Simulating synchronized traffic flow and wide moving jam based on the brake light rule

A new cellular automaton (CA) model based on brake light rules is proposed, which considers the influence of deterministic deceleration on randomization probability and deceleration extent. To describe the synchronized flow phase of Kerner’s three-phase theory in accordance with empirical data, we have changed some rules of vehicle motion with the aim to improve speed and acceleration vehicle behavior in synchronized flow simulated with earlier cellular automaton models with brake lights. The fundamental diagrams and spatial–temporal diagrams are analyzed, as well as the complexity of the traffic evolution, the emergence process of wide moving jam. Simulation results show that our new model can reproduce the three traffic phases: free flow, synchronized flow and wide moving jam. In addition, our new model can well describe the complexity of traffic evolution: (1) with initial homogeneous distribution and large densities, the traffic will evolve into multiple steady states, in which the numbers of wide moving jams are not invariable. (2) With initial homogeneous distribution and the middle range of density, the wide moving jam will emerge stochastically. (3) With initial mega-jam distribution and the density close to a point with the low value, the initial mega-jam will disappear stochastically. (4) For the cases with multiple wide moving jams, the process is analyzed involving the generation of narrow moving jam due to “pinch effect”, which leads to wide moving jam emergence.     

Cellular automaton model for traffic flow based on safe driving policies and human reactions

This paper proposes a new single-lane cellular automaton model for traffic flow. The model takes into account normal drivers’ spacing policies and transportation engineering practices to guarantee that microscopic vehicle behavior is more in line with vehicular movement in the real world. As a result, drivers’ reactions are based on a safety analysis that determines the most appropriate action for a vehicle to take. Hence, the model introduces a new set of simple rules to change the speed of vehicles that incorporates three important thresholds required by the follower vehicle to accelerate, slow down or maintain its speed. Thus, the space gap, relative speed and limited acceleration/deceleration capabilities are introduced into simulations. Simulation results obtained from a system with periodic conditions show that the model can smooth the speed drop when vehicles approach the upstream front of the traffic jam. Therefore, the model avoids unrealistic deceleration behavior found in most previous cellular automata models. Besides, the model is also capable of reproducing most empirical findings including the three states of traffic flow, the backward speed of the downstream front of the traffic jam, and different congested traffic patterns induced by a system with open boundary conditions with an on-ramp. Moreover, the new model preserves the computational simplicity of the cellular automata models.     

Cellular automaton model in the fundamental diagram approach reproducing the synchronized outflow of wide moving jams

Velocity effect and critical velocity are incorporated into the average space gap cellular automaton model [J.F. Tian, et al., Phys. A 391 (2012) 3129], which was able to reproduce many spatiotemporal dynamics reported by the three-phase theory except the synchronized outflow of wide moving jams. The physics of traffic breakdown has been explained. Various congested patterns induced by the on-ramp are reproduced. It is shown that the occurrence of synchronized outflow, free outflow of wide moving jams is closely related with drivers time delay in acceleration at the downstream jam front and the critical velocity, respectively.     

Instantaneous information propagation in free flow, synchronized flow, stop-and-go waves in a cellular automaton model

Recently, a number of efforts are underway to investigate inter-vehicle communications （IVC）. This paper studies the instantaneous information propagation behaviours based on IVC in three different tragic situations （free flow, synchronized flow and stop-and-go waves） in a cellular automaton model. It is shown that different behaviours appear in stop-and-go waves from those in free flow and synchronized flow. While the distribution of Multi-hop Communication Distance （MhCD） is either exponential or uniform in free flow and synchronized flow, the distribution of MhCD is either exponential or with a single peak in stop-and-go waves.     

Cellular automaton model within the fundamental-diagram approach reproducing some findings of the three-phase theory

We propose a simple cellular automaton for traffic flow within the fundamental diagram, which could reproduce aspects of the three-phase theory. This so-called average space gap model (ASGM) is based on the Nagel–Schreckenberg model with additional slow-to-start and anticipation rules. The anticipation rule takes into account the average space gap of multiple leading vehicles and conveys to the model its three-phase property. Due to the anticipation rule, ASGM can show the transition from free flow to synchronized flow. Due to the slow-to-start rule, ASGM can show the spontaneous wide moving jam emerges in the synchronized flow. Simulations are carried out for periodic and open boundary conditions. Under periodic boundary condition, the fundamental diagram, and the properties of synchronized flow are studied. Under open boundary condition, different congested patterns induced by an on-ramp are analyzed. We found that the ASGM produces the same spatiotemporal dynamics as many of the more complex three-phase models. Due to its simplicity and its close relation to conventional slow-to-start models, this model can shed light on the relation between ‘two-phase’ and three-phase models.     

Towards the bi-directional cellular automaton model with perception ranges

The traditional cellular automaton (CA) model assumes that drivers only receive information from the preceding vehicles, e.g. the brake light information. However, in reality, drivers not only perceive information from downstream but can also get upstream information, e.g. the honk stimulation. The CA model involving traffic information from downstream and upstream is called the bi-directional CA model here. Meanwhile, with the introduction of Connected Vehicle Technologies, the perception range of drivers is expected to significantly increase which can lead to more informed driving behavior. Such an impact cannot be easily modeled by traditional one-directional CA models. In this study, the perception ranges of both the brake light effect and honk stimulation are introduced into the bi-directional CA model. Fundamental diagrams and spatial–temporal diagrams are then analyzed and two methods, i.e. the traffic flow interruption effect and microscopic analysis of time series data, are utilized to distinguish the synchronized traffic flow. Further numerical results illustrate that the perception range and slow-to-start sensitivity threshold are two important factors to reproduce the synchronized flow, and consideration of the honk information and the larger perception range both benefit the stability of traffic flow, which implies the potential significance of the application of Connected Vehicle Technologies.     

Phase coexistence induced by a defensive reaction in a cellular automaton traffic flow model

Traffic flow modeling is an elusive example for the emergence of complexity in dynamical systems of interacting objects. In this work, we introduce an extension of the Nagel-Schreckenberg (NaSch) model of vehicle traffic flow that takes into account a defensive driver’s reaction. Such a mechanism acts as an additional nearest-neighbor coupling. The defensive reaction dynamical rule consists in reducing the driver’s velocity in response to deceleration of the vehicle immediately in front of it whenever the distance is smaller than a security minimum. This new mechanism, when associated with the random deceleration rule due to fluctuations, considerably reduces the mean velocity by adjusting the distance between the vehicles. It also produces the emergence of bottlenecks along the road on which the velocity is much lower than the road mean velocity. Besides the two standard phases of the NaSch model corresponding to the free flow and jammed flow, the present model also exhibits an intermediate phase on which these two flow regimes coexist, as it indeed occurs in real traffics. These findings are consistent with empirical results as well as with the general three-phase traffic theory.     

Synchronized flow and phase separations in single-lane mixed traffic flow

In this paper, we have studied synchronized flow and phase separations in mixed (heterogeneous) single-lane highway traffic. It is found that the flux–density (occupancy) curve of heterogeneous flow, as expected, lies in between two flux–density (occupancy) curves of homogeneous flow R=0$R=0$ (all vehicles are slow vehicles) and R=1$R=1$ (all vehicles are fast vehicles). However, unexpectedly, the velocity–density (occupancy) curve of heterogeneous flow does not. We also found that cross-correlation function (CCF) analysis shows that heterogeneous flow has almost the same strong coupling as homogeneous flow. In other words, when traffic is in free flow or jams, the value of CCF is approximate to be 1.0, while the value is about 0.1 in synchronized flow.     

On the modeling of synchronized flow in cellular automaton models

In this paper,we further analyze our cellular automaton(CA)traffic flow model.By changing some parameters,the characteristics of our model can be significantly varied,ranging from the features of phase transitions to the number of traffic phases.We also review the other CA models based on Kerner’s three-phase traffic theory.By comparisons,we find that the core concepts for modeling the synchronized flow in these models are similar.Our model can be a good candidate for modeling the synchronized flow,since there is enough flexibility in our framework.     

An improved cellular automaton model with the consideration of a multi-point tollbooth

Based on the classical Nagel–Schreckenberg model, we in this paper propose an improved cellular automaton (CA) model to study the influences of a multi-point tollbooth on traffic flow. The numerical results show that the multi-point tollbooth can be looked at as a bottleneck and that it can improve the road capacity compared with other tolling stations, which shows that the proposed model is more effective than other traffic flow models. In addition, the results can help readers to better understand the effects of a multi-point tollbooth on traffic flow and help traffic engineers to reasonably design the tolling station.     

Effect of acceleration threshold on the phase transition in a cellular automaton traffic flow model

In this paper, we incorporate new parameters into a cellular automaton traffic flow model proposed in our previous paper [Jin et al. 2010 J. Stat. Mech. 2010 P03018]. Through these parameters, we adjust the anticipated velocity and the acceleration threshold separately. It turns out that the flow rate of synchronized flow mainly changes with the anticipated velocity, and the F → S phase transition feature mainly changes with the acceleration threshold. Therefore, we conclude that the acceleration threshold is the major factor affecting the F → S phase transition.     

考虑意外事件对交通流影响的元胞自动机交通流模型

在NaSh模型的基础上,考虑交通事故和养护路段等意外事件对高速公路交通流的影响,建立了有意外事件影响的在车道管制下的高速公路交通流元胞自动机模型,并进行数值模拟. 研究发现:意外事件对高速公路交通流有明显影响,并且意外事件对交通流的影响在某一密度值范围内尤其明显,且意外事件堵塞点在第一车道比在第二车道对交通流的影响小;同时,在该密度值范围内,意外事件堵塞时间和堵塞路段长度越长,对交通流的影响就越大. 关键词： 元胞自动机 交通流 意外事件     

A cellular automata model for urban traffic with multiple roundabouts

Urban transportation with multiple roundabouts is facing significant challenges such as traffic congestion, gridlock and traffic accidents. In order to understand these behaviors, we propose a two-dimensional cellular automata (CA) model, where all streets are two-way, with one lane in each direction. To allow the turning movement, a roundabout is designed for each intersection where four roads meet. The distance between each pair of roundabouts is configured with the parameter K while the turning behavior of drivers is modeled by a parameter γ. To study the impact of these different parameters on the urban traffic, several traffic metrics are considered such as traffic flow, average velocity, accident probability and waiting time at the entrance of roundabout. Our simulation results show that the urban traffic is in free flow state when the vehicle’s density is low enough. However, when the density exceeds a critical density ρ_c, the urban traffic will be in gridlock state whenever γ is nonzero. In the case where $\gamma =0,$ the urban traffic presents a phase transition between free flow and congested state. Furthermore, detailed analysis of the traffic metrics shows that the model parameters (γ, K) have a significant effects on urban traffic dynamics.     

A cellular automaton model based on empirical observations of a driver’s oscillation behavior reproducing the findings from Kerner’s three-phase traffic theory

In this paper, we propose a new cellular automaton model based on the well known three-phase traffic theory. The model takes into account the mechanism of a driver’s oscillation behavior obtained from engineering experiments in real traffic conditions. This mechanism shows the inner competition between speed adaptation and distance adjustment effects. The speed adaptation effect leads to synchronized flow, whereas a pinch region emerges, associated with the spontaneous occurrence of wide moving jams, due to distance over-adjustment. Numerical simulations are carried out both with periodic and with open boundary conditions in order to investigate the spatiotemporal features of traffic flow. The results indicate that our model is able to reproduce the three distinct traffic phases and exhibit the four congested patterns upstream of an isolated on-ramp, which is in good consistency with the results predicted from the three-phase theory.     

基于安全驾驶的元胞自动机交通流模型

针对Nagel-Schreckenberg模型(NaSch模型)中存在的高速车辆可能发生追尾事故的不安全性，考虑了前车速度为零的情况，提出一种新的强调驾驶安全性的一维元胞自动机交通流模型：安全驾驶模型，并对该模型进行了数值模拟.由于安全概率的引入，使得系统在临界密度附近出现低速的同步相，而不是完全的堵塞相，减小了追尾事故发生的可能性，提高了高密度时道路的通行能力.模拟结果显示出了亚稳态、非平衡相变以及滞后效应等实际交通所具有的特性. 关键词： 交通流 安全驾驶 元胞自动机 同步流     

Prediction feedback in intelligent traffic systems

The optimal information feedback has a significant effect on many socioeconomic systems like stock market and traffic systems aiming to make full use of resources. In this paper, we studied dynamics of traffic flow with real-time information provided and the influence of a feedback strategy named prediction feedback strategy is introduced, based on a two-route scenario in which dynamic information can be generated and displayed on the board to guide road users to make a choice. Our model incorporates the effects of adaptability into the cellular automaton models of traffic flow and simulation results adopting this optimal information feedback strategy have demonstrated high efficiency in controlling spatial distribution of traffic patterns compared with the other three information feedback strategies, i.e., vehicle number and flux.     

开放边界条件下二维可转向主干道交通流模型的研究

在开放性边界条件下，利用改进的Nagel-Schreckenberg交通流模型，引入过路口车辆的可 转向机理，建立二维n速主干道元胞自动机交通流模型，研究了转向概率和边界条件对 干道交通状况的影响而导致的不同相变特性以及这两个因素对实现改善干道交通的组织作用 . 关键词： 元胞自动机 交通流 转向概率 相变     

多速混合车辆单车道元胞自动机交通流模型的研究

在交通流NS模型的基础上，建立了多速混合车辆单车道元胞自动机交通流模型， 通过计算机数值模拟，得到了混合车辆在不同参数下交通流模型的基本图，并对混合交通的 特性进行了分析和讨论. 关键词： 元胞自动机 混合交通流模型 计算机模拟     

A modified weighted probabilistic cellular automaton traffic flow model

This paper modifies the weighted probabilistic cellular automaton model (Li X L, Kuang H, Song T, et al 2008 Chin. Phys. B 17 2366) which considered a diversity of traffic behaviors under real traffic situations induced by various driving characters and habits. In the new model, the effects of the velocity at the last time step and drivers' desire for acceleration are taken into account. The fundamental diagram, spatial-temporal diagram, and the time series of one-minute data are analyzed. The results show that this model reproduces synchronized flow. Finally, it simulates the on-ramp system with the proposed model. Some characteristics including the phase diagram are studied.