Free Flow Phase Research Articles

Insights into vehicle conflicts based on traffic flow dynamics

The utilization of traffic conflict indicators is crucial for assessing traffic safety, especially when the crash data is unavailable. To identify traffic conflicts based on traffic flow characteristics across various traffic states, we propose a framework that utilizes unsupervised learning to automatically establish surrogate safety measures (SSM) thresholds. Different traffic states and corresponding transitions are identified with the three-phase traffic theory using high-resolution trajectory data. Meanwhile, the SSMs are mapped to the corresponding traffic states from the perspectives of time, space, and deceleration. Three models, including k-means, GMM, and Mclust, are investigated and compared to optimize the identification of traffic conflicts. It is observed that Mclust outperforms the others based on the evaluation metrics. According to the results, there is a variation in the distribution of traffic conflicts among different traffic states, wide moving jam (phase J) has the highest conflict risk, followed by synchronous flow (phase S), and free flow (phase F). Meanwhile, the thresholds of traffic conflicts cannot be fully represented by the same value through different traffic states. It reveals that the heterogeneity of thresholds is exhibited across traffic state transitions, which justifies the necessity of dynamic thresholds for traffic conflict analysis.

Numerical investigation on the impact of obstacles on phase transition in pedestrian counter-flow

In this paper, a modified real-coded microscopic model is utilized to investigate the influence of obstacles on the pedestrian counter-flow. The four typical phases, i.e., free-flow phase, lane-formation phase, intermediate phase and congestion phase are reproduced by this model. Through the numerical results, the influence of the geometric features of obstacles, such as the inclination angle and the major-to-minor axis ratio, on the pedestrian counter-flow are analyzed. With increasing the inclination angle of obstacle or reducing the ratio, it is found that the moving efficiency and the probability of asymmetric flow will be increased, the occurrence of congestion phase will be delayed. Furthermore, the occurrence density of congestion phase will be increased with the distance between sloped obstacles. Finally, from the view of engineering application, the optimal setting of obstacle is given by comparing the fundamental diagrams.

Group-walking effect on bidirectional pedestrian flow in a corridor

Groups are commonly found in general crowds and their behaviors are distinguished from that of isolated pedestrians. Thus, in recent five years researchers have started to investigate pedestrian group movement. In this paper, we considered group walking effect and introduced group floor field to the traditional floor field model. Furthermore, two different methods of generating group floor field were put forward, i.e. group center generation (method 1 for short) and group leader generation (method 2 for short), and we applied the proposed group model to simulate bidirectional pedestrian flow in a corridor. No matter which method of generating group floor field is adopted, the simulation results show that group members walk slower than singles, and with the group size increasing the transition point from the free flow phase to the jamming has a decrease trend. In addition, it seems that method 2 of generating group floor field makes group more cohesive and stable at the same crowd density than method 1. Afterwards it is found that the crowd with large group size is more easily affected by asymmetric injection rate. At last, people’s walking preference is shortly discussed, and it is obtained that people’s walking preference is also good for group movement from the perspective of movement efficiency.

Freeway traffic flow cellular automata model based on mean velocity feedback

Making full use of real-time feedback traffic information to guide road traffic is one of the hot spots in the field of intelligent transportation system, which has practical significance for improving travel efficiency and reducing congestion. This paper proposes a new average speed feedback strategy based on real-time information, and uses it to improve the MCD model. The fundamental diagram, space–time diagram and flow interruption effect diagram obtained by simulation show that the results are consistent with the three-phase flow theory. It is found that in the free flow phase, the mean velocity feedback enables vehicles to adjust the velocity, accelerate the dissipation of the deceleration wave and maintain the stability of the traffic flow. In contrast, in the synchronized flow phase, the mean velocity feedback strategy keeps the traffic flow constant, reduces the velocity disturbance caused by the drivers’ own factors and improves the road operation efficiency.

On the phase transition in the sublattice TASEP with stochastic blockage

We revisit the defect-induced nonequilibrium phase transition from a largely homogeneous free-flow phase to a phase-separated congested phase in the sublattice totally asymmetric simple exclusion process with local deterministic bulk dynamics and a stochastic defect that mimicks a random blockage. Exact results are obtained for the compressibility and density correlations for a stationary grandcanonical ensemble given by the matrix product ansatz. At the critical density the static compressibility diverges while in the phase separated state above the critical point the compressibility vanishes due to strong non-local correlations. These correlations arise from a long range effective interaction between particles that appears in the stationary state despite the locality of the microscopic dynamics.

A new cellular automata traffic flow model considering asynchronous update of vehicle velocity

This study examines the cellular automata traffic flow model, which considers the asynchronous update of vehicles’ velocities. Computer simulations are used to identify three typical phases: linear free flow phase, nonlinear moving phase and traffic jam phase. Compared to the original NaSch model, the system of the present model can reach the maximum flow when the vehicle density is higher. The influence of the delay probability and the maximum time step in which drivers intend to keep their current velocity on fundamental diagram is discussed.

A LANE-CHANGING BML MODEL CONSIDERING THE INFLUENCE OF BOTH LANE INFORMATION AND TURN SIGNALS

The lane-changing behaviors of vehicles are frequently adopted by drivers in order to get better driving conditions and turn signal plays an essential role in guiding vehicles' lane-changing behaviors. In this paper, based on the BML (Biham-Middleton-Levine model ) model, we proposed a lane- changing cellular automata model which takes the influence of both lane information and turn signals into account. When a vehicle cannot move forward, the driver will judge whether the vehicle meets the lane-changing conditions or not. If the driver can change his/her lane, then the lane-changing probability is calculated according to the lane information (such as average velocities and densities of those vehicles in his own and target lanes) and the state of turn signals. Finally, the driver can determine whether he/she changes lane or not by the corresponding probability. Numerical simulations were carried out to investigate the effect of lane-changing behaviors on the phase transition between the free flow phase and the global jamming phase. Two kinds of BML models were studied, one with traffic lights and the other without traffic lights. Numerical results show that the critical density of the BML model without traffic lights increases considerably due to the introduction of lane-changing rules. At a smaller scale, the critical density approximates that of the BML model with traffic light control. The effect of lane change is significant on traffic dynamics. Furthermore, a new coexisting phase of both the free flow phase and the local jamming phase was found. The underlying generation and evolution mechanism of the coexisting phase is discussed in detail. It is shown that the local congestions will result in the global congestion under higher densities. However, the lane-changing rules does not have distinct effect on the critical density of the BML model with traffic lights. But the region of phase transition becomes narrower. It indicates that lane-changing behaviors can lead to variations of local traffic features and take less effect on the global features of traffic system.

The energy dissipation at roundabout system

In this paper, we propose a cellular automata model to study the energy dissipation in the roundabout system. The energy dissipation and the phase diagram of the system in the space ([Formula: see text]) are constructed. The energy dissipation profile (SE[Formula: see text](i)), and the effect of the rate [Formula: see text] (i.e., the rate of vehicles with no aimed exit point) and the probability P[Formula: see text] of choosing the next exit point to leave the circulating lane on the energy dissipation are shown. The simulation results show that the energy dissipation explains the nature of the phases, the quasi-free-flow (Q-FF) phase take place on the free flow phase because some vehicles decelerate at the entry point. Likewise, the results also indicate that the energy dissipation takes small values with the increases of the two probability [Formula: see text] and P[Formula: see text] which enhance the environmental statutes of the roundabout system.

Pedestrian-vehicle interference at a signalized crossing based on detailed microscopic traffic flow models

Interference between pedestrians and motor vehicles at signalized intersections not only leads the traffic to delay and traffic efficiency to decrease, but also induces traffic crashes to happen frequently. In this paper, a microscopic discrete model for traffic flow is adopted to study the mutual interference mechanism between pedestrians and vehicles at signalized intersection. The vehicular traffic flow model is based on the refined NaSch model, and traffic lights are introduced to consider the driver anticipating in traffic signal switching. Based on the multi-step lattice gas model, the pedestrian flow model considers the fact that the pedestrians’ speed increases gradually during pedestrian cross-street green time. Both models reflect real features of movement of vehicles (pedestrians) in daily life. When the traffic light signal switches, the vehicles (pedestrians) staying in the conflict area result in the delay of pedestrians (vehicles). It is assumed that pedestrians and vehicles cannot coexist in the conflict area at the same time. In the simulation, the periodic boundary condition is applied to the lane, and the open boundary condition is applied to the crosswalk. The arrival rate of pedestrian is assumed to satisfy the Poisson distribution. Both the fundamental diagram of vehicular traffic flow and the pedestrian waiting time are calculated, and the phase diagram revealing the global nature of the presented model is obtained accordingly. The quantitative characteristics of vehicle (pedestrian) delay time caused by pedestrians (vehicles) staying in the conflict area are given as well. Simulation results show that there is a critical split. When the split is less than the critical value, three kinds of traffic phases, i.e., free flow phase, saturated flow phase, and jamming flow phase, appear with the increase of density. When the split is larger than the critical value, four kinds of traffic phases, i.e., free flow phase, coexisting phase, saturated flow phase, and jamming flow phase are distinguished. The delay caused by the mutual interference between pedestrians and motor vehicles is closely related to the state of vehicle flow and the state of pedestrian flow. When the arrival rate of pedestrians is quite large and the split is large enough, these pedestrians in the waiting area cannot be emptied once in a single pedestrian cross-street cycle. The qualitative and quantitative characteristics of mutual interference between pedestrians and vehicles are discussed in more detail. The setting of a reasonable split not only ensures the efficiency of traffic flow, but also reduces the waiting time of pedestrians to cross the street.

An existence result for a constrained two-phase transition model with metastable phase for vehicular traffic

In this paper we study a phase transition model for vehicular traffic flows. Two phases are taken into account, according to whether the traffic is light or heavy. We assume that the two phases have a non-empty intersection, the so called metastable phase. The model is given by the Lighthill–Whitham–Richards model in the free-flow phase and by the Aw–Rascle–Zhang model in the congested phase. In particular, we study the existence of solutions to Cauchy problems satisfying a local point constraint on the density flux. We prove that if the constraint F is higher than the minimal flux \(f_\mathrm{c}^-\) of the metastable phase, then constrained Cauchy problems with initial data of bounded total variation admit globally defined solutions. We also provide sufficient conditions on the initial data that guarantee the global existence of solutions also in the case \(F < f_\mathrm{c}^-\). These results are obtained by applying the wave-front tracking technique.

Traffic flow behavior at a single-lane urban roundabout

In this paper, we propose a stochastic cellular automata model to study the traffic behavior at a single-lane roundabout. Vehicles can enter the interior lane or exit from it via [Formula: see text] intersecting lane, the boundary conditions are stochastic. The traffic is controlled by a self-organized scheme. It has turned out that depending on the rules of insertion to the roundabout, five distinct traffic phases can appear, namely, free flow, congestion, maximum current, jammed and gridlock. The transition between the free flow and the gridlock is forbidden. The density profiles are used to study the traffic pattern at the interior lane of the roundabout. In order to quantify the interactions between vehicles in the interior lane of the roundabout, the velocity correlation coefficient (VCC) is also studied. Besides, the spatiotemporal diagrams corresponding to the entry/exit lanes are derived numerically. Furthermore, we have investigated the effect of displaying signal ([Formula: see text], as the [Formula: see text] decreases, the maximum current increases at the expense of the free flow and the jamming phase. Finally, we have investigated the effect of the braking probability [Formula: see text] on the interior lane of the roundabout. We have found that the increase of [Formula: see text] raises the spontaneous jam formation on the ring. Thus, enlarges the maximum current and the jamming phase while the free flow phase decreases.

Jamming transitions induced by an attraction in pedestrian flow.

We numerically study jamming transitions in pedestrian flow interacting with an attraction, mostly based on the social force model for pedestrians who can join the attraction. We formulate the joining probability as a function of social influence from others, reflecting that individual choice behavior is likely influenced by others. By controlling pedestrian influx and the social influence parameter, we identify various pedestrian flow patterns. For the bidirectional flow scenario, we observe a transition from the free flow phase to the freezing phase, in which oppositely walking pedestrians reach a complete stop and block each other. On the other hand, a different transition behavior appears in the unidirectional flow scenario, i.e., from the free flow phase to the localized jam phase and then to the extended jam phase. It is also observed that the extended jam phase can end up in freezing phenomena with a certain probability when pedestrian flux is high with strong social influence. This study highlights that attractive interactions between pedestrians and an attraction can trigger jamming transitions by increasing the number of conflicts among pedestrians near the attraction. In order to avoid excessive pedestrian jams, we suggest suppressing the number of conflicts under a certain level by moderating pedestrian influx especially when the social influence is strong.

Traffic flow behavior at a single lane traffic circle

In this paper, we propose a stochastic cellular automata (CA) model to study traffic dynamic at a single-lane traffic circle of [Formula: see text] entry/exit points. The boundaries are controlled by the injecting rates [Formula: see text], [Formula: see text] and the extracting rate [Formula: see text]. Both the cases with and without the splitter islands of width [Formula: see text] are considered. The phase diagrams in the space [Formula: see text] are constructed and the density profiles are also investigated. The variation of the phase diagram with the traffic circle size [Formula: see text], the number of entry point [Formula: see text], and the time needed for drivers to change their exit willingly [Formula: see text] is studied. The results show that the phase diagram in both cases consists essentially of three phases namely free flow, congestion and gridlock. However, the large sized traffic circle shows better performance in the free flow phase, in contrary, the increase of [Formula: see text] enlarges the congestion and the gridlock phases. We have also found that the decrease of [Formula: see text] enhances the traffic flow situation in the traffic circle. Furthermore, as the [Formula: see text] increases, the free flow phase enlarges while the congestion and gridlock ones shrink.

Numerical modeling based on a finite element method for simulation of flow in furrow irrigation

In this study, a zero-inertia finite element model (ZIFEM) is developed and applied for simulating all phases of furrow irrigation based on Saint–Venant equations. The complexity and nonlinear behavior of the Saint–Venant equations are the major difficulty in developing a finite element model to simulate furrow irrigation. Therefore, through the Galerkin FEM approach, the model assesses the free surface flow on a variable cell length at each time step and determines the suitable element length for each individual cell and the model solves the equations by using an iterative method. Along with the free surface flow phase, the infiltration phase is estimated by the Kostiakov–Lewis equation. The ZIFEM model is verified using seven experimental data sets collected from the literature and observed data from the farm consisting of two free drainage furrows with a length of 72 m, a top width of 0.8 m, a depth of 0.25 m and a slope of 0.2%. The model accuracy is studied to simulate advance and recession trajectories and runoff by calculating the root-mean-square error (RMSE), relative error and percentage error. It is observed that in all irrigation events, the proposed model reasonably agreed with field measurements. An evaluation of the RMSE shows that in 81.25% irrigation events the ZIFEM is more accurate than the WinSRFR model. In overall, the results of the model suggest that the ZIFEM can be introduced as a potential numerical tool for analyzing and evaluating furrow irrigation.

Routing optimization in networks based on traffic gravitational field model

For research on the gravitational field routing mechanism on complex networks, we further analyze the gravitational effect of paths. In this study, we introduce the concept of path confidence degree to evaluate the unblocked reliability of paths that it takes the traffic state of all nodes on the path into account from the overall. On the basis of this, we propose an improved gravitational field routing protocol considering all the nodes’ gravities on the path and the path confidence degree. In order to evaluate the transmission performance of the routing strategy, an order parameter is introduced to measure the network throughput by the critical value of phase transition from a free-flow phase to a jammed phase, and the betweenness centrality is used to evaluate the transmission performance and traffic congestion of the network. Simulation results show that compared with the shortest-path routing strategy and the previous gravitational field routing strategy, the proposed algorithm improves the network throughput considerably and effectively balances the traffic load within the network, and all nodes in the network are utilized high efficiently. As long as [Formula: see text], the transmission performance can reach the maximum and remains unchanged for different [Formula: see text] and [Formula: see text], which ensures that the proposed routing protocol is high efficient and stable.

A cellular automata traffic flow model for three-phase theory

This paper presents a newly-modified KKW model including the subdivided vehicles types, and introduces the changes for a driver’s sensitivity into the speed fluctuation. By means of the numerical simulation the following conclusions are obtained herewith: 1. Velocity disturbance propagation in traffic flow is caused by the speed adaptation among vehicles. 2. In free flow phase, very fewer vehicles are affected by the velocity disturbance and the effect can be dissipated quickly thus the time of disturbance in a single vehicle is quite shorter. On the contrary, the impact duration time of the disturbance on a single vehicle is longer in synchronous flow phase, thus, it will affect more vehicles accordingly. 3. Under the free flow phase, the continuous deceleration behavior of a high speed vehicle to adapt the preceding car with slow speed can cause the reduction of the driver’s sensitivity, lead to the vehicle over-deceleration and aggravate the effects of velocity perturbations While in the synchronous flow phase, though the reaction delay caused by the driver’s sensitivity reduction can induce speed wave dissolving in essence, it increases the impact of disturbance on the traffic flow. 4. The large acceleration and deceleration tendency of an aggressive driver in the free flow phase always increase the influence of the velocity disturbance, while a conservative driver often weakens the influence. However, in the synchronized flow, since the high traffic density and the synchronization between vehicles is very strong, also the main factor which affects the driver’s speed choice is the distance among vehicles, therefore the effect of a driver’s behavior tendency to the spread of velocity perturbation is not obvious under this state.

A macroscopic traffic model with phase transitions and local point constraints on the flow

In this paper we present a macroscopic phase transition model with a local point constraint on the flow. Its motivation is, for instance, the modelling of the evolution of vehicular traffic along a road with pointlike inhomogeneities characterized by limited capacity, such as speed bumps, traffic lights, construction sites, toll booths, etc. The model accounts for two different phases, according to whether the traffic is low or heavy. Away from the inhomogeneities of the road the traffic is described by a first order model in the free-flow phase and by a second order model in the congested phase. To model the effects of the inhomogeneities we propose two Riemann solvers satisfying the point constraints on the flow.

Fatigue effect on phase transition of pedestrian movement: experiment and simulation study

How to model pedestrian movement is an intriguing problem in the area of statistical physics. As a common phenomenon of pedestrian movement, fatigue has a significant negative effect on pedestrian movement, especially when pedestrians move or run with heavy luggage, rescue the wounded in disaster, climb stairs and etc. According to the field observations and previous researches, fatigue coefficient is defined as the decrease of desired velocity in this study. However, previous researches lacked quantitative analysis of the effect of fatigue on pedestrian speed. It has been a great challenge to study the effect of fatigue on pedestrian flow, since pedestrians of heterogeneous walking abilities and the change of pedestrians’ moving properties need to be taken into consideration. Thus, at first, a series of pedestrian experiments, under three different conditions, were conducted to formulate the empirical relationship among fatigue, average free velocity, and walking distance. Then the empirical formulation of pedestrian fatigue was imported into the multi-velocity field floor cellular automata (FFCA) model for following pedestrian dynamics analysis. The velocity ratio was adjusted dynamically to adapt the change of pedestrians’ velocity due to fatigue. The fatigue, entrance flow rate and pedestrian’s initial desired velocity are found to have significant effects on the pedestrian flow. The space-time distributions of pedestrian density and velocity were explored in detail, with phase transition analyses from a free flow phase to a congestion phase. Additionally, the ‘density wave’ in the system can be observed if a certain ratio of burdened pedestrians lay in the high density region. The envelope of the ‘density wave’ reaches its maximum amplitude around the entrance position, and gradually diminishes away from the entrance.

Simple stochastic cellular automaton model for starved beds and implications about formation of sand topographic features in terms of sand flux

A simple stochastic cellular automaton model is proposed for simulating bedload transport, especially for cases with a low transport rate and where available sediments are very sparse on substrates in a subaqueous system. Numerical simulations show that the bed type changes from sheet flow through sand patches to ripples as the amount of sand increases; this is consistent with observations in flume experiments and in the field. Without changes in external conditions, the sand flux calculated for a given amount of sand decreases over time as bedforms develop from a flat bed. This appears to be inconsistent with the general understanding that sand flux remains unchanged under the constant-fluid condition, but it is consistent with the previous experimental data. For areas of low sand abundance, the sand flux versus sand amount (flux–density relation) in the simulation shows a single peak with an abrupt decrease, followed by a long tail; this is very similar to the flux–density relation seen in automobile traffic flow. This pattern (the relation between segments of the curve and the corresponding bed states) suggests that sand sheets, sand patches, and sand ripples correspond respectively to the free-flow phase, congested phase, and jam phase of traffic flows. This implies that sand topographic features on starved beds are determined by the degree of interference between sand particles. Although the present study deals with simple cases only, this can provide a simplified but effective modeling of the more complicated sediment transport processes controlled by interference due to contact between grains, such as the pulsatory migration of grain-size bimodal mixtures with repetition of clustering and scattering.

The effects of overtaking strategy in the Nagel-Schreckenberg model

Based on the Nagel-Schreckenberg (NS) model with periodic boundary conditions, we proposed the NSOS model by adding the overtaking strategy (OS). In our model, overtaking vehicles are randomly selected with probability $q$ at each time step, and the successful overtaking is determined by their velocities. We observed that (i) traffic jams still occur in the NSOS model; (ii) OS increases the traffic flow in the regime where the densities exceed the maximum flow density. We also studied the phase transition (from free flow phase to jammed phase) of the NSOS model by analyzing the overtaking success rate, order parameter, relaxation time and correlation function, respectively. It was shown that the NSOS model differs from the NS model mainly in the jammed regime, and the influence of OS on the transition density is dominated by the braking probability $p$