Traffic states and jamming transitions induced by a bus in two-lane traffic flow

We study the traffic states and jamming transitions induced by a bus (slow car) in a two-lane traffic of cars. We use the dynamic model which is an extended one of the optimal velocity model to take into account the lane changing. The fundamental (flow-density) diagram is presented. The fundamental diagram changes highly by introducing a bus on a two-lane roadway. It is found that there are the six distinct states for the two-lane traffic flow including a bus. The spatio-temporal patterns are presented for the distinct traffic states. The dynamical state of traffic changes with density of cars. It is shown that the dynamical transitions among the distinct traffic states occur at some values of density. The phase diagram (region map) is shown for the two-lane traffic flow including a bus.     

Jam formation in traffic flow on a highway with some slowdown sections

We study the traffic jams appearing on a single-lane highway with a few slowdown sections. At low density, the flow (current) increases linearly with density, while it saturates at some values of intermediate density. In such case that some slowdown sections have the same speed limit, when the flow begins to saturate, a single discontinuous front (stationary shock wave) occurs before a slowdown section or some discontinuous fronts appear before some slowdown sections. For the case of different speed limits, the discontinuous front occurs before the section of strongest slowdown. The saturated flow is given by the maximal value of the current of the strongest slowdown section. The relationship between the densities is derived before and after the discontinuity. The dependence of jam lengths on density is derived numerically and analytically.     

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.     

Phase diagrams of noisy traffic states in the presence of a bottleneck

The traffic states are investigated for the noisy traffic flow in the presence of a bottleneck under the open boundary condition. The phase diagrams of the different kinds of congested traffic are presented for different values of sensitivity (the inverse of delay time). It is shown that the five different types of traffic states appear below the critical point: the free traffic with a pinned localized cluster, the weak standing shock, the moving localized cluster, the oscillatory congested traffic, and the strong standing shock. Above the critical point, the moving localized cluster and oscillatory congested traffic do not occur. Also, in the traffic flow without noise, the moving localized cluster and oscillatory congested traffic do not appear.     

Freezing transition in a four-directional traffic model for facing and crossing pedestrian flow

We study the traffic behavior in the facing and crossing traffic of pedestrians numerically and analytically. There are four kinds of walkers, those moving to east, to west, to north, and to south. We present the mean-field approximation (MFA) model for the four-directional traffic. The model is described in terms of four nonlinear difference equations. The excluded-volume effect and directionality are taken into account. The fundamental diagrams (current-density diagrams) are derived. When pedestrian density is higher than a critical value, the dynamical phase transition occurs from the free flow to the frozen (stopping) state. The critical density is derived by using the linear stability analysis. The velocity and current (flow) at the steady state are derived analytically. The analytical result is consistent with that obtained by the numerical simulation.     

Dynamics of traffic flows on crossing roads induced by real-time information

Traffic flows on crossing roads with an information board installed at the intersection have been simulated by a cellular automaton model. In the model, drivers have to enter the road with a shorter trip-time indicated on the information board, by making a turn at the intersection if necessary. The movement of drivers induces various traffic states, which are classified into six phases as a function of the car density. The dynamics of the traffic is expressed as the return map in the density–flow space, and analyzed on the basis of the car configuration on the roads.     

Mechanism of the jamming transition in the two-dimensional traffic networks

The mechanism of the jamming transition in two-dimensional traffic networks is discussed on the basis of several models, where the update rule is deterministic, though the initial car configuration is random. It has turned out that the introduced concept of the occupation probability, which depends upon time and the site, is useful. The fluctuation in the local   car density plays an important role to give rise to small initial clusters of the cars. To examine the growth of such clusters a time-dependent function C$C$ is introduced, which is the number of the neighboring car pairs, and C$C$ increases to a certain maximum value, correlated with the total jamming. The critical car density in the symmetric two-dimensional N×N/N×N$N\times N/N\times N$ system is found to be 0.22–0.23 for each of the east-bound (x)$\left(x\right)$ and the north-bound (y)$\left(y\right)$ cars.     

Phase diagram of a traffic roundabout

We propose a simple cellular automaton model to study the traffic dynamics in a roundabout. Both numerical and analytical results are presented. We are able to obtain exact solutions in the full parameter space. Exact phase diagrams are derived. When the traffic from two directions mixed, there are only five distinct phases. Some of the combinations from naive intuition are strictly forbidden. We also compare the results to a signaled intersection.     

A two-dimensional CA model for traffic flow with car origin and destination

Dynamic phase transitions in a two-dimensional traffic flow model defined on a decorated square-lattice are studied numerically. The square-lattice point and the decorated site denote intersections and roads, respectively. In the present model, a car has a finite deterministic path between the origin and the destination, which is assigned to the car from the beginning. In this new model, we found a new phase between the free-flow phase and the frozen-jam phase that is absent from previous models. The new model is characterized by the persistence of a macroscopic cluster. Furthermore, the behavior in this macroscopic cluster phase is classified into three regions characterized by the shape of the cluster. The boundary of the three regions is phenomenologically estimated. When the trip length is short and the car density is high, both ends of the belt-like cluster connect to each other through the periodic boundary with some probability. This type of cluster is classified topologically as a string on a two-dimensional torus.     

交通拥堵相变问题的同伦分析法

利用同伦分析法研究了一类基于洛伦兹系统的交通拥堵相变问题的非线性方程. 通过选取不同的初始解和不同的线性算子,分别得到了问题的近似解和相应的残留误差. 通过与前人结果的比较得出,在研究该类问题时同伦分析法优于微分变换法; 在应用同伦分析法时,要选取尽可能接近原算子线性部分作为线性算子. 本文还给出了一种新的初始解选取方法(双同伦分析法). 数值模拟的结果证实了理论分析的正确性. 关键词： 同伦分析法 交通拥堵 近似解 残留误差     

Modeling U-turn traffic flow

Median U-turns are sometimes installed to improve the traffic flow at busy intersections by eliminating left turns. Using a microscopic traffic model, we confirmed the presence of transitions from free flow to congested flow with increasing car inflow density. In addition, our proposed rules inside a U-turn curve, which accounted for safety issues and an asymmetric lane changing behavior (outer-to-inner vs. inner-to-outer lane transitions), predicted the speed distribution of cars after the U-turn curve. We found that U-turn curves installed for improving traffic flow at busy intersections produced their desired effects only when there is minimal interaction between cars.     

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.     

A study of wide moving jams in a new lattice model of traffic flow with the consideration of the driver anticipation effect and numerical simulation

In this paper, a new lattice model of traffic flow is proposed to investigate wide moving jams in traffic flow with the consideration of the driver anticipation information about two preceding sites. The linear stability condition is obtained by using linear stability analysis. The mKdV equation is derived through nonlinear analysis, which can be conceivably taken as an approximation to a wide moving jam. Numerical simulation also confirms that the congested traffic patterns about wide moving jam propagation in accordance with empirical results can be suppressed efficiently by taking the driver anticipation effect of two preceding sites into account in a new lattice model.     

Exploring jamming transitions and density waves in bidirectional pedestrian traffic

In this paper we propose a two-dimensional lattice hydrodynamic model considering path change in the bidirectional flow of pedestrians on the road. The stability condition and the mKdV equation describing the density wave of pedestrian traffic jamming are obtained by linear stability and nonlinear analyses. The phase diagram produced from these analyses indicates that the phase transition occurs amongst the freely moving phase, the coexisting phase and the uniformly congested phase below the critical point a_c. Additionally the results reveal the existence of a critical magnitude of path change (γ_c). Once the magnitude of path change exceeds the critical value, it gives rise to unstable density waves. Moreover, numerical simulations are performed and the results are in accordance with the theoretical analyses.     

Effect of adaptive cruise control systems on mixed traffic flow near an on-ramp

Mixed traffic flow consisting of vehicles equipped with adaptive cruise control (ACC) and manually driven vehicles is analyzed using car-following simulations. Simulations of merging from an on-ramp onto a freeway reported in the literature have not thus far demonstrated a substantial positive impact of ACC. In this paper cooperative merging for ACC vehicles is proposed to improve throughput and increase distance traveled in a fixed time. In such a system an ACC vehicle senses not only the preceding vehicle in the same lane but also the vehicle immediately in front in the other lane. Prior to reaching the merge region, the ACC vehicle adjusts its velocity to ensure that a safe gap for merging is obtained. If on-ramp demand is moderate, cooperative merging produces significant improvement in throughput (20%) and increases up to 3.6 km in distance traveled in 600 s for 50% ACC mixed flow relative to the flow of all-manual vehicles. For large demand, it is shown that autonomous merging with cooperation in the flow of all ACC vehicles leads to throughput limited only by the downstream capacity, which is determined by speed limit and headway time.     

Biham–Middleton–Levine model with four-directional traffic

We study the four-directional traffic flow on a two-dimensional lattice. In the case of discrete densities, we assume equal number of vehicles in each lane. Except for the minimum density, the gridlock emerges swiftly. Two kinds of gridlock have been observed. The global gridlock dominates the system when the density is twice the minimum value. At higher densities, the system is pervaded by local gridlocks. We also analyze the time evolution of average speed. In the case of continuous densities, the vehicle numbers vary from lane to lane. The global gridlock is then destroyed by the fluctuations; while the local gridlock can still be observed.     

Influence of inter-vehicle communication on peak hour traffic flow

Mixed traffic flow consisting of vehicles equipped with wireless inter-vehicle communication devices and non-equipped vehicles is analyzed using bidirectionally coupled network traffic and road traffic simulators in a peak hour scenario. For equipped vehicles a strategy to stabilize traffic flow and to reduce travel time is proposed. The strategy comprises rules to determine both how and when to change driving behavior. Vehicles that detect perturbations downstream try to keep a larger gap to their predecessor by which they aim to compensate traffic inhomogeneities. Improvement of traffic flow was observed even for a ratio of equipped vehicles as low as five percent.     

A new lattice model of traffic flow with the consideration of the traffic interruption probability

In this paper, we present a new lattice model which involves the effects of traffic interruption probability to describe the traffic flow on single lane freeways. The stability condition of the new model is obtained by the linear stability analysis and the modified Korteweg-de Vries (KdV) equation is derived through nonlinear analysis. Thus, the space will be divided into three regions: stable, metastable and unstable. The simulation results also show that the traffic interruption probability could stabilize traffic flow.     

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.     

Traffic jam and discontinuity induced by slowdown in two-stage optimal-velocity model

We study the traffic states and jams induced by a slowdown of vehicles in a single-lane highway. The two-stage optimal velocity model is used in which the optimal velocity function has two turning points. The fundamental (flow-density) diagrams are calculated. At low density, the flow (current) increases linearly with density, while it saturates at some values of intermediate density. When the flow saturates, the discontinuous front (stationary shock wave) appears before or within the section of slowdown. The values of saturated flow are determined by the extreme values of theoretical current curves. The relationship between the densities is derived before and after the discontinuity.