Model For Bidirectional Pedestrian Flow Research Articles

Modeling bidirectional pedestrian flow with the perceived uncertainty of preceding pedestrian information

Pedestrian flow models contribute to the effective design and operation of pedestrian spaces. In real traffic, pedestrians usually adjust their walking state in the movement procession according to perceptual information. Subject to the human capability, certain errors would exist between the perceptual information and the real traffic information, which can greatly affect the pedestrian flow performance. This paper proposes a bidirectional pedestrian flow model considering the effect of perceived uncertainty of preceding pedestrian information. In the linear and nonlinear stability analysis, we derive the stability criterion and modified Korteweg–de Vries (mKdV) equation of the proposed model. The kink–antikink solitary wave solution can be acquired via solving the above mKdV equations, which provides insight into the essential property of the formation and propagation of traffic jams near the neutral stability curve. Numerical examples demonstrate that the uncertainty terms and the perception time of pedestrians directly affect the pedestrian congestion.

Kinetic Model for Bidirectional Pedestrian Flow in an Evacuation Scenario

Kinetic Model for Bidirectional Pedestrian Flow in an Evacuation Scenario

A new lattice hydrodynamic model for bidirectional pedestrian flow with consideration of pedestrians’ honk effect

Understanding the pedestrian behavior contributes to traffic simulation and facility design/redesign. In practice, the interactions between individual pedestrians can lead to virtual honk effect, such as urging surrounding pedestrians to walk faster in a crowded environment. To better reflect the reality, this paper proposes a new lattice hydrodynamic model for bidirectional pedestrian flow with consideration of pedestrians’ honk effect. To this end, the concept of critical density is introduced to define the occurrence of pedestrians’ honk event. In the linear stability analysis, the stability condition of the new bidirectional pedestrian flow model is given based on the perturbation method, and the neutral stability curve is also obtained. Based on this, it is found that the honk effect has a significant impact on the stability of pedestrian flow. In the nonlinear stability analysis, the modified Korteweg–de Vries (mKdV) equation of the model is obtained based on the reductive perturbation method. By solving the mKdV equation, the kink-antikink soliton wave is obtained to describe the propagation mechanism and rules of pedestrian congestion near the neutral stability curve. The simulation example shows that the pedestrians’ honk effect can mitigate the pedestrians crowding efficiently and improve the stability of the bidirectional pedestrian flow.

Memory’s effect on bidirectional pedestrian flow based on lattice hydrodynamic model

In this paper, an extended lattice hydrodynamic model for bidirectional pedestrian flow is proposed to analyze the effect of pedestrian’s memory during a period of time on the pedestrian flow. The effect of pedestrian’s memory during a period of time is investigated by using analytical and numerical methods. The linear stability analysis indicates that the time length of pedestrian’s memory has an important effect on the stability of pedestrian flow. With increasing of the time length of pedestrian’s memory, pedestrian flow will become unstable and pedestrian congestion appear. By the use of nonlinear analysis method, three typical nonlinear wave equations including Burgers, Korteweg–de Vries (KdV) and modified Korteweg–de Vries (MKdV) equations are derived to describe the evolutions of pedestrian flow with a small amplitude disturbance in the stable, meta-stable and unstable regions, respectively. The theoretical results show that jams may be aggravated by considering the effect of pedestrian’s memory with a time length. Numerical simulations are carried out in order to clarify the theoretical results.

Impact of Intersecting Angles on Evacuation Efficiency of Pedestrian Flows in High Volume: A Case Study in Metro Station

The intersection of pedestrian flows is a general phenomenon in daily pedestrian traffic and emergency evacuation. However, lacking of effective controls in crowed areas will result in pedestrian deceleration, stopping, and even threats to safety in evacuation. This paper focused on exploring the influence of different intersecting angles on evacuation efficiency of pedestrian flows in high volume. Through establishing a bidirectional pedestrian flow model with different intersecting angles for a busy metro station in China based on the social force model, two factors, namely the impact between pedestrians and the conflict frequency, were firstly proposed and validated as that playing major roles in influencing the evacuation efficiency during the pedestrian intersection. With the case study, it is found that the best intersecting angle is 120 degree and angles between 40 and 80 degree are unfavorable in optimizing the average crowd speed and the crowd density. The results are verified based on the comparative analysis with some existing experimental results. The outcomes of this work can offer some guidelines to control the intersection of pedestrian flows during evacuation and can make contributions to a proposal for the related, optimized design of a structure to increasing the evacuation efficiency of a dense crowd.

An Investigation Capability Model for Bidirectional Pedestrian Flow

<p class="zhengwen"><span lang="EN-GB">The pedestrian traffic flow in bidirectional walkways is very crucial aspect influenced by the level of pedestrians’ decisions.</span><span lang="EN-GB"> In this article, the authors show that the simulated pedestrians walking based on crowd dynamics models of low level mechanism of navigation (operational level) are short-sighted in avoiding counter flow. Such limitation resulted in unrealistic formation of motion in bidirectional flow, that the movement is less systematic and the lanes are less coherent than what in real situation. To obtain a more representative model, the authors improve the investigation capability model as a tactical decision model to be incorporated into a crowd dynamics model to reproduce better formation of motion. This is accomplished by granting the pedestrians the ability to investigate the macroscopic behaviors in their investigation areas and make decisions for convenience flow. The new model considers the average density and flow inside such areas and models their effect on the pedestrians' decisions. Simulations are performed to validate the work qualitatively by tracing the behavior of the simulated pedestrians and studying the impact of this behavior on the self-organized phenomenon: lane formation. Furthermore, the fundamental diagram of bidirectional flow is reproduced and compared with experimental fundamental diagrams.</span></p>

A novel lattice hydrodynamic model for bidirectional pedestrian flow with the consideration of pedestrian’s memory effect

Due to the bad environmental conditions such as bad weather, smoky condition, insufficient light, it is difficult for a pedestrian to capture the precise position of others in these situations. Thus, memory effect could be influential and the pedestrian may walk with his/her memory. Considering the effect of pedestrian’s memory, an extended lattice hydrodynamic model for bidirectional pedestrian flow is proposed in this paper. The stability condition is obtained by the use of linear stability analysis. It is shown that the memory effect term can significantly reduce the stability region on the phase diagram. Based on nonlinear analysis method, the Burgers, Korteweg-de Vries and modified Korteweg-de Vries equations are derived to describe the shock waves, soliton waves and kink–antikink waves in the stable, metastable and unstable regions, respectively. The theoretical results show that jams may be aggravated by considering the effect of pedestrian’s memory. Numerical simulations are carried out in order to verify the theoretical results.

Experiment and simulation of the bidirectional pedestrian flow model with overtaking and herding behavior

In order to effectively depict the characteristics of bidirectional pedestrian flow, a novel pedestrian flow model is proposed based on cellular automata. At first, according to direction gain, velocity gain and herding gain, the calculation formula of target position is defined, and the walking rules by combining overtaking behavior and herding behavior are given in the model. Meanwhile, the actual channel is used for experiments, where the self-organizing effect formed by pedestrian flow is observed. The simulation platform is established to study the key factors influencing pedestrian flow characteristics. The numerical analysis results showed that when the pedestrian density in the channel reached to the critical degree, the overtaking behavior can easily produce jamming. Moreover, pedestrians' rational choice is good for relieving jamming.

Lattice hydrodynamic model for bidirectional pedestrian flow with the consideration of pedestrian density difference

Considering the effect of density difference, an extended lattice hydrodynamic model for bidirectional pedestrian flow is proposed in this paper. The stability condition is obtained by the use of linear stability analysis. It is shown that the stability of pedestrian flow varies with the reaction coefficient of density difference. Based on nonlinear analysis method, the Burgers, Korteweg–de Vries (KdV) and modified Korteweg–de Vries (MKdV) equations are derived to describe the triangular shock waves, soliton waves and kink–antikink waves in the stable, metastable and unstable regions, respectively. The results show that jams may be alleviated by considering the effect of density difference. The findings also indicate that in the process of building and subway station design, a series of auxiliary facilities should be considered in order to alleviate the possible pedestrian jams.

A new lattice hydrodynamic model for bidirectional pedestrian flow with the consideration of pedestrian’s anticipation effect

Considering the effect of pedestrian’s anticipation, an extended lattice hydrodynamic model for bidirectional pedestrian flow with passing is proposed in this paper. The stability condition is obtained by the use of linear stability analysis. It is shown that the anticipation term can significantly enlarge the stability region on the phase diagram, and the passing term may reduce the stability region and aggravate the pedestrian jam. Based on nonlinear analysis method, the Burgers, Korteweg–de Vries and modified Korteweg–de Vries equations are derived to describe the shock waves, soliton waves and kink–antikink waves in the stable, metastable and unstable region, respectively. The theoretical results show that jams may be alleviated efficiently by considering the effect of pedestrian’s anticipation. Numerical simulations are carried out in order to verify the theoretical results.

A new lattice hydrodynamic model for bidirectional pedestrian flow with the consideration of lateral discomfort

Pedestrians always walk optionally and disorderly. Considering the visual angle and other factors, pedestrians do not walk orderly even in a crowded environment, such as railway entrance. The deviation may cause discomfort to the neighboring pedestrian, which is referred to lateral discomfort (or lateral friction). Considering the effect of lateral discomfort, an extended lattice hydrodynamic model for bidirectional pedestrian flow is proposed in this paper. The stability condition is obtained by the use of linear stability analysis. It is shown that the stability of pedestrian flow varies with the coefficient of the lateral discomfort. The Burgers, Korteweg–de Vries and modified Korteweg–de Vries equations are derived to describe the triangular shock waves, soliton waves and kink–antikink waves in the stable, metastable and unstable region, respectively. The results show that jams may be alleviated by reducing the lateral discomfort.

A bidirectional pedestrian flow model with the effect of friction parameter

In this paper, a new lattice model for bidirectional pedestrian flow on single path which involves the effect of friction parameter is presented. Linear stability analysis is used to obtain the stability condition. The modified Korteweg–de Vries (mKdV) equation and time-dependent Ginzburg–Landan (TDGL) equation are deduced by means of the reductive perturbation method respectively. Further, the influence of the friction parameters upon pedestrian flow has been discussed. Our results also indicate that pedestrians moving along both directions uniformly are most stable.

A Lattice Model for Bidirectional Pedestrian Flow on Gradient Road

Ramps and sloping roads appear everywhere in the built environment. It is obvious that the movement pattern of people in the sloping path may be different as compared with the pattern on level roads. Previously, most of the studies, especially the mathematical and simulation models, on pedestrian movement consider the flow at level routes. This study proposes a new lattice model for bidirectional pedestrian flow on gradient road. The stability condition is obtained by using linear stability theory. The nonlinear analysis method is employed to derive the modified Korteweg-de Vries (mKdV) equation, and the space of pedestrian flow is divided into three regions: the stable region, the metastable region, and the unstable region respectively. Furthermore, the time-dependent Ginzburg—Landan (TDGL) equation is deduced and solved through the reductive perturbation method. Finally, we present detailed results obtained from the model, and it is found that the stability of the model is enhanced in uphill situation while reduced in downhill situation with increasing slope.

A new lattice hydrodynamic model for bidirectional pedestrian flow considering the visual field effect

In this paper, a new lattice hydrodynamic model for bidirectional pedestrian flow is proposed by considering the pedestrian’s visual field effect. The stability condition of this model is obtained by the linear stability analysis. The mKdV equation near the critical point is derived to describe the density wave of pedestrian jam by applying the reductive perturbation method. The phase diagram indicates that the phase transition occurs among the freely moving phase, the coexisting phase, and the uniformly congested phase below the critical point \(a_c\). Furthermore, the analytical results show that the visual field effect plays an important role in jamming transition. To take into account the visual information about the motion of more pedestrian in front can improve efficiently the stability of pedestrian system. In addition, the numerical simulations are in accordance with the theoretical analysis.

The Korteweg-de Vires equation for the bidirectional pedestrian flow model considering the next-nearest-neighbor effect

This paper focuses on a two-dimensional bidirectional pedestrian flow model which involves the next-nearest-neighbor effect. The stability condition and the Korteweg-de Vries (KdV) equation are derived to describe the density wave of pedestrian congestion by linear stability and nonlinear analysis. Through theoretical analysis, the soliton solution is obtained.

The Korteweg-de Vires Equation for Bidirectional Pedestrian Flow Model

This paper focuses on a two-dimensional bidirectional pedestrian flow model which involves the next-nearest-neighbor effect. The Korteweg-de Vries equation is derived to describe the density wave of pedestrian congestion by nonlinear analysis. The soliton solution is obtained.

Numerical simulation of a continuum model for bi-directional pedestrian flow

An algorithm for an extended reactive dynamic user equilibrium model of pedestrian counterflow as a continuum is developed. It is based on a cell-centered high-resolution finite volume scheme with a fast sweeping method for an Eikonal-type equation on an orthogonal grid. A high-order total variation diminishing Runge–Kutta method is adopted for the time integration of semi-discrete equations. The numerical results demonstrate the rationality of the model and efficiency of the algorithm. Some crowd pedestrian flow phenomena, such as dynamic lane formation in bi-directional flow, are observed which are helpful for a global comprehension of pedestrian dynamics. Also, the model can be utilized with different potential applications.

Bi-directional pedestrian flow model with traffic convention

In this paper, we extend a cellular-automata model recently proposed by Baek et al. to simulate traffic dynamics of the bi-direction pedestrians. And we present two improved strategies for the moving rules of the pedestrians. Numerical studies of average velocity-density diagram, spatial density distribution and position distribution of the pedestrians are given. We find that the two improved strategies can not only increase the average velocity of pedestrian flow, but also improve the utilization of the road, especially for the central region, reduce the degree of congestion, and avoid the occurrence of serious congestion. The two improved strategies have more comprehensive considerations of psychological and behavioral characteristics of pedestrians, which are also proper to simulate bi-directional pedestrian dynamics under a high traffic density.

Dynamic continuum model for bi-directional pedestrian flows

The development of a bi-directional pedestrian-flow model based on the reactive dynamic user equilibrium principle and the look-ahead behaviour that induces a viscosity effect on movement patterns is described. The pedestrian density in this model is governed by the conservation law, in which the flow flux is implicitly dependent on the density through the stationary Hamilton-Jacobi equation that is solved using a pseudo time-marching approach. A solution algorithm is proposed and a numerical example is used to demonstrate the effectiveness of the methodology.