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Generic gas-kinetic traffic systems modeling with applications to vehicular traffic flow
Abstract
This article presents a generic continuum modeling approach for the description of flow operations for a general class of traffic systems. That is, the traffic flow model presented in this paper models traffic flows independently of the type of traffic (vehicular traffic on motorways or rural roads, pedestrian flows). Key to the approach is the introduction of the so-called generalized phase-space density (g-PSD). This density concept is a generalization of traffic density with respect to both discrete attibutes, such as user-class, roadway lane, and destination, and continuous attributes, such as velocity, and desired velocity. In the approach, we distinguish continuum and non-continuum processes. The continuum processes reflect smooth changes in the g-PSD, while the non-continuum processes describe non-smooth changes in the g-PSD. These non-continuum processes are either caused by events experienced by a traffic entity, or by the condition of a traffic entity. To show the potential of this new and powerful modeling framework, a simple model specification example for platoon-based description of traffic flow is presented.
... An overview of the different modelling methodologies is given in Refs. [3,4]. These modelling methodologies include microscopic, macroscopic and mesoscopic approaches. ...
... These modelling methodologies include microscopic, macroscopic and mesoscopic approaches. Microscopic traffic models [3][4][5][6] describe the motion of each individual vehicle with a high level of detail. Hao et al. [7,8] recently proposed a model predictive control (MPC) termed urban cell transmission model (UCTM) for optimal switching of traffic lights at intersections based on the predicted traffic. ...
... In macroscopic models [9,10], traffic state is represented by aggregating behaviour of the traffic, usually in terms of the average speed and the average density over a given period of time. Mesoscopic models [3] employ some features of microscopic and macroscopic approaches by utilising varying levels/degrees of detail to model traffic behaviour. This is achieved by modelling some locations with aggregated measurements as in macroscopic and the remaining locations are modelled down to the details of individual vehicles as is done in the case of microscopic. ...
Intelligent transportation systems require the knowledge of current and forecasted traffic states for effective control of road networks. The actual traffic state has to be estimated as the existing sensors does not capture the needed state. Sensor measurements often contain missing or incomplete data as a result of communication issues, faulty sensors or cost leading to incomplete monitoring of the entire road network. This missing data poses challenges to traffic estimation approaches. In this work, a robust spatio-temporal traffic imputation approach capable of withstanding high missing data rate is presented. A particle based approach with Kriging interpolation is proposed. The performance of the particle based Kriging interpolation for different missing data ratios was investigated for a large road network comprising 1000 segments. Results indicate that the effect of missing data in a large road network can be mitigated by the Kriging interpolation within the particle filter framework.
... Most traffic estimation approaches are model based [1], while the new trend is to develop data driven approaches [2], [3]. Traffic modelling methods are used to understand the evolution of traffic and estimate the traffic state [4]- [7]. ...
... An overview of different models is given in [7]- [9]. These include microscopic, macroscopic and mesoscopic models. ...
... These include microscopic, macroscopic and mesoscopic models. Microscopic traffic models [7], [9]- [11], describe the motion of each individual vehicle with a high level of detail. Macroscopic models [12], [13] represent the aggregated behaviour of the traffic, usually in terms of the average speed and the average density. ...
Traffic prediction approaches face challenges when presented with sparse or missing data. This can be caused by numerous factors such as: i) sensors not being operational; ii) communication issues; iii) cost prohibiting full monitoring of a road network. This present work adds to existing body of knowledge by proposing a particle based framework for dealing with these challenges. An expression of the likelihood function is derived for the case when the missing value is calculated based on Kriging interpolation. With the Kriging interpolation, the missing values of the measurements are predicted, which are subsequently used in the computation of likelihood terms in the particle filter algorithm. The results show 23% to 36.34% improvement in RMSE values for the synthetic data used.
... Some years latter the Paveri-Fontana kinetic equation was proposed in an extended phase space, where it is considered the drivers desired speed as an independent variable [15]. The ideas behind such kinetic equations were taken to develop macroscopic models as the proper averages over the distribution function [16,17,18,19,20,21,22]. Kinetic equations in traffic flow, as in any other subject, have mathematical characteristics which make them somewhat complicated. ...
... we should notice that equations (18) do not correspond to conservation equations, the source of the density of a-class vehicles is the negative of the b-class vehicles. It is only the total density ρ a +ρ b the conserved quantity, which means that the total number of vehicles a + b remains constant, in the cases with no entrance or exit ramps. ...
... respectively for each vehicle class. However, balance equations (18)(19) constitute a non closed set of equations until the traffic pressure is specified in terms of the relevant variables. If we chose to calculate the traffic pressure and speed variance in (20,21) using the distribution function in (10), the result is P ...
The over-acceleration and adaptation effects in a two vehicle-class mixture of aggressive drivers is studied. A first order model for each vehicle-class is constructed through a kinetic model equation and an iterative procedure. The constructed model is numerically solved with different parameters and under several initial conditions. Numerical results show the onset of the Kerner's phase and suggest that besides the drivers' aggressivity, the most relevant aspect in the adaptation process is the existence of a more numerous vehicle-class.
... The traffic flow models developed so far, whether in microscopic or macroscopic approaches, have been concerned with the synchronizing state because controlling this metastable state enhances the efficiency of the traffic flow field. There are several types of traffic models that have been developed following microscopic [5][6][7][8][9][10][11][12][13][14], macroscopic [15][16][17][18][19][20][21][22][23], lattice hydrodynamic [24][25][26][27][28][29][30], gas kinetic [31][32][33][34], and cellular automated [35][36][37][38][39][40][41][42] approaches. The models [43][44][45], in which the eye-tracking device's effect was introduced to investigate the driver's attention to study an actual traffic flow, revealed a new dimension of traffic flow modeling. ...
In this study, a traffic flow model, the so-called Taillight Adapting (TA) traffic model, is developed considering the driver's activities impact following the taillight effect of the preceding vehicle, which is switched on and off based on the vehicle's accelerations and decelerations. To quantify a driver's sensitivity to the velocity gap, we introduced the concept of the new driver's sensitivity function, which has twofold formulations. The first formulation follows the HDDS model (Hossain and Tanimoto in Sci Rep 12:1–4, 2022), which presumes sensitivity depends on a headway distance. The second formulation presumes that the sensitivity depends on a velocity gap, which the taillight might inform of a preceding vehicle. We have calibrated the neutralizing proficiency of a traffic flow field for the HDDS and proposed the TA model by utilizing the linear stability theory. Finally, a series of numerical simulations of the improved TA model and conventional FVD model have been carried out to investigate how the traffic flow field for the TA model behaves differently from the conventional FVD model.
... The traffic flow models developed so far, whether in microscopic or macroscopic approaches, have been concerned with the synchronizing state because controlling this metastable state enhances the efficiency of the traffic flow field. There are several types of traffic models that have been developed following microscopic 2-11 , macroscopic 12-20 , lattice hydrodynamic [21][22][23][24][25][26][27] , gas kinetic [28][29][30][31] , and cellular automated [32][33][34][35][36][37][38][39] approaches. The models [40][41][42] , in which the eye-tracking device's effect has been introduced for investigating driver's attention to study an actual traffic flow, revealed a new dimension of traffic flow modeling. ...
In this study, a traffic flow model, the so-called Taillight Adapting traffic model, is developed considering the driver's activities impact following the taillight effect of the preceding vehicle, which is switched on and off based on the vehicle's accelerations and decelerations. To quantify a driver's sensitivity to the velocity gap, we introduced the concept of the new driver's sensitivity function, which has twofold formulations. The first formulation follows the HDDS model1, which presumes the sensitivity is dependent on a headway distance. The second formulation presumes that the sensitivity depends on a velocity gap, which might be informed by the taillight of a preceding vehicle. We have calibrated the neutralizing proficiency of a traffic flow field for the HDDS and proposed the Taillight Adapting model by utilizing the linear stability theory. Finally, a series of numerical simulations have been carried out of the improved Taillight Adapting model and conventional FVD model to investigate how the traffic flow field for the Taillight Adapting model behaves differently from the conventional FVD model.
PACS: 89.40.-a (Transportation); 87.15. Aa (Theory and modeling; Computer simulation)
... Capturing both, the individual and collective behaviors in pedestrian dynamics, is rather complex [2,7]. Many different approaches have been proposed in the literature: for example, models based on magnetic forces proposed by S. Okazaki and S. Matsushita in which pedestrians are modeled as magnetic charges in a magnetic field [33]; the gas-kinetic model which treats pedestrians as molecules in liquefied gas [22]; cellular automata [4,5,13]; models incorporating anticipative, rational behavior [1,11,12] and (smooth) sidestepping [15,34]. Another group of pedestrian models has emerged from the pioneering work on social forces [20] and can be classified as force-based [9,34] and the overview given in [8]. ...
We propose an extension of the anisotropic interaction model which allows for collision avoidance in pairwise interactions by a rotation of forces (Totzeck (2020) Kinet. Relat. Models 13 (6), 1219–1242.) by including the agents’ body size. The influence of the body size on the self-organisation of the agents in channel and crossing scenarios as well as the fundamental diagram is studied. Since the model is stated as a coupled system of ordinary differential equations, we are able to give a rigorous well-posedness analysis. Then we state a parameter calibration problem that involves data from real experiments. We prove the existence of a minimiser and derive the corresponding first-order optimality conditions. With the help of these conditions, we propose a gradient descent algorithm based on mini-batches of the data set. We employ the proposed algorithm to fit the parameter of the collision avoidance and the strength parameters of the interaction forces to given real data from experiments. The results underpin the feasibility of the method.
... Controlling traffic accounts for a judicious choice of green/amber/red timings at each traffic light in a road network. Systems deployed in realworld [4]- [6] typically use a traffic model [7], [8] that heavily influences the run-time performance of the overall system. ...
p>The manuscript introduces a novel perspective and approach to tackling traffic control. Bypassing the need for computationally expensive constrained optimization of spatiotemporal cues describing the road traffic state, the system exploits the causal relation between traffic light green light timing and the flow of cars. This way the system can store traffic contexts as memories used to simply recall plausible green time timings matching the flow of cars. This behavior amounts to an autoassociative memory, efficiently implemented in spiking neural networks, that provides a good trade-off between execution time and accuracy. We believe the approach has very high potential in real-world deployments. Our initial results on four real datasets demonstrate the benefits that the approach has and, of course, the lightweight and efficient computation steps and learning paradigm. Our goal is to raise awareness in the traffic engineering community on how neural associative memories can be a suitable candidate for traffic control, a problem without straightforward solutions. The flexibility in representing traffic data through vectors, causal learning of memories, and fast recall provide outstanding benefits demonstrated through our experiments. We hope the work will contribute to both the neural network community, through a novel autoassociative memory system using high-dimensional vectors, and the traffic engineering community, through a novel solution to traffic control.</p
... Controlling traffic accounts for a judicious choice of green/amber/red timings at each traffic light in a road network. Systems deployed in realworld [4]- [6] typically use a traffic model [7], [8] that heavily influences the run-time performance of the overall system. ...
p>The manuscript introduces a novel perspective and approach to tackling traffic control. Bypassing the need for computationally expensive constrained optimization of spatiotemporal cues describing the road traffic state, the system exploits the causal relation between traffic light green light timing and the flow of cars. This way the system can store traffic contexts as memories used to simply recall plausible green time timings matching the flow of cars. This behavior amounts to an autoassociative memory, efficiently implemented in spiking neural networks, that provides a good trade-off between execution time and accuracy. We believe the approach has very high potential in real-world deployments. Our initial results on four real datasets demonstrate the benefits that the approach has and, of course, the lightweight and efficient computation steps and learning paradigm. Our goal is to raise awareness in the traffic engineering community on how neural associative memories can be a suitable candidate for traffic control, a problem without straightforward solutions. The flexibility in representing traffic data through vectors, causal learning of memories, and fast recall provide outstanding benefits demonstrated through our experiments. We hope the work will contribute to both the neural network community, through a novel autoassociative memory system using high-dimensional vectors, and the traffic engineering community, through a novel solution to traffic control.</p
... The work of Zheng et al. (2018) proposes a stochastic formulation of the model of Newell (1961). Other approaches to stochastic modeling include gas-kinetic (Boltzmann-like) models of traffic (Paveri-Fontana;Hoogendoorn and Bovy;2001), aggregated traffic modeling approach (e.g., (sub)regionbased models of Ramezani et al. (2015)) and uncertainty propagation approaches (Sayegh et al.;2017). ...
This thesis tackles two major challenges of urban transportation optimization problems: (i) high-dimensionality and (ii) uncertainty in both demand and supply. These challenges are addressed from both modeling and algorithm design perspectives. The first part of this thesis focuses on the formulation of analytical transient stochastic link transmission models (LTM) that are computationally tractable and suitable for large-scale network analysis and optimization. We first formulate a stochastic LTM based on the model of Osorio and Flötteröd (2015). We propose a formulation with enhanced scalabil-ity. In particular, the dimension of the state space is linear, rather than cubic, in the link's space capacity. We then propose a second formulation that has a state space of dimension two; it scales independently of the link's space capacity. Both link models are validated versus benchmark models, both analytical and simulation-based. The proposed models are used to address a probabilistic formulation of a city-wide signal control problem and are benchmarked versus other existing network models. Compared to the benchmarks, both models derive signal plans that perform systematically better considering various performance metrics. The second model, compared to the first model, reduces the computational runtime by at least two orders of magnitude. The second part of this thesis proposes a technique to enhance the computational efficiency of simulation-based optimization (SO) algorithms for high-dimensional discrete SO problems. The technique is based on an adaptive partitioning strategy. It is embedded within the Empirical Stochastic Branch-and-Bound (ESB&B) algorithm of Xu and Nelson (2013). This combination leads to a discrete SO algorithm that is both globally convergent and has good small sample performance. The proposed algorithm is validated and used to address a high-dimensional car-sharing optimization problem.
... Mesoscopic model aggregation level is in between of those of microscopic and macroscopic models [14]. Classical mesoscopic approach describes aggregated vehicle behaviour by a specific probability distribution function, while single vehicle behaviour rules are defined individually [2],e.g., gaskinetic models [15,16]. Finally, hybrid mesoscopic models appeared most recently: they combine microscopic and macroscopic approaches by modeling the traffic at different aggregation levels simultaneously [2]. ...
We propose a multiagent, large-scale, vehicle routing modeling framework for the simulation of transportation system. The goal of this paper is twofold. Firstly, we investigate how individual and social knowledge interact and ultimately influence the effectiveness of resulting traffic flow. Secondly, we evaluate how different discrete-event simulation designs (delays vs. queuing) affect conclusions within the model. We present a new agent-based model that combines the efficient discrete-event approach to modeling with the intelligent drivers who are capable to learn about their environment in the long-term perspective from both, individual experience, and widely available social knowledge. The approach is illustrated as practical application to modeling commuter behavior in the city of Winnipeg, Manitoba, Canada. All simulations in the paper are fully reproducible as they have been carried out by utilizing a set of opensource libraries and tools that we have developed for the Julia programming language and that are openly available on GitHub.
... The analytical models are developed based on accurate physical laws and can be classified into microscopic, macroscopic, and mesoscopic. The microscopic approaches [1,2,3] represent individual characteristics of vehicles such as speed and position; Macroscopic approaches [4,5,6], on the other hand, describe the traffic flow using group-based characteristics of vehicles such as volume and flow; Finally, the mesoscopic approaches [7,8] merge the individual and group-based behaviors of vehicles. ...
Urban traffic flow prediction using data-driven models can play an important role in route planning and preventing congestion on highways. These methods utilize data collected from traffic recording stations at different timestamps to predict the future status of traffic. Hence, data collection, transmission, storage, and extraction techniques can have a significant impact on the performance of the traffic flow model. On the other hand, a comprehensive database can provide the opportunity for using complex, yet reliable predictive models such as deep learning methods. However, most of these methods have difficulties in handling missing values and outliers. This study focuses on hybrid deep neural networks to predict traffic flow in the California Freeway Performance Measurement System (PeMS) with missing values. The proposed networks are based on a combination of recurrent neural networks (RNNs) to consider the temporal dependencies in the data recorded in each station and convolutional neural networks (CNNs) to take the spatial correlations in the adjacent stations into account. Various architecture configurations with series and parallel connections are considered based on RNNs and CNNs, and several prevalent data imputation techniques are used to examine the robustness of the hybrid networks to missing values. A comprehensive analysis performed on two different datasets from PeMS indicates that the proposed series-parallel hybrid network with the mean imputation technique achieves the lowest error in predicting the traffic flow and is robust to missing values up until 21% missing ratio in both complete and incomplete training data scenarios when applied to an incomplete test data.
... Capturing both, the individual and collective behaviours in pedestrian dynamics, is rather complex [2,7]. Many different approaches have been proposed in the literature: for example models based on magnetic forces proposed by S. Okazaki and S. Matsushita in which pedestrians are modeled as magnetic charges in a magnetic field [33]; the gas-kinetic model which treats pedestrians as molecules in liquefied gas [22]; cellular automata [4,5,13]; models incorporating anticipative, rational behaviour [1,11,12] and (smooth) sidestepping [15,34]. Another group of pedestrian models has emerged from the pioneering work on social forces [20] and can be classified as force-based [9,34] and the overview given in [8]. ...
We propose an extension of the anisotropic interaction model which allows for collision avoidance in pairwise interactions by a rotation of forces \cite{arXiv:1912.04234} by including the agents' body size. The influence of the body size on the self-organization of the agents in channel and crossing scenarios as well as the fundamental diagram is studied. Since the model is stated as a coupled system of ordinary differential equations, we are able to give a rigorous well-posedness analysis. Then we state a parameter calibration problem that involves data from real experiments. We prove the existence of a minimizer and derive the corresponding first-order optimality conditions. With the help of these conditions we propose a gradient descent algorithm based on mini-batches of the data set. We employ the proposed algorithm to fit the parameter of the collision avoidance and the strength parameters of the interaction forces to given real data from experiments. The results underpin the feasibility of the method.
... In macroscopic models [1][2][3][4][5][6][7][8][9][10][11][12][13][14], the traffic flow is treated as a compressible fluid, and the comprehensive collective behavior of vehicles is studied. The mesoscopic models [15,16], as the links between macromicro model, can describe the inflow and outflow behavior of the queue at sections and nodes and the interactions between vehicles based on the gas dynamic theory model. The microscopic models depict the interaction behavior of individual vehicles, and its categories mainly include cellular automata [17][18][19][20][21], car-following model [22][23][24][25][26][27][28][29], and the explanation of various traffic phenomena from microscopic view [30][31][32][33][34][35]. ...
In car following states, the reaction of drivers is closely related to the space headway at given speed difference. Unlike the constant velocity difference reaction coefficient in traditional traffic model, this work designed a dynamic function, which can realize the switch between models according to the dynamic headway between vehicles, and developed a new car-following model to investigate the influences of dynamic safe headway (DSH) on car-following behavior. First, the following behavior of vehicle with DSH under urgent situation is simulated to demonstrate that DSH has the ability to prevent the occurrence of collision. Then, the prediction of delay time of car motion and the kinematic wave speed is reasonable and the evolution from free flow to congested flow is well reproduced. In addition, the result of excitation simulation shows that DSH can absorb the disturbance and suppress the propagation of traffic oscillations effectively, which is hard to achieve for traditional traffic model. Finally, the numerical experiment under period condition demonstrate that the new model is conducive to improving driving performance and further to smooth traffic flow. In addition, calibration and validation results show that the empirical data can be modeled with a quantitative agreement.
... deployed in real-world [6,10,14] use a traffic model [7,24] that heavily influences the run-time performance of the overall system. Basically, the role of the traffic model is to describe the dynamics of the traffic flow and to cope, eventually, with unforeseen deviations (i.e. ...
Whether efficient road traffic control needs accurate modelling is still an open question. Additionally, whether complex models can dynamically adapt to traffic uncertainty is still a design challenge when optimizing traffic plans. What is certain is that the highly nonlinear and unpredictable real-world road traffic situations need timely actions. This study introduces TRAMESINO (TRAffic Memory System INtelligent Optimization). This novel approach to traffic control models only relevant causal action-consequence pairs within traffic data (e.g. green time - car count) in order to store traffic patterns and retrieve plausible decisions. Multiple such patterns are then combined to fully describe the traffic context over a road network and recalled whenever a new, but similar, traffic context is encountered. The system acts as a memory, encoding and manipulating traffic data using high-dimensional vectors using a spiking neural network learning substrate. This allows the system to learn temporal regularities in traffic data and adapt to abrupt changes, while keeping computation efficient and fast. We evaluated the performance of TRAMESINO on real-world data against relevant state-of-the-art approaches in terms of traffic metrics, robustness, and run-time. Our results emphasize TRAMESINO’s advantages in modelling traffic, adapting to disruptions, and timely optimizing traffic plans.
... Mesoscopic models, linking microscopic to macroscopic models, characterize traffic flows using a probability distribution function of vehicle velocities (van Wageningen-Kessels et al., 2015). The most popular mesoscopic models are gas-kinetic models (Hoogendoorn, 1999;Hoogendoorn and Bovy, 2001;Hoogendoorn and HL Bovy, 2003). Since mesoscopic models lack clear physical interpretation and cannot be directly applied in simulations, they are not as well-studied as other models by the transportation community. ...
This paper serves as an introduction and overview of the potentially useful models and methodologies from artificial intelligence (AI) into the field of transportation engineering for autonomous vehicle (AV) control in the era of mixed autonomy when AVs drive alongside human-driven vehicles (HV). It is the first-of-its-kind survey paper to comprehensively review literature in both transportation engineering and AI for mixed traffic modeling. We will discuss state-of-the-art applications of AI-guided methods, identify opportunities and obstacles, and raise open questions. We divide the stage of AV deployment into four phases: the pure HVs, the HV-dominated, the AV-dominated, and the pure AVs. This paper is primarily focused on the latter three phases. Models used for each phase are summarized, encompassing game theory, deep (reinforcement) learning, and imitation learning. While reviewing the methodologies, we primarily focus on the following research questions: (1) What scalable driving policies are to control a large number of AVs in mixed traffic comprised of human drivers and uncontrollable AVs? (2) How do we estimate human driver behaviors? (3) How should the driving behavior of uncontrollable AVs be modeled in the environment? (4) How are the interactions between human drivers and autonomous vehicles characterized? We also provide a list of public datasets and simulation software related to AVs. Hopefully this paper will not only inspire our transportation community to rethink the conventional models that are developed in the data-shortage era, but also start conversations with other disciplines, in particular robotics and machine learning, to join forces towards creating a safe and efficient mixed traffic ecosystem.
... Among mesoscopic approaches, the most known models are gas-kinetic models, in which an analogy between the gas dynamics and the traffic dynamics is drawn. [PA60,THH99,HHST01,HB01a]. ...
Virtualized traffic via various simulation models and real‐world traffic data are promising approaches to reconstruct detailed traffic flows. A variety of applications can benefit from the virtual traffic, including, but not limited to, video games, virtual reality, traffic engineering and autonomous driving. In this survey, we provide a comprehensive review on the state‐of‐the‐art techniques for traffic simulation and animation. We start with a discussion on three classes of traffic simulation models applied at different levels of detail. Then, we introduce various data‐driven animation techniques, including existing data collection methods, and the validation and evaluation of simulated traffic flows. Next, we discuss how traffic simulations can benefit the training and testing of autonomous vehicles. Finally, we discuss the current states of traffic simulation and animation and suggest future research directions.
... The complex phenomena emerging in the evolution of traffic flow attract researchers to explore the mechanism of traffic flow with traffic flow models proposed from different perspectives (Nagel and Schreckenberg 1992;Xue and Dai 2003;Helbing 1996;Hoogendoorn and Bovy 2001;Bando et al. 1995;Jiang et al. 2001;Tian et al. 2010;Takayasu and Takayasu 1993;Benjamin et al. 1996; Barlovic et al. 1998;Xue et al. 2001;Li et al. 2001;Kerner et al. 2002;Knospe et al. 2000;Jiang and Wu 2003;Lee et al. 2004;Tian et al. 2009;Xiang et al. 2013). The cellular automaton (CA) models focus on the micro-interaction behaviors among vehicles, which are widely used due to the simulation ability of the traffic evolution process. ...
Based on the brake light (BL) model, Knospe et al. proposed a symmetric two-lane cellular automaton (BL-STCA) model, which could reproduce various empirically observed two-lane phenomena. In real traffic, the effect of brake light on the lane-changing behavior cannot be ignored. Therefore, BL-STCA model is interesting. However, there are two problems with BL-STCA model, too strong exchange of vehicles between lanes and unreasonable phenomenon in some special scenarios, such as a broken-down vehicle parked on one lane due to traffic accident. In order to solve the problems, we introduce the dynamic lane-changing probability and proposed an improved BL-STCA model with modification of lane-changing rules. The simulation results show as below. (1) Our new model effectively solves the above two problems of BL-STCA model. In addition, the lane-changing frequency is consistent with the real traffic data, which means the validity of our new model. (2) Compared with single-lane scenario, the lane-changing behaviors in two-lane scenario can effectively suppress the emergence of wide moving jam. (3) From the microcosmic level, the lane-changing behaviors can well explain the moving blank phenomenon within wide moving jam.
... Future research also includes further development of the framework to include a wider range of models such as those with moving bottlenecks [24], stochasticity Ngoduy [23], other multi-lane models and higher order models Hoogendoorn and Bovy [36], Bagnerini and Rascle [37]. Furthermore, newly developed models not presently included can be assessed. ...
Since the beginning of this millennium, many models of multiclass continuum traffic flow have been proposed. A set of qualitative requirements is presented for this type of model, including nonincreasing density–speed relationships and anisotropy. The requirements are cast into a framework that applies a generalized model of deterministic multiclass kinematic wave traffic flow. A step-by-step plan is developed to apply the framework to models that fit into the generalized model. The plan could be developed only with the Lagrangian formulation of the generic model but could also be applied to models in the traditional Eulerian formulation. It was concluded that only a few models known from the literature satisfied all requirements unconditionally. The step-by-step plan can furthermore be applied in the development of new models, the adaptation of existing models, and the calibration of model parameters.
... The microscopic models, such as the car-following models [1][2][3] and the cellular automata models [4][5][6], treat each individual vehicle as a particle, and the traffic is considered as a system of interacting particles driven far from equilibrium. The macroscopic models, mainly containing the continuum models [7][8][9][10][11][12][13], the gas kinetic models [14,15], and the lattice hydrodynamic models , regard the whole road traffic system as compressible fluid formed by vehicles and the traffic characteristics are revealed by analyzing the relation among traffic flow, mean speed, and traffic density. The dynamics of traffic flow and many real traffic phenomena can be reproduced in these models. ...
In this paper, the explicit lane changing effect for two-lane traffic system with interruption is studied based on lattice hydrodynamic model. Through linear stability analysis, the neutral stability criterion for the two-lane traffic system is derived, and the density–sensitivity space is divided into the stable and unstable regions by the neutral stability curve. By applying nonlinear reductive perturbation method, the Burgers equation and modified Korteweg–de Vries (mKdV) equation are obtained to depict the density waves in the stable and unstable regions, respectively. Numerical simulations confirm the theoretical results showing that the traffic characteristics in the stable and unstable regions can be described respectively by the triangular shock waves of the Burgers equation and the kink–antikink solution of the mKdV equation. Also it is proved that lane changing can average the traffic situation of each lane for two-lane traffic system and enhance the stability of traffic flow, but traffic interruption of the current lattice can deteriorate the stable level of traffic flow and easily result in traffic congestion.
... Future research also includes further development of the framework to include a wider 25 range of models such as those with moving bottlenecks [24], stochasticity Ngoduy [23], other multi-lane models and higher order models Hoogendoorn and Bovy [36], Bagnerini and Rascle [37]. Furthermore, newly developed models not presently included can be assessed. ...
Since the beginning of this millennium many multi-class continuum traffic flow models have been proposed. We present a set of qualitative requirements for this type of models, including nonincreasing density-speed relations and anisotropy. The requirements are cast into a framework that applies a generalised deterministic multi-class kinematic wave traffic flow model. A step-by-step plan is developed to apply the framework to models that fit into the generalised model. The plan could only be developed using the Lagrangian formulation of the generic model, but it can also be applied to models in the traditional Eulerian formulation. We conclude that only few models known from literature satisfy all requirements unconditionally. The step-by-step plan can furthermore be applied in the development of new models, the adaptation of existing models and the calibration of model parameters.
... A realistic fluid-dynamic theory for pedestrians must contain corrections due to their interactions (avoid collision, rapid acceleration and deceleration). Although such theory can be formulated [Hel92b,Hel92a,HB01c], such methods are unsuitable for microscopic pedestrian simulation in practical cases [HFMV02]. [Thi01] proposes the possibility of using Navier Stokes equations to visualize pedestrian flow as incompressible fluids, thereby simulate the flow movement of pedestrians. ...
Today, more and more simulation tasks with a traditionally non-geometric background need to be embedded into some geometric context, in order to provide spatial context to non-spatial data. This holds especially true for graph-based applications in some location-aware context. As an example, one might think of a theme park or a large commercial center, where the customers shall be provided with some navigation and scheduling information such as where to go and when - either a priori or even in real time via some mobile device. This can be done by analyzing the pedestrian traffic and waiting time situation by simulating the pedestrian movement and using the simulation data to optimally navigate and schedule the tasks that are to be executed by the customer. The main issues addressed in this thesis are as follows.
Initially, a flexible simulation framework is built to simulate the pedestrian movement in a 3D scenario, for example, a commercial building. Since the pedestrians strongly interact with the environment surrounding them, the geometry is taken into account. Architectural data such as paths, type and capacity of the paths, destinations and its properties, etc., is extracted from the CAD-model and are organized in a graph structure. The movement of the pedestrians and the waiting queues at the destinations are modeled as queuing systems using the discrete event simulation technique. These queuing systems are then embedded into the geometry model. The necessary input modeling parameters are also defined. The resulting scenario, when simulated, gives an overview of congestions and waiting times across the scenario for different time stages.
Apart from the simulation, the geometry data - or here the graph - is hierarchically organized in an octree structure. An octree-based model is chosen since octrees have the natural property of hierarchically storing 3D data. The octree data is used to identify the position of the pedestrian within the scenario. The potential destinations in the neighborhood that can be visited by the customer are also identified using neighbor search algorithms. Combining the simulation data with the octree modeling, the customer is navigated to the optimal destination.
Furthermore, when visiting several destinations, combinatorial optimization methods are used to optimally schedule the set of tasks to be executed by the customer. The optimization methods take into account the congestion information obtained from the simulation data, and the octree structure for navigation. This approach results in an effective pedestrian navigation system.
... Mesoscopic traffic flow models can be subdivided into the following three categories Hoogendoorn & Bovy (2001b): headway distribution models Buckley (1968); Branston (1976), cluster models (Kühne et al., 2002), and the gas-kinetic continuum models (Paveri-Fontana, 1975;Hoogendoorn & Bovy, 2001a). The most popular mesoscopic models are gas-kinetic continuum models which are also the oldest models among the three categories. ...
Traffic becomes more congested due to the growing demand. As a consequence,
improving traffic flow by means of traffic control is a key focus in many countries.
However, road traffic is one of the most complex systems to control.
In this thesis, a distributed solution for traffic prediction and control is proposed
to reduce this complexity and achieve fast computation for the purpose of on-line usage
in a large-scale network.
As the core of reproducing the real nonlinear phenomena of traffic congestion, the investigation of car-following models, which take into account human factors, has consistently assumed a central role within the domain of transportation science. Nevertheless, it is noteworthy that prior studies have invariably employed a fixed value for driver reaction time to stimuli, whereas it is imperative to recognize the dynamic nature of this parameter, closely associated with the instantaneous vehicle speed. To address this issue, this paper constructs a dynamic sensitivity coefficient (DSC), and further develops a nonlinear human factoring car-following model to reveal the relation between the reaction time and the current speed. Firstly, the linear critical stability condition and the mKdV equation of the model are derived by the linear stability analysis and kink–antikink solution analytic method, respectively. Then, the numerical experiments are conducted to demonstrate that the proposed model is more practical and can reproduce the real driving behavior and phenomena. Finally, calibration and validation results exhibit the actual vehicle trajectory can be simulated well.
Desired velocity, Chapman–Enskog method, Grad’s moment method, Traffic continuum model},
abstract = {In Prigogine's traffic kinetic model, the expected velocity of each driver is assumed to be independent of time, and its relaxation term is ignored. In Paveri–Fontana’s model, the vehicle accelerates to the desired velocity by means of a relaxation term. Méndez’s model assumed that the desired velocity is proportional to the instantaneous velocity, reflecting that all drivers want to drive at a higher velocity, which is a characteristic of aggressive drivers. In order to restrain the character of drivers, considering the relationship between a driver’s desired velocity and the surrounding environment and local instantaneous velocity, a new relaxation process is adopted, which describes that the desired velocity is adaptively adjusted toward the local equilibrium velocity within the relaxation time. We use Chapman-Enskog method and Grad’s moments method to derive the Navier-Stokes traffic equation. The stability condition is obtained by the linear stability analysis. Compared with the steady situation of both Kerner–Konhäuser model and Helbing’s model, it is shown that the extended continuum model has the ability to simulate stop-and-go traffic under medium and high density. Numerical simulation results show that the extended continuum model has a better control effect of traffic congestion than the Paveri–Fontana equation. Finally, the rationality of the extended continuum model is verified by simulations of partially reduced lane traffic and high-density traffic flow.
As traffic systems are becoming increasingly interconnected and automated, it is crucial to protect important systems from cyberattacks nowadays. In this study, we propose the Self-Stabilizing Cyberattack (SS-CA) model to investigate the connection between self-stabilizing control and the impact of cyberattacks on traffic flow dynamics in the context of connected vehicles. The linear stability analysis examines the stability criteria for the SS-CA model. Nonlinear analysis uses reductive perturbation methods to derive soliton solutions, providing descriptions of traffic density wave propagation. From the findings, it is evident that, as a cyberattack’s intensity increases, traffic stability decreases while increasing the self-stabilization control parameter enhances traffic stability. Furthermore, the effect of self-stabilizing control over headway is found effective in avoiding the negative impact of cyberattacks, which decreases traffic flow stability. The study validates theoretical insights through numerical simulations demonstrating the significance of self-stabilizing behavior in mitigating traffic disruptions caused by cyberattacks.
In actual transportation systems, the response time of drivers to the stimulus from the preceding vehicle varies at different speeds. The traditional car-following model cannot capture the heterogeneity of drivers for the response time is regarded as a constant. This paper designed a sigmoid function to describe the relation between the response time of drivers and the current speed. Then, a new hydrodynamic lattice model is developed by introducing the proposed nonlinear function. The model is analyzed by using Fourier series, and the linear stability criterion is derived. Numerical experiments are conducted in a ring road. Simulation results show that the evolution of density waves occurring in actual traffic is reproduced well. Finally, the model is calibrated and verified with the real data, and the simulation results are quantitatively consistent with the detector data.
Under the context of rapid development of the Internet of vehicles and vehicle-road collaboration system, active traffic management (ATM) becoming the mainstream means of road traffic control and developing toward refinement. In this paper, to study the high-precision lane-level dynamic induction control strategy in different scenarios, based on the NaSch model of cellular automata and combined with the characteristics of the failure section area, a fuzzy lane-changing bypass vehicle-following model considering lane-changing pressure in multi-lane failure scenarios was built. The simulation results show that (i) if the lane failure occurs on the middle lane, the lane should be induced in advance, and the induced lane change effect is the best at about 100 m. When the lane failure occurs in the left lane and right lane, the prompt is best at about 250 m. (ii) The induced distance should be based on actual traffic conditions, free combination of different early warning distances between 100 and 300 m can save about 20–30 s congestion time. (iii) The lane-level dynamic coordinated guidance control measures can effectively improve the road traffic efficiency compared with the static unified control measures, improve the traffic efficiency of road performance, and alleviate traffic congestion time. The conclusion of this paper can provide some reference for dynamic active control management and achieve higher accuracy of traffic flow lane-level control.
In this chapter, we focus on the modeling of the behavior of cyclists. This behavior encompasses different types of interconnected decisions: from the split-second decisions that cyclists make when they are riding their bike and are interacting with the road and other traffic participants to choices pertaining to the activities they want to perform and the locations where they can perform these activities. These different decisions are often related to different temporal (and spatial) scales. The detail in which these decisions need to be accurately modeled is often dependent on what the model is applied for, as will be explained in the ensuing of this chapter. Therefore, different (types of) models have been developed, as introduced in the last part of this chapter.
Vehicle-to-vehicle communication enables inter-vehicle interactions by sending a message or exchanging data. So a vehicle is affected not only by the ones in front but also by the ones behind. The mutual influence changes the feature of traffic flow from the anisotropy to the isotropy. In this paper, I model vehicle interactions by a stochastic game and formulate the isotropic flow in lane-based traffic by a kinetic
approach. Specifically, a scalar variable, called the cooperation
willingness, is introduced, which may evolve as time passes. Also,
I formulate a mapping between the cooperation willingness and
the cooperation probability. I embed the cooperation probability
into the stochastic game. Also, a general expression of the
evolution equation of cooperation willingness is derived. The
equilibrium solutions for a given choice of five and seven discrete
classes of the cooperation willingness are solved. Finally, the
proposed kinetic model of the isotropic lane-based traffic flow
is used to simulate the merging of two clusters of vehicles. The
results show that the nudging of vehicles ahead can improve the
efficiency of traffic flow. It also confirms the theoretical analysis
results.
https://ieeexplore.ieee.org/document/9713757
This paper proposes a new car-following (CF) model to capture the realistic behaviors of connected and automated vehicles (CAVs), whose communication topology (CT) among vehicles is characterized by graph theory in the V2V communication environment. By considering the heterogeneous time delays under the fixed and switching CTs, a generalized CF model is proposed. Based on the Lyapunov-Krasovskii method, a convergence analysis has been implemented for this new CF model with multiple time delays to obtain the convergence condition. Meanwhile, provides an estimate of the time delay bound. Finally, numerical experiments are performed under three typical fixed CTs (i.e., PF topology, BDLF topology, and TPLF topology) and the corresponding switching topology. Results support that the proposed CF model is capable of accurately reproducing the velocity, acceleration, position, and space headway profiles of CAVs traffic flow.
This book constitutes the refereed proceedings of the 6th ECML PKDD Workshop on Advanced Analytics and Learning on Temporal Data, AALTD 2021, held during September 13-17, 2021. The workshop was planned to take place in Bilbao, Spain, but was held virtually due to the COVID-19 pandemic.
The 12 full papers presented in this book were carefully reviewed and selected from 21 submissions. They focus on the following topics: Temporal Data Clustering; Classification of Univariate and Multivariate Time Series; Multivariate Time Series Co-clustering; Efficient Event Detection; Modeling Temporal Dependencies; Advanced Forecasting and Prediction Models; Cluster-based Forecasting; Explanation Methods for Time Series Classification; Multimodal Meta-Learning for Time Series Regression; and Multivariate Time Series Anomaly Detection.
Lane markings are painted on the ground to permit movement turns along traffic lanes at signalized junctions. Drivers have to follow the guidance to turn different directions to enter different downstream lanes. A new two-dimensional lattice hydrodynamic model is proposed to model the effects of a shared lane marking. The control method is used to analyze the model and new stability conditions are derived. A shared lane marking can divert traffic with different directions to enter different downstream lanes. Under different turning proportion, intensities of traffic at downstream vary. Results show that the traffic diversion could influence the flow stability. Shared lane marking is able to divert traffic flows to different downstream lanes. A feedback control signal is added in the proposed model. Revised stability conditions are obtained using the proposed control method. Numerical simulations present the results for the stability under different traffic conditions.
This paper presents scalable traffic stability analysis for both pure connected and autonomous vehicle (CAV) traffic and mixed traffic based on continuum traffic flow models. Human-drive vehicles (HDVs) are modeled by a non-equilibrium traffic flow model, i.e., Aw-Rascle-Zhang (ARZ) to capture HDV traffic's unstable nature. CAVs are modeled by a mean field game describing their non-cooperative behaviors as rational utility-optimizing agents. Working with continuum models helps avoiding scalability issues in microscopic multi-class traffic models. We demonstrate from linear stability analysis that the mean field game traffic flow model behaves differently from traditional traffic flow models and stability can only be proved when the total density is in a certain regime. We also show from numerical experiments that CAVs help stabilize mixed traffic. Further, we quantify the impact of CAV's penetration rate and controller design on traffic stability. The results may provide qualitative insights on traffic stability in mixed-autonomy for human drivers and city planners. The results also provide suggestions on CAV controller design for CAV manufacturers.
Mesoscopic traffic flow models were developed to fill the gap between the family of microscopic models that describe the behavior of individual vehicles and the family of macroscopic models that describe traffic as a continuum flow. Traditional mesoscopic models describe vehicle flow in aggregate terms such as in probability distributions. However, behavioral rules are defined for individual vehicles. The family includes headway distribution models, cluster models, gas-kinetic models and macroscopic models derived from them. Most recently, hybrid mesoscopic models have appeared as a new branch on the tree: they combine microscopic and macroscopic models.
Besides macroscopic traffic flow models, traffic modelling in freeway systems has also been treated with other general approaches, resulting in microscopic and mesoscopic models. Macroscopic models can surely represent large networks efficiently, since they adopt an aggregate representation of the traffic dynamics, but they generally lack the level of detail needed in modelling the individual drivers’ behaviours and choices. Microscopic models are, instead, conceived to explicitly reproduce the drivers’ responses to traffic patterns, reactions to traffic variations, interactions with other vehicles and route choices, i.e. most of the individual behaviours. Consequently, microscopic models are able to provide a lot of information about the features of traffic flow but they require a high computational effort, especially for large road networks. Mesoscopic models fill the gap between microscopic and macroscopic models, by representing the choices of individual drivers at a probabilistic level, but limiting the level of detail on driving behaviours.
Recently, the influence of driver's individual behaviors on traffic stability is research hotspot with the fasting developing Transportation Cyber-Physical Systems. In this paper, a new traffic lattice hydrodynamic model is proposed with consideration of driver's feedforward anticipation optimal flux difference. The neutral stability condition of the new model is obtained through linear stability analysis theory. The results show that the stable region will be enlarged on the phase diagram when the feedforward anticipation optimal flux difference effect is taken into account. In order to depict traffic jamming transition properties theoretically, the mKdV equation near the critical point is derived via nonlinear reductive perturbation method. The propagation behavior of traffic density waves can be described by the kink-antikink solution of the mKdV equation. Numerical simulations are conducted to verify the analytical results and all the results confirms that traffic stability can be enhanced significantly by considering the feedforward anticipation optimal flux difference in traffic lattice hydrodynamic theory.
A brief historical overview of empirical and theoretical investigations of vehicular traffic in traffic and transportation networks is presented. This critical overview is based on a consideration of works made by several generations of traffic researchers. It includes more than 1200 references to most well-known empirical results and theoretical approaches. The main focus of this overview is to explain the reason for a paradigm shift that happened in transportation science during last 20 years through the understanding of the empirical nucleation nature of traffic breakdown at highway bottlenecks. We consider also the basic terms and definitions of traffic characteristics of traffic and transportation networks that are used in the book, the objectives of this book as well as the book structure.
This article presents a review of the use of optimisation models for pedestrian evacuation and design problems. The articles are classified according to the problem type that is studied, the level of model realism, and the modelling or solution technique. To substantiate the classification criteria and to provide a background for the reader, relevant empirical research and descriptive models (e.g., social-force and cellular automata models) are discussed. We conclude that most of the recent models explicitly include pedestrian dynamics, specifically congestion, but more attention should be given to calibration and implementation of the proposed models. Furthermore, optimisation models could benefit from including some of the modelling techniques used in descriptive models.
Based on the lattice gas model, this paper improved the lattice gas model considering both the interference factors of opposing pedestrians and the impact of synclastic pedestrian due to different speed. It proposed a lattice gas simulation model of pedestrian crossing and compiled simulation software, combining with pedestrian crossing characteristics at countdown signalised crosswalk. The study carried out the pedestrian crossing simulation at different speed pedestrian ratio, different bi-direction pedestrian ratio and different specifications crosswalks by the simulation software. The results indicate that slow pedestrians will increase the overall delay of pedestrians and the pedestrian arrival rate higher, the slow pedestrian impact greater. When pedestrian arrival rate is low, the greater the gap between bi-direction pedestrian, the smaller the delay is. When the pedestrian arrival rate exceeds a certain value, the greater the gap between bi-direction pedestrian, the greater the delay is. The wider the crosswalk, the smaller pedestrian delay is. And the longer the crosswalk, pedestrian delay increased significantly. When other factors are the same, changing the pedestrian phase, delay reduced significantly with the increase of time in a certain range. And over this range increasing pedestrian phase time has little effect on delay.
In order to reveal the influence of driver's individual behavior on traffic flow more accurately, a new car-following model is proposed with consideration of multiple drives' desired velocities. The stability criterion of the new model is derived through linear stability theory and the results show that the current driver's desired velocity can stabilize traffic flow but the preceding driver's desired velocity can damage traffic stability. Through nonlinear analysis, the traffic jamming transition characteristics near the critical point can be described by the kink-antikink soliton of the mKdV equation. Numerical simulation confirms the analytical results, which shows that the multiple drivers' desired velocities play an important role in traffic evolution.
Chapter 6 describes a framework for Network Management of Road Traffic. The framework is called QHM, which stands for Quantitative Hierarchical Model. It describes a recursive (i.e. hierarchical), scalable approach to managing road traffic in networks, which is applicable to networks of any size. In addition, the chapter compares the model with an operational system, the Scenario Coordination Module, which is an implementation of an early version of QHM, in the Amsterdam area in The Netherlands.
In recent years, the influence of drivers' behaviors on traffic flow has attracted considerable attention according to Transportation Cyber Physical Systems. In this paper, an extended car-following model is presented by considering drivers' timid or aggressive characteristics. The impact of drivers' timid or aggressive characteristics on the stability of traffic flow has been analyzed through linear stability theory and nonlinear reductive perturbation method. Numerical simulation shows that the propagating behavior of traffic density waves near the critical point can be described by the kink–antikink soliton of the mKdV equation. The good agreement between the numerical simulation and the analytical results shows that drivers' characteristics play an important role in traffic jamming transition.
Following the approach initially proposed in Maury and Venel,30,31 we consider here crowd motion from the standpoint of granular media, and we investigate how theoretical and numerical tools in nonsmooth analysis can help better understanding some paradoxical features. We shall be especially interested in evacuation processes, jams, and we will detail how the granular nature of the flow helps to understand two well-known phenomena, the so-called "Faster is Slower" effect, and "Stop-and-Go" waves.
The use of traffic control systems can potentially improve the traffic flows on traffic networks. However, for the implementation of such control systems both in simulation and in practice many steps should be taken, and many choices are to be made. In this paper a list of considerations is provided for developing model-based traffic control systems in general, with a more detailed discussion on the use of model-predictive control for traffic regulation. A case study of designing a traffic controller is provided for the Dutch A12 freeway.
A new lattice hydrodynamic model for two-lane traffic system is proposed with consideration of drivers’ timid or aggressive characteristics. The effect of drivers’ timid or aggressive characteristics on the stability of traffic flow is studied via linear analysis theory and nonlinear reductive perturbation method. The linear analysis results show that the stable region for aggressive drivers is much larger than that for timid drivers, which means that aggressive drivers are much more prompt than timid drivers in stabilizing traffic flow. Moreover, we derive the mKdV equation near the critical point and obtain its kink–antikink soliton solution to describe the feature of traffic jamming transition. The good agreement between numerical simulations and analytical results reveals that drivers’ characteristics have an important role in the stability of traffic flow and traffic jamming transition in two-lane traffic system.
On the basis of assumptions about the behavior of driver-vehicle units
concerning acceleration, deceleration, overtaking, and lane-changing maneuvers,
a gas-kinetic traffic model for uni-directional multi-lane freeways is
constructed. Queuing effects are explicitly taken into account in an overall
manner. The resulting model is a generalization of Paveri-Fontana's
Boltzmann-like traffic model and allows the derivation of macroscopic traffic
equations for interacting lanes, including velocity equations. The related
effective macroscopic traffic model for the total freeway cross-section is also
derived. It provides corrections with respect to previous traffic models, but
agrees with them in special cases.
In this report we derive a macroscopic Multiple User-Class traffic model from mesoscopic principles. These principles yield equilibrium relationships between traffic density and equilibrium velocities as a function of the current traffic conditions, the traffic composition, and the distribution of user-class dependent desired velocities, rather than these relations need to be defined exogenously. These relations encompass contributions of drivers accelerating towards their user-class specific desired velocity on the one hand, and contributions resulting from interaction between vehicles of the same or different classes on the other hand. Additionally, the velocity variance variable is introduced describing deviations from the average speed within the user-classes.
We discuss several mathematical properties of the MUC equations. One of the results is an alternative model formulation, namely using the so-called conservative variables desity, momentum and energy, rather than the primitive variables density, velocity and velocity variance. Using this formulation, several new approaches are derived to numerically approximate solutions of the flow model.
We discuss first results from macroscopic simulation using the developed multiple user-class traffic flow model. The simulation results are employed to investigate whether fundamental traffic flow model-equations hold. It is concluded that the MUC-model satisfies the anisotropy condition, the 'invariant personality condition', and the 'unaffected slow vehicles' condition. A test case illustrates the self-formation of congestion.
The basic features of the Boltzmann-like model for traffic flow, due to Prigogine and coworkers, are reviewed. Comments are presented concerning a recent controversy on the collision integral. For a set of “ideal experiments” results are obtained that are physically unsatisfactory. This shown to be due to the form of the relaxation term appearing in Prigogine's vehicular Boltzmann equation. An alternative model is proposed for dilute traffic conditions. The main properties of the new model are discussed.
Traffic flow in a single lane (no passing) with all vehicles having the same desired speed is considered, with a view toward developing a kinetic equation in which speeding-up interactions are treated in the same fundamental manner as traditionally has been the case for slowing-down interactions. Such a kinetic equation is developed, based upon a specific correlation model expressing the leading-vehicle distribution function in terms of the single-vehicle distribution function and a specific mechanical model describing the circumstances and manner in which drivers change speeds in response to their situation vis-à-vis the vehicle immediately ahead of them. The mechanical model employs an extension (the generalized vehicular chaos hypotheses) of the limited form of the vehicular chaos hypothesis that classically has been employed for the term representing slowing-down interactions. The distributions that represent (local) equilibrium solutions of this equation on the time scale of interactions of individual vehicles are shown to comprise a family of bimodal distributions, with peaks at zero speed and at the desired speed. Interpretations and consequences of such equilibria are discussed from the view of traffic flow theory, especially in regard to the corresponding traffic stream model (flow-density relation) and to stop-and-go traffic patterns.
Theory of Highway Trac Flow: 1945±1965. Institute of Transportation Studies On Boltzmann-like treatments for trac ¯ow: a critical review of the basic model and an alternative proposal for dilute trac analysis Kinetic Theory of Vehicular Trac
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Advanced Synergetics Modelling multi-lane trac ¯ow with queuing eects
- H Haken
Haken, H., 1983. Advanced Synergetics. Springer, Berlin. Helbing, D., 1997a. Verkehrsdynamik. Springer, Berlin. Helbing, D., 1997b. Modelling multi-lane trac ¯ow with queuing eects. Physica A 242, 175±194.
A Gas-Kinetic Model for Pedestrian Flows. Accepted for publication for
- S P Hoogendoorn
- P H L Bovy