Traffic Flow Model Research Articles

The vanishing pressure limits of Riemann solutions for the Aw-Rascle hydrodynamic traffic flow model with the logarithmic equation of state

Two kinds of Riemann solutions for the Aw-Rascle hydrodynamic traffic flow model with the logarithmic equation of state are explicitly obtained by using the combination between 1-rarefaction or 1-shock wave along with 2-contact discontinuity. The formation of vacuum state and delta shock wave is identified and analyzed when the perturbation parameter in the pressure term drops to zero, where the intrinsic cavitation and concentration phenomena are surveyed and explored concretely. Additionally, several numerical results displaying the formation process of vacuum state and delta shock wave are also presented by taking three different perturbation parameters for comparison.

Cooperative control of dynamic CAV dedicated lanes and vehicle active lane changing in expressway bottleneck areas

Bottleneck areas on expressways plague the operational efficiency of entire road systems. In mixed traffic flow environments consisting of connected and autonomous vehicles (CAVs) and connected human-driven vehicles (CHVs), it is believed that road capacity can be improved to relieve traffic congestion in bottleneck areas by setting CAV dedicated lanes (CDLs) on expressways. Existing static CDL setup methods provide fixed exclusive right-of-way for CAVs but cannot accommodate dynamic changes in traffic demand. To address this issue, utilizing lane control signals and CAV active lane-changing technology, a cooperative method involving dynamic CAV dedicated lane control (CDLC) and active lane-changing control (LCC) in the bottleneck areas of expressways is proposed in this paper. First, a fundamental diagram of traffic flow with CDLs is established based on the microscopic car-following model of mixed traffic flow, which can be used to determine the conditional thresholds for setting the CDLs of multilane expressways. Second, an expressway traffic model with CDLs is established by improving the lane-level cell transmission model. Finally, cooperative control of dynamic CAV dedicated lanes and active lane changing (CDLLC) is proposed based on the model predictive control (MPC) framework for solving the congestion problem at expressway bottlenecks in a mixed driving environment. The simulation results show that the proposed CDLLC strategy can effectively reduce the total vehicle travel time and decrease the risk of congestion propagation at expressway bottlenecks when compared to the LCC-only strategy.

Urban Traffic Flow Prediction Based on Bayesian Deep Learning Considering Optimal Aggregation Time Interval

Predicting short-term urban traffic flow is a fundamental and cost-effective strategy in traffic signal control systems. However, due to the interrupted, periodic, and stochastic characteristics of urban traffic flow influenced by signal control, there are still unresolved issues related to the selection of the optimal aggregation time interval and the quantifiable uncertainties in prediction. To tackle these challenges, this research introduces a method for predicting urban interrupted traffic flow, which is based on Bayesian deep learning and considers the optimal aggregation time interval. Specifically, this method utilizes the cross-validation mean square error (CVMSE) method to obtain the optimal aggregation time interval and to establish the relationship between the optimal aggregation time interval and the signal cycle. A Bayesian LSTM-CNN prediction model, which extends the LSTM-CNN model under the Bayesian framework to a probabilistic model to better capture the stochasticity and variation in the data, is proposed. Experimental results derived from real-world data demonstrate gathering traffic flow data based on the optimal aggregation time interval significantly enhances the prediction accuracy of the urban interrupted traffic flow model. The optimal aggregation time interval for urban interrupted traffic flow data corresponds to a multiple of the traffic signal control cycle. Comparative experiments indicate that the Bayesian LSTM-CNN prediction model outperforms the state-of-the-art prediction models.

Modeling of mixed traffic flow and safety evaluation in the upstream area of the bus station

The mixed traffic flow of various types of vehicles at bus station is severe, which has an impact on the overall safety of traffic. Especially upstream of bus station, since buses need to change lane in order to stop at the bus station, it interacts with social vehicles. Thus, in this paper, a two-lane CA model considering the mixed traffic flow composing of buses, cars and nonmotorized vehicles upstream of a bus station is proposed. Through several field surveys, the movement characteristics of the vehicles are obtained and the basic parameters are calibrated. For comparison, five cases about bus stops are studied. Several indexes (i.e. parallel time, blind area dwell time, time to collision, potential collision energy) are analyzed to assess the safety upstream of the bus station. Four safety indices are used to examine, based on simulation findings, the impact of bus station on vehicle safety and the significance of establishing exclusive nonmotorized vehicle lanes and exclusive bus lanes. Finally, several safety-related recommendations for drivers and management are provided. These findings offer a theoretical basis for driver management and optimal design of bus stations.

Multicriteria Assessment Method for Network Structure Congestion Based on Traffic Data Using Advanced Computer Vision

Overloading of network structures is a problem that we encounter every day in many areas of life. The most associative structure is the transport graph. In many megacities around the world, the so-called intelligent transport system (ITS) is successfully operating, allowing real-time monitoring and making changes to traffic management while choosing the most effective solutions. Thanks to the emergence of more powerful computing resources, it has become possible to build more complex and realistic mathematical models of traffic flows, which take into account the interactions of drivers with road signs, markings, and traffic lights, as well as with each other. Simulations using high-performance systems can cover road networks at the scale of an entire city or even a country. It is important to note that the tool being developed is applicable to most network structures described by such mathematical apparatuses as graph theory and the applied theory of network planning and management that are widely used for representing the processes of organizing production and enterprise management. The result of this work is a developed model that implements methods for modeling the behavior of traffic flows based on physical modeling and machine learning algorithms. Moreover, a computer vision system is proposed for analyzing traffic on the roads, which, based on vision transformer technologies, provides high accuracy in detecting cars, and using optical flow, allows for significantly faster processing. The accuracy is above 90% with a processing speed of more than ten frames per second on a single video card.

Phase transition in a new heterogeneous macro continuum model of traffic flow under rain and snow weather environment

Rain and snow will affect the safe speed and safe distance between vehicles. Therefore, a new macroscopic continuum traffic model for mixed heterogeneous vehicles including adaptive cruise control (ACC) and conventional vehicles is provided by taking into account the safe speed and safe distance under rain and snow weather. Moreover, the stability conditions and KdV-Burgers equation related to rain and snow weather are inferred for mixed heterogeneous vehicles. Numerical simulation results show that traffic state is smoothed owing to reducing the current safe speed of vehicles and increasing the safe distance between vehicles under the rainy and snowy weather when the penetration rate of ACC vehicles is constant. Additionally, the traffic system runs more smoothly with the increase of ACC vehicles’ permeability, which means that the ACC vehicles are worth developing.

Fourier neural operator for learning solutions to macroscopic traffic flow models: Application to the forward and inverse problems

Deep learning methods are emerging as popular computational tools for solving forward and inverse problems in traffic flow. In this paper, we study a neural operator framework for learning solutions to first-order macroscopic traffic flow models with applications in estimating traffic densities for urban arterials. In this framework, an operator is trained to map heterogeneous and sparse traffic input data to the complete macroscopic traffic density in a supervised learning setting. We chose a physics-informed Fourier neural operator (π-FNO) as the operator, where an additional physics loss based on a discrete conservation law regularizes the problem during training to improve the shock predictions. We also propose to use training data generated from random piecewise constant input data to systematically capture the shock and rarefaction solutions of certain macroscopic traffic flow models. From experiments using the LWR traffic flow model, we found superior accuracy in predicting the density dynamics of a ring-road network and urban signalized road. We also found that the operator can be trained using simple traffic density dynamics, e.g., consisting of 2−3 vehicle queues and 1−2 traffic signal cycles, and it can predict density dynamics for heterogeneous vehicle queue distributions and multiple traffic signal cycles (≥2) with an acceptable error. The extrapolation error grew sub-linearly with input complexity for a proper choice of the model architecture and training data. Adding a physics regularizer aided in learning long-term traffic density dynamics, especially for problems with periodic boundary data.

Effect of speed humps on instantaneous traffic emissions in a microscopic model with limited deceleration capacity

As a common transportation facility, speed humps can control the speed of vehicles on special road sections to reduce traffic risks. At the same time, they also cause instantaneous traffic emissions. Based on the classic instantaneous traffic emission model and the limited deceleration capacity microscopic traffic flow model with slow-to-start rules, this paper has investigated the impact of speed humps on traffic flow and the instantaneous emissions of vehicle pollutants in a single lane situation. The numerical simulation results have shown that speed humps have significant effects on traffic flow and traffic emissions. In a free-flow region, the increase of speed humps leads to the continuous rise of CO2, NO X and PM emissions. Within some density ranges, one finds that these pollutant emissions can evolve into some higher values under some random seeds. Under other random seeds, they can evolve into some lower values. In a wide moving jam region, the emission values of these pollutants sometimes appear as continuous or intermittent phenomenon. Compared to the refined NaSch model, the present model has lower instantaneous emissions such as CO2, NO X and PM and higher volatile organic components (VOC) emissions. Compared to the limited deceleration capacity model without slow-to-start rules, the present model also has lower instantaneous emissions such as CO2, NO X and PM and higher VOC emissions in a wide moving jam region. These results can also be confirmed or explained by the statistical values of vehicle velocity and acceleration.

Bifurcation analysis of macroscopic traffic flow models based on driver behavior

This paper proposes a novel nonuniform continuous traffic flow model, which takes into account the differences in drivers’ expected headway and further improves the model by incorporating the influences of relative distance and relative velocity of vehicles through linear weighting. Additionally, the model also considers the dynamic response time of drivers for further refinement. With this model, bifurcation theory can also be applied in the stability analysis of traffic systems to study the stability mutation behavior of traffic systems at bifurcation points. Through linear and nonlinear analysis methods, the stability conditions of the model and the KdV–Burgers equation can be derived, the type of equilibrium point of the model can be judged, the conditions for the existence of Hopf bifurcations and the type of bifurcations can be proved, and the traffic flow problem can be transformed into the stability analysis problem of the system. Through numerical simulations in both high-density and low-density scenarios, it is shown that the model can well describe the actual traffic phenomena and can describe the stability abrupt behavior of the traffic system at Hopf bifurcation points and saddle-node bifurcation points through density-time and phase plane diagrams.

A Hierarchy of Kinetic Discrete-Velocity Models for Traffic Flow Derived from a Nonlocal Prigogine–Herman Model

A Hierarchy of Kinetic Discrete-Velocity Models for Traffic Flow Derived from a Nonlocal Prigogine–Herman Model

Modeling the mixed traffic capacity of minor roads at a priority intersection

As technology for autonomous driving continues to advance, a mixed traffic flow comprising of autonomous vehicles (AVs) and regular vehicles (RVs) is gradually taking shape. Priority intersection is an important type of intersection that connects road networks for traffic efficiency. Essentially, vehicles on major road are given the right of way at these priority intersections, while vehicles on minor road must wait for a safe gap to proceed. Thus, the operation of minor road traffic is a crucial factor that can limit the efficiency of priority intersections. This effect becomes even more complex and diverse in mixed traffic flow consisting of both AVs and RVs. This paper proposes a capacity model for the mixed AVs-RVs traffic flow on minor road at priority intersections. To begin with, we mathematically derive control strategies for homogeneous platoons of AVs or RVs as well as heterogeneous platoons of both AVs and RVs with a specific number of AVs on minor road at priority intersection. Following the framework of the control strategies above, the maximum capacity of mixed traffic on minor road can be optimized under each penetration rate of AVs. Furthermore, we take into account headway distribution on major road in the aforementioned control strategies to complete the capacity modeling approach. We then conduct numerical experiments to evaluate the effectiveness of the proposed capacity model in the mixed traffic. Results show that the proposed model can be applied to quantitatively calculate the mixed traffic capacity at priority intersections, and several important factors have significant impacts on the capacity, such as penetration rate of AVs, traffic volume on major road, and headways of both AVs and RVs on minor road. As the penetration rate of AVs increases, it has a positive impact on the capacity of mixed flow on minor roads. However, this effect is offset by negative impacts of traffic volume on major road and the headway of both AVs and RVs. More specifically, when comparing pure AVs traffic to pure RVs traffic on minor roads, we observe a considerable improvement in capacity ranging from 115.82% to 120.89% under various conditions.

Dynamic capacity drop propagation in incident-affected networks: Traffic state modeling with SIS-CTM

Mitigating the impact of traffic incidents on incident-affected networks is a critical requirement for traffic incident management. To this end, previous studies have focused on the capacity drop (CD) phenomenon at lane-drop bottlenecks. However, investigations of CD and propagation of CD in a network-level traffic flow modeling context have been limited, especially considering their dynamic interactions and temporal characteristics. This study presents a network-level traffic flow model for an incident-affected network to describe the time-varying characteristics of traffic flow on links. The cell transmission model (CTM) is adopted as the fundamental dynamic model. However, previous research on CTM and its stochastic characteristics has focused on unraveling the inherent stochasticity of the fundamental diagram. In this study, a new approach to investigate the stochastic nature of CD and congestion is used; the susceptible-infectious-susceptible (SIS) model is introduced and the SIS-CTM is proposed. This provides a probabilistic description of the link state. The proposed model can differentiate states with potential congestion and describe the unstable transitions as links switch between congested and uncongested conditions. It also can describe the influence of CD, congestion spread, and the propagation of CD with congestion spread. Numerical simulations in the Nguyen–Dupuis and Ziliaskopoulos networks case studies demonstrate the superiority of SIS-CTM. SIS-CTM can reflect the stochasticity of congestion and CD in time and space, while CTM cannot. Further, CTM underestimates the impact of congestion and CD, which is demonstrated as SIS-CTM spends 9.26% more time dissipating traffic demand in the network.

Microscopic Derivation of a Traffic Flow Model with a Bifurcation

Microscopic Derivation of a Traffic Flow Model with a Bifurcation

Modeling and analysis of heterogeneous traffic flow considering dynamic information flow topology and driving behavioral characteristics

Connected vehicles (CVs) have demonstrated significant potential for addressing traffic issues. This paper presents a mathematical framework for stochastic heterogeneous traffic flow, integrating regular vehicles (RVs) and CVs, considering stochasticity, driver’s dynamic time headway (DTH) characteristics, and the information flow topology (IFT) of CVs. We develop a novel car-following model (CFM) for RVs, accounting for both driver’s stochasticity and DTH characteristics. Furthermore, we propose a dynamic model for CVs by integrating connected assisted driving strategies (CADS) into the RVs’ model, which includes a dynamic information flow topology (DIFT) based on the time headway (TH) between vehicles within the communication range. We derive second-order exponential stability conditions for both RVs and CVs by employing the Lyapunov stochastic stability theory. We investigate the impact of driver stochasticity, DTH characteristics, and CADS on heterogeneous traffic flow characteristics through extensive numerical experiments. Model calibration results indicate that, in comparison to the state-of-the-art model, the proposed model exhibits superior prediction accuracy, achieving a 9.09% improvement at the group-driver level and a 10.47% improvement at the individual-driver level. Theoretical and numerical experimental results demonstrate that CVs with the proposed assisted driving strategy effectively mitigate traffic oscillations, and traffic flow stability improves as the CV penetration rate increases. Moreover, CVs can efficiently suppress stochasticity in traffic flow, with the strength of traffic fluctuations decreasing as the CV penetration rate grows. Different CV spatial distributions result in different propagation strengths of disturbances in traffic flow, adhering to a specific dual Gaussian distribution. Under various conditions, the average decline rates of speed fluctuations and energy consumption for traffic with the increasing CV penetration rate are 20%–50% and 10%–30%, respectively.

Comparative Analysis of Deterministic Fundamental Diagrams Representative of Continuous and Interrupted Traffic Flow on Selected Regional Road in Croatia

Since the inception of the traffic flow theory, numerous traffic flow models have been formulated by scholars in an effort to more accurately delineate the relationships between various traffic flow parameters. However, only a limited number of studies have explored the distinctions between fundamental traffic diagrams, which characterize continuous and interrupted traffic flow conditions. Addressing this research lacuna, we compared twelve “speed–density” and “flow–density” models fitted to empirical data collected under continuous and interrupted traffic flow conditions on a selected regional road in Croatia. The empirical data used to develop these models were extracted from video footage captured by an unmanned aerial vehicle on two representative road segments during characteristic peak and off-peak hours on workdays. Our analysis reveals that, depending on the selected traffic flow model and prevailing traffic flow conditions, the practical capacity of the observed regional road is estimated to be in the range from 799 to 2333 veh/h/lane. It was also discovered that the considered models reach practical capacity at a significantly different density under continuous and interrupted traffic stream conditions, i.e., between 37 and 129 veh/km/lane. The conducted t-tests underscore the need to employ distinct “speed–density” and “flow–density” regression functions for modeling continuous and interrupted traffic stream conditions.

Revealing the impact of stochastic driving characteristics on car-following behavior with locally collected vehicle trajectory data

This study investigates the impact of Chinese drivers’ stochastic behaviour on local car-following situations using localized trajectory data. An extended stochastic car-following model (S-IDM) is established, which considers both internal and external stochasticity. External stochasticity is characterized by different driver types, while internal stochasticity is characterized by the standard deviation of acceleration under different headway and velocity differences for the same driver. The proposed model shows advantages in terms of single-vehicle simulation accuracy and traffic shock reproduction ability, compared to traditional and existing car-following models. The model can also be extended to the evolution analysis of mixed traffic flow models, where reducing the stochasticity of human-driven vehicles is critical for optimizing and controlling traffic flow.

Coordinated Planning of EV Charging Stations and Mobile Energy Storage Vehicles in Highways With Traffic Flow Modeling

Coordinated Planning of EV Charging Stations and Mobile Energy Storage Vehicles in Highways With Traffic Flow Modeling

POLARIS-LC: A Multi-Class traffic Flow Model in Lagrangian Coordinates for Large-Scale Simulation

Agent-based modeling has become increasingly prevalent in transportation systems simulation as the scenarios around new technologies and policies become increasingly complex. This increased complexity, in terms of traveler behavior, traffic flow, modal operations, system management, and so on, requires increasingly sensitive and detailed representation of the core components of the simulation, especially as it relates to traffic flow. Many future mobility solutions rely on connectivity, communication, advanced sensing, and detailed information flows, while the simulation also needs to remain computationally tractable. In this paper, we propose a new Lagrangian Coordinate within the POLARIS Agent-Based-Modeling Framework (LC-POLARIS) of traffic flow, which combines computational efficiency while adding microscopic features. This model allows multi-class traffic flow by setting different speed-spacing relationships. In this modeling, automated vehicles have lower reaction time, while light-duty trucks have lower free-flow speed and higher jam spacing. The model captures the reduction in capacity and higher queue spillback because of higher jam spacing of trucks. Also, the model yields higher capacity for both passenger and light duty automated vehicles on expressways. The LC-ABM traffic flow model is validated in Bloomington, IL, USA, in a scenario with different rates of four vehicle types.

Road Network-Guided Fine-Grained Urban Traffic Flow Inference.

Accurate inference of fine-grained traffic flow from coarse-grained one is an emerging yet crucial problem, which can help greatly reduce the number of the required traffic monitoring sensors for cost savings. In this work, we note that traffic flow has a high correlation with road network, which was either completely ignored or simply treated as an external factor in previous works. To facilitate this problem, we propose a novel road-aware traffic flow magnifier (RATFM) that explicitly exploits the prior knowledge of road networks to fully learn the road-aware spatial distribution of fine-grained traffic flow. Specifically, a multidirectional 1-D convolutional layer is first introduced to extract the semantic feature of the road network. Subsequently, we incorporate the road network feature and coarse-grained flow feature to regularize the short-range spatial distribution modeling of road-relative traffic flow. Furthermore, we take the road network feature as a query to capture the long-range spatial distribution of traffic flow with a transformer architecture. Benefiting from the road-aware inference mechanism, our method can generate high-quality fine-grained traffic flow maps. Extensive experiments on three real-world datasets show that the proposed RATFM outperforms state-of-the-art models under various scenarios. Our code and datasets are released at https://github.com/luimoli/RATFM.

A non-local traffic flow model for 1-to-1 junctions with buffer

<abstract><p>In this paper, we introduce a non-local PDE-ODE traffic model devoted to the description of a 1-to-1 junction with buffer. We present an existence result in the free flow case as well as a numerical method to approximate weak solutions in the general case. In addition, we show a maximum principle, which is uniform in the non-local interaction range. Further, we exploit the limit models as the support of the kernel tends to zero and to infinity. We compare them with other already existing models for traffic and production flow and presented numerical examples.</p></abstract>