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A novel hyperbolic system of partial differential equations is introduced to model traffic flows. This system comprises three equations, with two being linearly degenerate; its main feature is the inclusion of a hysteretic term in a generalized Aw–Rascle–Zhang (ARZ) model. First, a maximum principle for the diffusive version of the model is proven. Then, it is demonstrated that a solution to the Riemann problem exists, which is unique among solutions that are monotone in velocity; all waves exploited in the construction have suitable viscous profiles. Through several examples it is shown how, as a consequence of different driving habits, the system can model the decay, emergence, or persistence of stop‐and‐go waves (a feature that is missing in the ARZ model), and such behavior is characterized by a simple geometric condition. Furthermore, the model allows the study of traffic flows with a mixture of drivers whose hysteresis loops are either clockwise or counterclockwise. In particular, the presence of sufficiently many of the former dampens speed oscillations. [ABSTRACT FROM AUTHOR]

Stop-and-go waves in congested road traffic are complex collective phenomena with significant implications for traffic engineering, road safety and the environment. Despite decades of research, understanding and controlling these oscillatory dynamics remains challenging. This article examines two classes of heterogeneous car-following models with quenched disorder to shed light on the underlying mechanisms that drive traffic instability and stop-and-go dynamics. Specifically, a scaled heterogeneity model and an additive heterogeneity model are investigated, each of which affects the stability of linear and nonlinear car-following models differently. We derive general linear stability conditions that we apply to specific models and illustrate by simulation. The study provides insight into the role of individual heterogeneity in vehicle behaviour and its influence on traffic stability.

We propose pro-social control strategies for connected automated vehicles (CAVs) to mitigate jamming waves in mixed-autonomy multi-lane traffic, resulting from car-following dynamics of human-driven vehicles (HDVs). Different from existing studies, which focus mostly on ego vehicle objectives to control CAVs in an individualistic manner, we devise a pro-social control algorithm. The latter takes into account the objectives (i.e., driving comfort and traffic efficiency) of both the ego vehicle and surrounding HDVs to improve smoothness of the entire observable traffic. Under a model predictive control (MPC) framework that uses acceleration and lane change sequences of CAVs as optimization variables, the problem of individualistic, altruistic, and pro-social control is formulated as a non-convex mixed-integer nonlinear program (MINLP) and relaxed to a convex quadratic program through converting the piece-wise-linear constraints due to the optimal velocity with relative velocity (OVRV) car-following model into linear constraints by introducing slack variables. Low-fidelity simulations using the OVRV model and high-fidelity simulations using PTV VISSIM simulator show that pro-social and altruistic control can provide significant performance gains over individualistic driving in terms of efficiency and comfort on both single- and multi-lane roads.

This article proposes a new microscopic speed model for one-dimensional pedestrian movement. Most existing modeling approaches consider only the distance and relative speed between a pedestrian and the person in front resulting in totally asymmetric interaction models. However, the distance with the pedestrian behind may also influence the behavior of a pedestrian. Based on this assumption, we elaborate a new asymmetric microscopic model considering the relative distances with the nearest neighbors behind and ahead using a fine-tuning asymmetry parameter. We analyze the stability of the new model and calibrate the parameters using two different single-file movement datasets. The numerical simulation results show that the new model has fewer backward movements and pedestrian overlaps than the totally asymmetric model making the stop-and-go waves in crowded situations more realistic. Furthermore, the proposed fine-tuned model better describes the fundamental diagram and its scattering. [ABSTRACT FROM AUTHOR]

• Humanoid pedestrian model with 3D skeleton and 11 degrees of freedom was proposed. • The effect of body rotation on stepping behavior was discussed. • Single-file experiments and bidirectional flow experiments were conducted. • The step synchronization was quantitatively compared with a public dataset. This paper presents a novel humanoid pedestrian model (HPM) incorporating stepping behavior and body rotation. The HPM is composed of two main components: (a) body modeling and (b) gait planning. A pedestrian is represented as a three-dimensional skeleton with 11 degrees of freedom in the body modeling component, which provides a universal approach for explaining the mathematical correlations between joint rotation angles and critical gait parameters such as step length, step width, and projected shoulder width. A framework for designing gaits that accounts for step-synchronization behavior and the effect of body rotation on stepping behavior is offered by the gait planning process. To validate the model, two types of experiments were conducted: nine sets of single-file experiments and 10 sets of bidirectional flow experiments, in which pedestrians walked in a 0.5-m-wide circular corridor and rotated their bodies to avoid collisions. It was suggested by the fundamental diagrams that body rotation reduces the walking speed of a pedestrian and consequently affects the overall flow rate. Furthermore, it was found that pedestrians were more resistant to moving forward in narrow bidirectional flow environments and tend to wait for a larger gap in front to take a longer or faster step. This behavior led to the formation of stop-and-go waves in the narrow-corridor scenario. The simulation results were consistent with the experimental findings in terms of flow-density relationships and the reproduction of stop-and-go waves. Additionally, synchronized steps were detected in the simulation and quantitatively compared with a publicly available dataset. The HPM offers a new perspective on modeling pedestrian dynamics and emphasizes the necessity of accounting for micro-characteristics at the step level in pedestrian models. [ABSTRACT FROM AUTHOR]

• Formulation of a precise definition of string stability for macroscopic models of traffic flows. • Formulation and stability analysis of a microscopic model with hysteresis. • The Lighthill-Whitham-Richards and Aw-Rascle-Zhang models are proved to be string stable under wide classes of perturbation. • Both string stability and instability may occur in a macroscopic traffic flow model with hysteresis. String stability or instability is a fundamental issue in traffic flow about whether the speed oscillations of the leading vehicle are damped or amplified as such oscillations pass through the platoon. If they are amplified, then traffic jams will occur. In this paper, we propose a suitable notion of string stability for continuum models of traffic flows, and study what kinds of driving behaviors lead to string stability or instability. We find that the well-known Lighthill-Whitham-Richards model and Aw-Rascle-Zhang model are string stable for wide classes of perturbations. As a consequence, the driving behaviors described by these models suppress speed oscillations and hence do not cause traffic jams. Once the hysteresis behavior is added to the Lighthill-Whitham-Richards model, an example is given to show that string instability can occur for large perturbations, leading to phantom jams. Under small perturbations, however, examples as well as approximate solution analysis suggest that the hysteretic traffic flow is string stable. The approximation solution analysis is developed to replace linear stability analysis, as hysteretic flow model cannot be linearized. [ABSTRACT FROM AUTHOR]

This work presents a second-order predictive dynamic model for pedestrian flow to investigate movement patterns and non-equilibrium phenomena in pedestrian traffic. This model is described as a system of nonlinear hyperbolic conservation laws with relaxation under the hypothesis that a group of pedestrians are regarded as a continuous anisotropic medium. The desired or preferred walking direction of pedestrians is assumed to minimize the total actual walking cost based on predictive traffic conditions, which satisfies the predictive dynamic user-equilibrium assignment. To solve this model, a cell-centered finite volume method for hyperbolic conservation laws coupled with a self-adaptive method of successive averages for an arisen discrete fixed point problem is adopted. The proposed model and algorithm are validated by comparing the results carried out by the model with experimental observations under non-congested conditions. Numerical examples are designed to investigate macroscopic features and path-choice behaviors of pedestrian flow. Numerical results indicate that the proposed model is able to reproduce some complex nonlinear phenomena in pedestrian traffic, such as the formation of congestions and stop-and-go waves. [ABSTRACT FROM AUTHOR]

Local density, which is an indicator for comfortable moving of a pedestrian, is rarely considered in traditional force based and heuristics based pedestrian flow models. However, comfortable moving is surely a demand of pedestrian in normal situations. Recently, Voronoi diagram had been successfully adopted to obtain the local density of a pedestrian in empirical studies. In this paper, Voronoi diagram is introduced into the heuristics based pedestrian flow model. It provides not only local density but also other information for determining moving velocity and direction. Those information include personal space, safe distance, neighbors, and three elementary characteristics directions. Several typical scenarios are set up to verify the proposed model. The simulation results show that the velocity-density relations and capacities of bottleneck are consistent with the empirical data, and many self-organization phenomena, i.e., arching phenomenon and lane formation, are also reproduced. The pedestrians are likely to be homogeneously distributed when they are sensitive to local density, otherwise pedestrians are non-uniformly distributed and the stop-and-go waves are likely to be reproduced. Such results indicate that the Voronoi diagram is a promising tool in modeling pedestrian dynamics. [ABSTRACT FROM AUTHOR]

This paper formulates the reactive and predictive dynamic models for pedestrian flow and presents a comparison of the two models. The path-choice behavior of pedestrians in the reactive dynamic model is described that pedestrians tend to walk along a path with the lowest instantaneous cost. The desired walking direction of pedestrians in the predictive dynamic model is chosen to minimize the actual cost based on predictive traffic conditions. An algorithm used to solve the two models encompasses a cell-centered finite volume method for a hyperbolic system of conservation laws and a time-dependent Hamilton–Jacobi equation, a fast sweeping method for an Eikonal-type equation, and a self-adaptive method of successive averages for an arisen discrete fixed point problem. The two models and their algorithm are applied to investigate the spatio-temporal patterns of flux or density and path-choice behaviors of pedestrian flow marching in a facility scattered with an obstacle. Numerical results show that the two models are able to capture macroscopic features of pedestrian flow, traffic instability and other complex nonlinear phenomena in pedestrian traffic, such as the formation of stop-and-go waves and clogging at bottlenecks. Different path-choice strategies of pedestrians cause different spatial distributions of pedestrian density specially in the high-density regions (near the obstacle and exits). [ABSTRACT FROM AUTHOR]

Abstract: The fractal behavior of traffic flow is studied by the adaptive fractal analysis method on the basis of the vehicle headway time series, which are obtained from the numerical simulation of the NaSch model. We find that the vehicle headway time series has a fractal behavior that is similar to the standard Brownian motion (BM) over a wide range of scales when the density is low. As the density increases well-defined sharp spectral peaks, corresponding to the stop-and-go waves, appear while the scale range showing BM-like behavior rapidly shrinks. In the high density regime, a new type of fractal behavior with long-range correlations appears, accompanying the worsening of traffic congestions. The underlying dynamics of traffic flow is analyzed, and some meaningful results are obtained. [Copyright &y& Elsevier]

Abstract: This paper takes into account three regimes for the description of traffic dynamics, which include the introduction of a pseudo-density transformed from the velocity, the pressure as a function of the pseudo-density and the relaxation of velocity to equilibrium. The resultant characteristic variables can be used to measure the deviation of the phase state to a desired state and derive physically bounded solutions. Taking the pseudo-density as a conserved variable, the approach is able to describe both equilibrium and non-equilibrium flows in a systematic and unified manner, and thus complex traffic phenomena. The theoretical properties of the model are thoroughly investigated, and numerical examples are used to demonstrate the ability of the model to reproduce some notable traffic phenomena. [Copyright &y& Elsevier]

This paper deals with the effects of traffic bottlenecks using an extended Lighthill-Whitham-Richards (LWR) model. The solution structure is analytically indicated by the study of the Riemann problem characterized by a discontinuous flux. This leads to a typical solution describing a queue upstream of the bottleneck and its width and height, and informs the design of a δ-mapping algorithm. More significantly, it is found that the kinetic model is able to reproduce stop-and-go waves for a triangular fundamental diagram. Some simulation examples, which are in agreement with the analytical solutions, are given to support these conclusions. [ABSTRACT FROM AUTHOR]

Abstract: A class of traffic flow models that capture the nonlinear dynamics of traffic jams are proposed. The class of discrete models originate from equations satisfied by the discrete traveling waves of some inviscid nonequilibrium continuum models. The self-organized oscillatory behavior and chaotic behavior in traffic are identified and formulated. The results can help to explain the appearance of a phantom traffic jam observed in real traffic flow. There is a qualitative agreement when the analytical results are compared with the empirical findings for freeway traffic and with the previous numerical simulations. [Copyright &y& Elsevier]

• An improved bicycle flow model that considers centrifugal effect was developed. • Single-individual experiments were conducted to investigate the centrifugal effect. • We conducted multi-individual experiments on a ring-shaped track for calibration. • We conducted multi-individual experiments on a playground-like track for validation. Cycling is a popular and sustainable mode of transportation. However, few studies have examined experimental and modeling studies on bicycle flow dynamics. In particular, for wide roads, the characteristics of high-density regimes in the fundamental diagram have not been well addressed, and the emergence of stop-and-go waves has not been fully understood. This study experimentally investigated bicycle flow dynamics on wide roads, using two types of 3-m-wide track. Different riding behaviors, namely, free riding, following, and overtaking, were analyzed. The bicycle flow dynamics were found to be essentially the same on the two tracks: (i) The bicycle flow rate remained nearly constant across a wide range of densities, in marked contrast to the single-file bicycle flow, which exhibited a unimodal fundamental diagram. By studying the weight density of the radial and lateral locations of cyclists, we argue that this behavior arises from the formation of more lanes with increase in global density. The newly formed lanes prevented the flow rate from decreasing. (ii) When the density exceeded 0.5 bicycles/m2, the flow rate began to decrease, and stop-and-go traffic emerged. Based on these behavioral observations, we propose an improved heuristic-based model to simulate bicycle flow on roads of different radii and explicitly account for the centrifugal effect of bicycles. The calibration and validation results demonstrate that the proposed model can reproduce the traffic dynamics of bicycle flow. [ABSTRACT FROM AUTHOR]

• FollowerStopper Autonomous Vehicle (FS-AV) was modelled to reproduce field experiment. • Multiple FS-AVs in a single-lane ring road impair wave dissipation. • FS-AVs increase vehicle cut-ins in double lane ring road which cause traffic waves. • FS-AVs in double-lane ring road worsen average flow, speed and delay time metrics. • Simulations do not support extrapolating the ring road results to linear roads. The traffic jam phenomenon known as stop-and-go waves is commonplace on many roadways and is unavoidable due to the imperfect nature of human driving behaviour. Previous research by Stern et al. (2018) has demonstrated experimentally that a single Autonomous Vehicle (AV) can be harnessed to dissipate stop-and-go waves produced by 20 other passenger vehicles driving in a cycle. However, the experiment was conducted in an idealistic situation of a single-lane ring road with one AV; meaning no lane changing was possible and multiple AV interaction was left untested. To address these limitations, the AV driving behaviour used to achieve this, known as FollowerStopper (FS), was modelled for use in the Aimsun traffic simulation software and validated before further numerical experiments were conducted. The microsimulation scenarios were designed to observe how multiple AVs driven by the FS controller (referred to as FS-AVs in this paper) affect their traffic wave dissipation capability. Both single and double-lane ring roads experimental designs were used with the latter capturing the untested effect of lane changes. FS-AV was found to be less effective than originally documented in both cases. Multiple FS-AVs included within one lane were still able to improve traffic flow and dissipate the stop-and-go waves, although it is sensitive to the combination of different factors and any deviation away from the ideal condition is likely to produce worse-off traffic operations in terms of traffic flow. For double-lanes, human-driven vehicles (HDVs) would change lanes at heightened rates to occupy the larger gap the FS-AV needs for its dissipating strategy, causing it to further pullback and set off a chain reaction to upstream traffic. Stop-and-go waves had not been dissipated and decreased traffic performance in terms of flow, speed and delay time resulted. Our results also showed that the wave dampening effect of the FS-AV does not translate between the ring road and its linear equivalent. On the other hand, our preliminary simulation results using a real-life freeway model did not suggest multiple FS-AVs worsen traffic conditions. The contradicting results might be due to different traffic conditions such as vehicle density. Further research is required to investigate what factors could adversely affect FS-AV's ability to dampen shockwaves and explore possible improvement to its driving algorithm. [ABSTRACT FROM AUTHOR]