phase theory (KTPT) is the existence of a unique gap–speed (or flow–density) relationship in the former class. In order to verify this relationship, empirical data are analyzed with the following findings: (1) linear relationship between the actual space gap and speed can be identified when the speed difference between vehicles approximates zero; (2) vehicles accelerate or decelerate around the desired space gap most of the time. To explain these phenomena, we propose that, in congested traffic flow, the space gap between two vehicles will oscillate around the desired space gap in the deterministic limit. This assumption is formulated in terms of a cellular automaton. In contrast to FDA and KTPT, the new model does not have any congested steady-state solution. Simulations under periodic and open boundary conditions reproduce the empirical findings of KTPT. Calibrating and validating the model to detector data produces results that are better than that of previous studies.     

Network operation reliability in a Manhattan-like urban system with adaptive traffic lights

Traffic breakdown to global gridlock occurring in congested traffic network makes the serious traffic congestion even much worse. This paper has proposed to use Network Operation Reliability (NOR) to quantitatively depict the probabilistic feature of traffic breakdown to global gridlock. The Nagel–Schreckenberg cellular automaton model has been used to simulate the traffic flow in a Manhattan-like urban network. A simple adaptive traffic light strategy has been proposed. It has been shown that if vehicles choose to use geometric shortest path, the adaptive traffic signals are able to remarkably enhance the NOR and sometimes the average velocity and the arrival rate as well. The vehicle distribution has been investigated, which has heuristically explained the enhancement of the NOR. A simple perimeter control strategy has been shown to fail to enhance the NOR. Finally, we show that if the time shortest path information could be provided and updated timely, then the NOR can be remarkably enhanced but the adaptive traffic signals have only trivial effect on NOR.     

Three-phase traffic theory and two-phase models with a fundamental diagram in the light of empirical stylized facts

Despite the availability of large empirical data sets and the long history of traffic modeling, the theory of traffic congestion on freeways is still highly controversial. In this contribution, we compare Kerner’s three-phase traffic theory with the phase diagram approach for traffic models with a fundamental diagram. We discuss the inconsistent use of the term “traffic phase” and show that patterns demanded by three-phase traffic theory can be reproduced with simple two-phase models, if the model parameters are suitably specified and factors characteristic for real traffic flows are considered, such as effects of noise or heterogeneity or the actual freeway design (e.g. combinations of off- and on-ramps). Conversely, we demonstrate that models created to reproduce three-phase traffic theory create similar spatiotemporal traffic states and associated phase diagrams, no matter whether the parameters imply a fundamental diagram in equilibrium or non-unique flow-density relationships. In conclusion, there are different ways of reproducing the empirical stylized facts of spatiotemporal congestion patterns summarized in this contribution, and it appears possible to overcome the controversy by a more precise definition of the scientific terms and a more careful comparison of models and data, considering effects of the measurement process and the right level of detail in the traffic model used.     

Vehicle headway modeling and its inferences in macroscopic/microscopic traffic flow theory: A survey

Vehicle headway distribution models are widely used in traffic engineering fields, since they reflect the fundamental uncertainty in drivers' car-following maneuvers and meanwhile provide a concise way to describe the stochastic feature of traffic flows. This paper presents a systematic review of vehicle headway distribution studies in the last few decades. Since it is impossible to enumerate the merits and drawbacks of all of existing distribution models, we emphasize four advances of headway distribution modeling in this paper. First, we highlight the chronicle of key assumptions on the existing distribution models and explain why this evolution occurs. Second, we show that departure headways measured for interrupted flows on urban streets and headways measured for uninterrupted flows on freeways have common features and can be simulated by a unified microscopic car-following model. The interesting finding helps gather two kinds of headway distribution models under one umbrella. Third, we review different approaches that aim to link microscopic car-following models and mesoscopic vehicle headway distribution models. Fourth, we show that both the point scattering on the density-flow plot and the shape of traffic flow breakdown curve implicitly depend on the vehicular headway distribution. These findings reveal pervasive connections between macroscopic traffic flow models and mesoscopic headway distribution. All these new insights bring new vigor into vehicle headway studies and open research frontiers in this field.     

A probabilistic stationary speed–density relation based on Newell’s simplified car-following model

Probabilistic models describing macroscopic traffic flow have proven useful both in practice and in theory. In theoretical investigations of wide-scatter in flow–density data, the statistical features of flow density relations have played a central role. In real-time estimation and traffic forecasting applications, probabilistic extensions of macroscopic relations are widely used. However, how to obtain such relations, in a manner that results in physically reasonable behavior has not been addressed. This paper presents the derivation of probabilistic macroscopic traffic flow relations from Newell’s simplified car-following model. The probabilistic nature of the model allows for investigating the impact of driver heterogeneity on macroscopic relations of traffic flow. The physical features of the model are verified analytically and shown to produce behavior which is consistent with well-established traffic flow principles. An empirical investigation is carried out using trajectory data from the New Generation SIMulation (NGSIM) program and the model’s ability to reproduce real-world traffic data is validated.     

Stochastic cell transmission model (SCTM): A stochastic dynamic traffic model for traffic state surveillance and assignment

The paper proposes a first-order macroscopic stochastic dynamic traffic model, namely the stochastic cell transmission model (SCTM), to model traffic flow density on freeway segments with stochastic demand and supply. The SCTM consists of five operational modes corresponding to different congestion levels of the freeway segment. Each mode is formulated as a discrete time bilinear stochastic system. A set of probabilistic conditions is proposed to characterize the probability of occurrence of each mode. The overall effect of the five modes is estimated by the joint traffic density which is derived from the theory of finite mixture distribution. The SCTM captures not only the mean and standard deviation (SD) of density of the traffic flow, but also the propagation of SD over time and space. The SCTM is tested with a hypothetical freeway corridor simulation and an empirical study. The simulation results are compared against the means and SDs of traffic densities obtained from the Monte Carlo Simulation (MCS) of the modified cell transmission model (MCTM). An approximately two-miles freeway segment of Interstate 210 West (I-210W) in Los Ageles, Southern California, is chosen for the empirical study. Traffic data is obtained from the Performance Measurement System (PeMS). The stochastic parameters of the SCTM are calibrated against the flow-density empirical data of I-210W. Both the SCTM and the MCS of the MCTM are tested. A discussion of the computational efficiency and the accuracy issues of the two methods is provided based on the empirical results. Both the numerical simulation results and the empirical results confirm that the SCTM is capable of accurately estimating the means and SDs of the freeway densities as compared to the MCS.     

Collecting ambient vehicle trajectories from an instrumented probe vehicle: High quality data for microscopic traffic flow studies

This paper presents the methodology and results from a study to extract empirical microscopic vehicular interactions from a probe vehicle instrumented with sensors to monitor the ambient vehicles as it traverses a 28 mi long freeway corridor. The contributions of this paper are two fold: first, the general method and approach to seek a cost-effective balance between automation and manual data reduction that transcends the specific application. Second, the resulting empirical data set is intended to help advance traffic flow theory in general and car following models in particular. Generally the collection of empirical microscopic vehicle interaction data is either too computationally intensive or labor intensive. Historically automatic data extraction does not provide the precision necessary to advance traffic flow theory, while the labor demands of manual data extraction have limited past efforts to small scales. Key to the present study is striking the right balance between automatic and manual processing. Recognizing that any empirical microscopic data for traffic flow theory has to be manually validated anyway, the present study uses a “pretty good” automated processing algorithm followed by detailed manual cleanup using an efficient user interface to rapidly process the data. The study spans roughly two hours of data collected on a freeway during the afternoon peak of a typical weekday that includes recurring congestion. The corresponding data are being made available to the research community to help advance traffic flow theory in general and car following models in particular.     

Distribution models for start-up lost time and effective departure flow rate

Due to its importance, lots of investigations had been carried out in the last four decades to study the relationship between phase duration and vehicle departure amount. In this paper, we aim to build appropriate distribution models for start-up lost time and effective departure flow rate, by considering their relations with the frequently mentioned departure headway distributions. The motivation behind is that distribution models could provide richer information than the conventional mean value models and thus better serve the need of traffic simulation and signal timing planning. To reach this goal, we first check empirical data collected in Beijing, China. Tests show that the departure headways at each position in a discharging queue are very weakly dependent or almost independent. Based on this new finding, two distribution models are proposed for start-up lost time and effective flow rate, respectively. We also examine the dependences of departure headways that are generated by three popular traffic simulation software: VISSIM, PARAMICS and TransModeler. Results suggest that in VISSIM, the departure headways at different positions are almost deterministically dependent and may not be in accordance with empirical observations. Finally, we discuss how the dependence of departure headways may influence traffic simulation and signal timing planning.     

Logistic modeling of the equilibrium speed-density relationship

The fundamental diagram, as the graphical representation of the relationships among traffic flow, speed, and density, has been the foundation of traffic flow theory and transportation engineering. Seventy-five years after the seminal Greenshields model, a variety of models have been proposed to mathematically represent the speed-density relationship which underlies the fundamental diagram. Observed in these models was a clear path toward two competing goals: mathematical elegance and empirical accuracy. As the latest development of such a pursuit, this paper presents a family of speed-density models with varying numbers of parameters. All of these models perform satisfactorily and have physically meaningful parameters. In addition, speed variation with traffic density is accounted for; this enables statistical approaches to traffic flow analysis. The results of this paper not only improve our understanding of traffic flow but also provide a sound basis for transportation engineering studies.     

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.     

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.     

Microscopic Analysis of Cellular Automata Based Traffic Flow Models and an Improved Model

Abstract

A large number of cellular automata (CA) based traffic flow models have been proposed in the recent past. Often, the speed‐flow‐density relations obtained from these models are only presented and their apparent similarities with observed relations are cited as reasons for considering them as valid models of traffic flow. Hardly any attempt has been made to comprehensively study the microscopic properties (like time‐headway distribution, acceleration noise, stability in car‐following situations, etc.) of the simulated streams. This article proposes a framework for such evaluations. The article also presents the results from the evaluation of six existing CA‐based models. The results show that none of them satisfy all the properties. A new model proposed by the authors to overcome these shortcomings is briefly presented, and results supporting the improved performance of the proposed model are also provided.     

Modelling a signal controlled traffic stream using cellular automata

Cellular automata models have formed the theory for the development of several transportation models to simulate various types of elements such as vehicles, pedestrians or even railway traffic. Furthermore, they have been applied to simulate several scenarios from very simple (freeway traffic) to rather complicated ones (lane reduction and signal optimisation). However, the properties of the model when used to simulate a signal controlled traffic stream have not been dealt with in great detail. This paper discusses several issues that arise while using the model for the simulation of traffic at signalised intersections. It also investigates the relationships between the randomisation parameter of the model, the model dynamics and the estimated saturation flow. For the deterministic version of the model, the formulas describing traffic quantities at the intersection are derived and are dependent on the desired speed – a parameter of the model. For the stochastic version, one can adopt several different approaches for the application of the randomisation rule, depending on the simulation needs.     

Heterogeneous platoon flow dispersion model based on truncated mixed simplified phase‐type distribution of travel speed

Existing research on platoon dispersion models either describe homogeneous traffic flow feature, or are in lack of analytical solutions. By analyzing the field data, the truncated mixed simplified phase‐type distribution is proved to be capable of capturing the characteristics of heterogeneous traffic flow with an excellent fitting result. In light of this, we derive a generic heterogeneous platoon dispersion model with truncated mixed simplified phase‐type of speed in the forms of integrable functions. Numerical case studies are conducted to compare the performance of the proposed model and the conventional models (i.e., the Robertson model and truncated mixed Gaussian model). The results show that the proposed model not only better captures the platoon dispersion laws of heterogeneous traffic flow, but also presents higher computational efficiency, which provides practical implications on traffic signal control. Copyright © 2017 John Wiley & Sons, Ltd.     

A review on travel behaviour modelling in dynamic traffic simulation models for evacuations

Dynamic traffic simulation models are frequently used to support decisions when planning an evacuation. This contribution reviews the different (mathematical) model formulations underlying these traffic simulation models used in evacuation studies and the behavioural assumptions that are made. The appropriateness of these behavioural assumptions is elaborated on in light of the current consensus on evacuation travel behaviour, based on the view from the social sciences as well as empirical studies on evacuation behaviour. The focus lies on how travellers’ decisions are predicted through simulation regarding the choice to evacuate, departure time choice, destination choice, and route choice. For the evacuation participation and departure time choice we argue in favour of the simultaneous approach to dynamic evacuation demand prediction using the repeated binary logit model. For the destination choice we show how further research is needed to generalize the current preliminary findings on the location-type specific destination choice models. For the evacuation route choice we argue in favour of hybrid route choice models that enable both following instructed routes and en-route switches. Within each of these discussions, we point at current limitations and make corresponding suggestions on promising future research directions.     

Definition of a merging assistant strategy using intelligent vehicles

In the area of active traffic management, new technologies provide opportunities to improve the use of current infrastructure. Vehicles equipped with in-car communication systems are capable of exchanging messages with the infrastructure and other vehicles. This new capability offers many opportunities for traffic management. This paper presents a novel merging assistant strategy that exploits the communication capabilities of intelligent vehicles. The proposed control requires the cooperation of equipped vehicles on the main carriageway in order to create merging gaps for on-ramp vehicles released by a traffic light. The aim is to reduce disruptions to the traffic flow created by the merging vehicles. This paper focuses on the analytical formulation of the control algorithm, and the traffic flow theories used to define the strategy. The dynamics of the gap formation derived from theoretical considerations are validated using a microscopic simulation. The validation indicates that the control strategy mostly developed from macroscopic theory well approximates microscopic traffic behaviour. The results present encouraging capabilities of the system. The size and frequency of the gaps created on the main carriageway, and the space and time required for their creation are compatible with a real deployment of the system. Finally, we summarise the results of a previous study showing that the proposed merging strategy reduces the occurrence of congestion and the number of late-merging vehicles. This innovative control strategy shows the potential of using intelligent vehicles for facilitating the merging manoeuvre through use of emerging communications technologies.     

Hybrid artificial neural network and locally weighted regression models for lane-based short-term urban traffic flow forecasting

ABSTRACT

In recent years, there has been considerable research interest in short-term traffic flow forecasting. However, forecasting models offering a high accuracy at a fine temporal resolution (e.g. 1 or 5?min) and lane level are still rare. In this study, a combination of genetic algorithm, neural network and locally weighted regression is used to achieve optimal prediction under various input and traffic settings. The genetically optimized artificial neural network (GA-ANN) and locally weighted regression (GA-LWR) models are developed and tested, with the former forecasting traffic flow every 5-min within a 30-min period and the latter for forecasting traffic flow of a particular 5-min period of each for four lanes of an urban arterial road in Beijing, China. In particular, for morning peak and off-peak traffic flow prediction, the GA-ANN 5-min traffic flow model results in average errors of 3–5% and most 95th percentile errors of 7–14% for each of the four lanes; for the peak and off-peak time traffic flow predictions, the GA-LWR 5-min traffic flow model results in average errors of 2–4% and most 95th percentile errors are lower than 10% for each of the four lanes. When compared to previous models that usually offer average errors greater than 6–15%, such empirical findings should be of interest to and instrumental for transportation authorities to incorporate in their city- or state-wide Advanced Traveller Information Systems (ATIS).