Lane Formation Research Articles

The Impact of Pedestrian Lane Formation by Obstacles on Fire Evacuation Efficiency in the Presence of Unfair Competition

After a fire breaks out, pedestrians simultaneously move towards the exit and quickly form a crowded area near the exit. With the intensification of pedestrians’ tendencies towards unfair competition, there is an increase in pushing and collisions within the crowd. The possibility of stampedes within the crowd also gradually increases. Analyzing the causes and psychological tendencies behind pedestrian pushing and collisions has a positive effect on reducing crowd instability and improving evacuation efficiency. This research proposes a modified social force model considering the unfair competition tendency of pedestrians. The model considers factors such as the gap between pedestrians’ actual and maximum achievable speed, effective radius, and their distance from the exit. In order to overcome the shortage of “deadlock” in the classical social force model in a high-density environment, this research introduces the feature of variable pedestrian effective radius. The effective radius of pedestrians dynamically changes according to the density of the surrounding crowd and queuing time. Through validation, the evacuation efficiency of this model aligns well with the actual situation and effectively reflects pedestrians’ pushing and squeezing behaviors in high-density environments. This research also analyzes how to strategically arrange obstacles to mitigate the exacerbating effect of unfair pedestrian competition on exit congestion. Five experiments were conducted to analyze how the relative position of obstacles and exits, the number of evacuation paths, and the size of the obstacle-free area before the exit affect evacuation efficiency in the presence of unfair pedestrian competition. The results show that evacuation efficiency can be improved when obstacles play a role in guiding or reducing the interaction of pedestrians in different queues. However, when obstacles hinder pedestrians, the evacuation efficiency is reduced to a certain extent.

Understanding pedestrian crowd dynamics on ramps: An empirical study triggered by Seoul Halloween crowd crush

Pedestrian safety on ramps demands greater attention compared to flat surfaces, as exemplified by a tragic crowd crush accident that claimed the lives of over 150 individuals on a densely populated ramp in South Korea in 2022. Understanding the dynamics of pedestrian movement on ramps is crucial for effectively managing mass events and daily pedestrian transportation. This paper presents an empirical study investigating bidirectional pedestrian flows on a simulated ramp with varying inclinations. Flow ratios, indicating the group size of major and minor flows in both directions, were examined. Results show that bidirectional pedestrian streams exhibit self-organizing behavior, characterized by the emergence of distinct lane formation phenomenon in both level and ramp walking scenarios. The shortest overall time required for pedestrians to exit the ramp was observed at a 3° inclination. As the ramp inclination increases, the disparities between upward and downward directions become more pronounced. Specifically, the uphill flow consistently exhibits a lower average speed compared to the downhill flow at the same inclination. In general, an increase in inclination is associated with a decrease in forward speed, an increase in lateral speed, and a greater utilization of handrails. Handrail plays a particularly important role in assisting pedestrians down very steep ramps. Furthermore, we found that the influence of flow ratio on walking parameters undergoes a change from level walking to ramp walking scenarios. Notably, for the same flow ratio, the results can vary significantly depending on whether the major flow is uphill or downhill. Our findings provide valuable insights into crowd management on ramps and hold significant implications for the safer design of ramps in subway stations, underpasses, and overpasses.

Lane formation in gravitationally driven colloid mixtures consisting of up to three different particle sizes.

Brownian dynamics simulations are utilized to study segregation phenomena far from thermodynamic equilibrium. In the present study, we expand upon the analysis of binary colloid mixtures and introduce a third particle species to further our understanding of colloidal systems. Gravitationally driven, spherical colloids immersed in an implicit solvent are confined in two-dimensional linear microchannels. The interaction between the colloids is modeled by the Weeks-Chandler-Andersen potential, and the confinement of the colloids is realized by hard walls based on the solution of the Smoluchowski equationin half space. In binary and ternary colloidal systems, a difference in the driving force is achieved by differing colloid sizes but fixed mass density. We observe for both the binary and ternary systems that a driving force difference induces a nonequilibrium phase transition to lanes. For ternary systems, we study the tendency of lane formation to depend on the diameter of the medium-sized colloids. Here we find a sweet spot for lane formation in ternary systems. Furthermore, we study the interaction of two differently sized colloids at the channel walls. Recently we observed that driven large colloids push smaller colloids to the walls. This results in small particle lanes at the walls at early simulation times. In this work we additionally find that thin lanes are unstable and dissolve over very long time frames. Furthermore, we observe a connection between lane formation and the nonuniform distribution of particles along the channel length. This nonuniform distribution occurs either alongside lane formation or in shared lanes (i.e., lanes consisting of two colloid types).

Analyzing factors causing deadlock events of bi-directional pedestrian flow when moving on stairs using a personal space model

Comprehending crowd dynamics on staircases is imperative for preventing accidents, particularly in emergency scenarios. In this context, our study delves into bi-directional pedestrian flow. When confronted with limited staircase space, the occurrence of two distinct lanes—one for upstairs and another for downstairs—is a common observation. However, there has been no quantitative investigation conducted to understand this phenomenon. To facilitate such an analysis, we employ a velocity-based personal space model that accurately reproduces the formation of upstairs and downstairs lanes in bi-directional staircases. The study of lane formation mechanisms and the exploration of factors influencing deadlock are essentially two sides of the same coin. This is due to the fact that, the occurrence of deadlock signifies a disruption in the anticipated lane behavior during counter flow. As a result, we have devised various scenarios to meticulously analyze the factors contributing to both deadlock formation and its subsequent performance. This involves manipulating parameters such as speed, speed dispersion, pedestrian count, initial density, right-hand preference weight, minimum personal space size, same-direction following intensity, and time step. The findings hold the potential to enhance the overall quality of service in stairway movement and offer significant contributions to the understanding and management of pedestrian behavior in such settings.

Lane formation in an active particle model with chirality for pedestrian traffic

We analyze the pattern formation in systems of active particles with chiral forces in the context of pedestrian dynamics. To describe the interparticle interactions, we use the standard social force model and supplement it with a new type of force that reflects chirality. We perform numerical simulations of two pedestrian flows moving in opposite directions along a corridor. We observe two dynamic phase transitions that occur for varying number densities of particles and strengths of the chirality force: one from disordered motion to multi-lane motion and another from multi-lane to two-lane motion. We develop a qualitative theory that describes the demarcation lines for these phase transitions in the phase diagram chirality-density. The results of our analysis agree fairly well with the simulation data. A comparison with previously reported experimental data has been provided. Our findings may find applications in urban and transportation-planning problems.

Robust spatial self-organization in crowds of asynchronous pedestrians.

Human crowds display various self-organized collective behaviours, such as the spontaneous formation of unidirectional lanes in bidirectional pedestrian flows. In addition, parts of pedestrians' footsteps are known to be spontaneously synchronized in one-dimensional, single-file crowds. However, footstep synchronization in crowds with more freedom of movement remains unclear. We conducted experiments on bidirectional pedestrian flows (24 pedestrians in each group) and examined the relationship between collective footsteps and self-organized lane formation. Unlike in previous studies, pedestrians did not spontaneously synchronize their footsteps unless following external auditory cues. Moreover, footstep synchronization generated by external cues disturbed the flexibility of pedestrians' lateral movements and increased the structural instability of spatial organization. These results imply that, without external cues, pedestrians marching out of step with each other can efficiently self-organize into robust structures. Understanding how asynchronous individuals contribute to ordered collective behaviour might bring innovative perspectives to research fields concerned with self-organizing systems.

Simulating the bi-directional pedestrian flow under high densities by a floor field cellular automaton model

In this paper we propose one floor field cellular automaton model, which can simulate the bi-directional pedestrian flow at high densities. Based on the model rules proposed by Nowak and Schadschneider, we make some modifications, including changes of cell size, realistic velocity configurations and extended lateral movement. The best parameters are determined by the results of sensitivity analysis. Some data extracted from pedestrian flow experiments, including the fundamental diagrams and the lane numbers after lane formation, are used for model validations. When the corridor width is 2m, the simulation results show that the fundamental diagrams of bi-directional flow are quantitatively similar to the experimental results, and the lane formation could be successful at high densities. By comparing with the statistical results in the experiments, we find the probabilities of the occurrence of different lanes are similar to the experimental results: two-lane and three-lane states usually emerge, while the probability for more lanes is low. The inhomogeneous distributions of pedestrians also could be observed. We think our model could be a good choice for simulating the lane formation process at high densities.

Pedestrian lane formation with following–overtaking model and measurement of system order

Pedestrian self-organizing movement plays a significant role in evacuation studies and architectural design. Lane formation, a typical self-organizing phenomenon, helps pedestrian system to become more orderly, the majority of following behavior model and overtaking behavior model are imprecise and unrealistic compared with pedestrian movement in the real world. In this study, a pedestrian dynamic model considering detailed modelling of the following behavior and overtaking behavior is constructed, and a method of measuring the lane formation and pedestrian system order based on information entropy is proposed. Simulation and analysis demonstrate that the following and avoidance behaviors are important factors of lane formation. A high tendency of following results in good lane formation. Both non-selective following behavior and aggressive overtaking behavior cause the system order to decrease. The most orderly following strategy for a pedestrian is to overtake the former pedestrian whose speed is lower than approximately 70% of his own. The influence of the obstacle layout on pedestrian lane and egress efficiency is also studied with this model. The presence of a small obstacle does not obstruct the walking of pedestrians; in contrast, it may help to improve the egress efficiency by guiding the pedestrian flow and mitigating the reduction of pedestrian system orderliness.

Lane formation of colloidal particles driven in parallel by gravity.

We investigate the lane formation in nonequilibrium systems of colloidal particles moving in parallel that are driven by the force of gravity. For this setup, an experimental implementation of a channel on a slope can be conceptualized. We employ the Brownian dynamics algorithm and confine the repulsive particles with hard walls based on the solution of the Smoluchowski equationin the half space. A difference of the driving force acting on the colloids could be achieved by using two spherical particle types with differing diameters but equal mass density. First, we investigate how a difference in the channel slope affects the lane formation of the systems, after which we analyze the lanes that formed. We find that the large particles push the small particles to the walls, resulting in exclusively small particle lanes at the walls. This contrasts the equilibrium state, where depletion forces push the larger particles to the walls. Additionally, we have a closer look at the mechanisms by which the lanes form. Finally, we find system parameter values that foster lane formation to lay the foundation for an experimental realization of our proposed setup. To round this off, we give an exemplary calculation of the slope angle needed to get the experimental system into a state of lane order. With the examination of lane order in systems that are driven in parallel, we hope to deepen our understanding of nonequilibrium order phenomena.

Spontaneous Chiral Symmetry Breaking and Lane Formation in Ferromagnetic Ferrofluids.

Ferromagnetic ferrofluids are synthetic materials consisting of magnetic nanoplatelets dispersed in an isotropic fluid. Their main characteristics are the formation of stable magnetic domains and the presence of macroscopic magnetization even in the absence of a magnetic field. Here, the authors report on the experimental observation of spontaneous stripe formation in a ferromagnetic ferrofluid in the presence of an oscillating external magnetic field. The striped structure is identified as elongated magnetic domains, which exhibit reorientation upon reversal of the magnetic field. The stripes are oriented perpendicular to the magnetic field and are separated by alternating flow lanes. The velocity profile is measured using a space-time correlation technique that follows the motion of the thermally excited fluctuations in the sample. The highest velocities are found in the depleted regions between individual domains and reach values up to several µms-1 . The fluid in adjacent lanes moves in the opposite directions despite the applied magnetic field being uniform. The formation of bidirectional flow lanes can be explained by alternating rotation of magnetic nanoparticles in neighboring stripes, which indicates spontaneous breaking of the chiral symmetry in the sample.

Simulation of bi-directional pedestrian flow under high densities using a modified social force model

The social force model has been widely used in pedestrian flow studies, but its limitations are also clear. Especially at high densities, it cannot simulate the lane formation in bi-directional flow. Therefore, in order to solve this problem, we propose a new modified social force model. The values of many parameters are reset by sensitivity analysis. In particular, we introduce a new parameter named deflection distance, which becomes a great help for modeling. Based on the video data collected from four large-scale experiments, the validity and robustness of our model are verified. The simulation results in the ring road show that the proposed model can describe the bi-directional movement well: the lane formation can be successful even when the density is as high as 9 ped/m2, and the fundamental diagrams after lane formation can be quantitatively similar to that reported in the experiments. In addition, the simulation results in the straight corridor also help to validate our model.

Lane formation in 3D driven pair-ion plasmas: II Non-Parallel External Forcing

In Part 1 of the companion paper, we have investigated lane formation dynamics of driven three-dimensional (3-D) pair-ion plasmas (PIP) in the presence of parallel external forcing using extensive Langevin dynamics (LD) simulation. In continuation of the work, in this Part 2, we investigate lane formation dynamics in the presence of non-parallel external forcing, and the effect of both constant and time varying forces are studied. In our model, positively charged PIP particles are pushed into the field direction by an external force $\boldsymbol{F}_{A} = E_A\cos \omega _At$ while the negatively charged PIP particles are pulled by an external force $\boldsymbol{F}_{B} = E_B\cos \omega _Bt$ in a direction perpendicular to the external force $\boldsymbol{F}_{A}$ . We show that in the case of non-parallel forces, the lanes are observed with an orientation (characterised by angle of inclination $\theta$ ) tilted in the direction of the force difference vector ( $\boldsymbol{F}_{A} - \boldsymbol{F}_{B}$ ). The instantaneous lane order parameter, order parameter with gradient of angle of inclination ( $\phi (\theta )$ ) and distribution function of $\Delta \theta$ have been implemented to characterise the phase transition. A spontaneous formation and breaking of lanes are observed when under the influence of time-varying forces. The effect is further investigated for three different situations: first, when $\omega _A \neq 0$ and $\omega _B = 0$ ; second, when $\omega _A = \omega _B \neq 0$ ; and third, for $\omega _A \neq \omega _B \neq 0$ . Our study reveals that for the first case, a periodic oscillation of angle of inclination is observed. If oscillating forces of the same frequency are applied, the oscillation in angle of inclination disappears, and spontaneous formation and breaking of lanes is observed. However, in the presence of forces with different frequencies, flipping of lane inclination between the positive and negative domain of $\theta$ is observed. Further, some aspects of the lane formation dynamics of a PIP system is also studied in the presence of an external magnetic field where the lane formation dynamics is found to be accelerated.

A force-based model for adaptively controlling the spatial configuration of pedestrian subgroups at non-extreme densities

The study of crowd dynamics has provided new insights into the understanding of human collective motion. However, most previous studies treated large-scale crowds as consisting of isolated individuals, but ignored the fact that pedestrian subgroups are prevalent in reality. With the increasing advancement of computer simulations, the critical role of subgroups in crowd modeling has been gradually recognized. Here, we develop a force-based model to reproduce the walking behaviors of pedestrian subgroups, in which the quantitative laws extracted from public datasets are incorporated for controlling their spatial configurations at different non-extreme densities. Numerical simulations indicate that our model achieves the simulation of pedestrian subgroups that coincides with empirical observations, and presents better simulation performance than existing subgroup models. The presence of pedestrian subgroups has also been confirmed to have certain effects on both fundamental diagrams and lane formation. Overall, this paper contributes a valuable framework to the modeling of pedestrian subgroups for guiding relevant implementations in potential application areas.

Lane formation in 3D driven pair-ion plasmas: I Parallel External Forcing

Lane formation dynamics of driven three-dimensional pair-ion plasmas (PIP) is investigated. Extensive Langevin dynamics simulation is performed to study the influence of an external electric field on the behaviour of the PIP system. In our model, one half of the particles are pushed into the field direction by an external force $\boldsymbol {F}_{A}$ while the other half are pulled into the opposite direction by an external force $\boldsymbol {F}_{B}$ . We show that if $\boldsymbol {F}_{A}$ and $\boldsymbol {F}_{B}$ are parallel, the system undergoes a non-equilibrium phase transition from a disordered state to a lane formation state parallel to the field direction with increasing field strength. The lanes are formed by the same kind of particles moving collectively with the field. The lane order parameter has been implemented to detect phase transition. Further, we show the lane formation in the presence of a time-varying external electric field. In particular, the effect of parallel forces are investigated. Unlike the previously reported two-dimensional case (Sarma, et al., Phys. Plasmas, vol. 27, 2020, p. 012106; Baruah, et al., J. Plasma Phys., vol. 87, issue 2, 2021, p. 905870202), for the time-varying electric field case, spontaneous formation and the breaking of lanes are not observed for all values of applied frequencies; however, the orderness varies and spontaneous formation and breaking of lanes is observed for values close to a critical frequency $\omega _c$ . Further, some aspects of the lane formation dynamics of a PIP system are also studied in the presence of an external magnetic field, which reveals that the presence of an external magnetic field accelerates the lane formation process and introduces a drift of the lanes in a direction perpendicular to both electric and magnetic fields.

Velocity-based model for pedestrian dynamics considering direction preferences

To reflect the direction preferences of the individual moving process, a velocity-based model is developed based on the Collision Free Speed (CFS) model. Our model used the local optimal direction selection algorithm based on a greedy algorithm that considers individual direction preferences for greater headway distance and dynamic willingness to turn during movement. The headway distance is calculated based on the principle of conflict avoidance, while gaussian distribution is used to fit individual willingness to turn and the optimal velocity (OV) function is used to determine the magnitude of the velocity. The concept of competition coefficient is proposed to quantitatively describe individual variability of direction preferences. The lane formation phenomena are reproduced in the bidirectional flow. In high-competition bottleneck, flow-width relation and pedestrian concentration fit better in the experimental data of our new model compared with the original CFS model. Furthermore, we analyze the competition coefficient and reproduce the typical phenomenon of fast-is-slow.

Limited visual range in the Social Force Model: Effects on macroscopic and microscopic dynamics

The Social Force Model has been widely used to simulate pedestrian dynamics. Its simplicity and ability to reproduce some collective patterns of behavior make it an adequate tool in the field of pedestrian dynamics. However, its ability to reproduce common macroscopic empirical results, such as pedestrian flows through a bottleneck and the speed-density fundamental diagram, has scarcely been studied. In addition, the effect of each parameter of the model on the dynamics of the system has rarely been shown. In this contribution, a comprehensive parameter-sensitivity analysis in the social force model is provided, and an optimal set is introduced, capable of reproducing both macroscopic experimental flow data and collision avoidance between pedestrians in simple trajectories on the microscopic scale. We show that the incorporation of asymmetric visual range models in the inter-pedestrian interactions is required for quantitative agreement. The model is also capable of showing collision avoidance in simple pedestrian trajectories and lane formation in non-crowded bidirectional pedestrian flows.

Multi-scale description of pedestrian collective dynamics with port-Hamiltonian systems

<abstract><p>Port-Hamiltonian systems (PHS) theory is a recent but already well-established modelling approach for non-linear physical systems. Some studies have shown lately that PHS frameworks are relevant for modelling and control of swarm and multi-agent systems. We identify in this contribution a general class of microscopic force-based pedestrian models that can be formulated as a port-Hamiltonian system. The pedestrian PHS has linear structure and dissipation components. Non-linear effects come from isotropic pedestrian interactions. Simulation results on a torus with disordered initial states show that the port-Hamiltonian pedestrian model can exhibit different types of dynamics. They range from relaxed speed models with no interaction, dynamical billiards, or crystallization dynamics to realistic pedestrian collective behaviors, including lane and strip formation for counter and crossing flow. The port-Hamiltonian framework is a natural multiscale description of pedestrian dynamics as the Hamiltonian turns out to be a generic order parameter that allows us to identify specific behaviours of the dynamics from a macroscopic viewpoint. Particular cases even enable through energy balance to determine the Hamiltonian behavior without requiring the tedious computation of the microscopic dynamics. Using PHS theory, we systematically identify a critical threshold value for the Hamiltonian, which relies only on exogenous input and can be physically interpreted.</p></abstract>

Analysis of movement behavior of pedestrian social groups through a bottleneck

Pedestrian social groups are an essential part of a crowd. In emergency situations, they may become principal victims during evacuation from buildings, such as bottlenecks in corridors. However, empirical data on the dynamics of social groups through bottlenecks are limited. In this paper, a controlled experiment was performed to study movement features of social groups through a bottleneck with different widths (i.e., 0.8, 1.4 and 2.4 m). There were 60 participants in the experiment, forming four crowd compositions (i.e., 60 groups of singles, 30 groups of dyads, 20 groups of triads and 15 groups of four-person groups). After extracting their movement trajectories in the video recordings, offset angles, passing performance, interpersonal distances and angles in group walking, relative positions in social groups, etc. were analyzed. The results highlight that the negative effect of bottleneck width on instantaneous speed for larger groups is more significant than for smaller groups. The cooperative behavior of large groups is beneficial to the instantaneous speed of pedestrians under wide bottlenecks. The size of the groups has no evident influence on lane formation. Singles adjust their movement directions more flexibly, and the offset angles of large groups are smaller. Good passing performance can be reflected in large groups through wide bottlenecks. It is proved that interpersonal distances and angles between group members depend on the group size, bottleneck width and pedestrian flow state (free and congested flow). Under the limitation of narrow bottlenecks, the walking structures of large groups can lead to diverse walking structures. The phenomenon of recurring splitting and rejoining of pedestrian social groups can be observed. These findings are helpful for crowd management in buildings.

The effect of obstacle layouts on regulating luggage-laden pedestrian flow through bottlenecks

Previous studies found that regulating luggage-laden pedestrian flow helps to reduce the negative influence caused by luggage. Inspired by this, we experimentally study the effect of obstacle layout on regulating luggage-laden pedestrian flow. Five distances between the obstacle and exit are considered. The main findings are as follows: (i) The obstacle position affects the lane formation but does not affect the spatial distance between luggage-laden pedestrians and the boundary. It is revealed that the exact distance parameter can be implied regardless of the distance from the exit when modelling luggage-laden pedestrian movement. (ii) The average speed at the bottleneck increases with the distance between the exit and obstacle regardless of the pedestrian with and without luggage. The sooner the luggage-laden crowd is regulated, the higher the crowd speed can be at the bottleneck. (iii) The deviation angles all rise immediately before the exit, which means that the actual movement direction of pedestrians before the exit is not towards the midpoint of the exit. In addition, the inflection point of the deviation angle is approximately 0.5 m from the exit regardless of the obstacle position, which is the validation parameter of the luggage-laden crowd modelling. The results concluded that luggage-laden pedestrian flow could be regulated, and quantitative parameters were proposed to model luggage-laden pedestrian movement through the bottleneck.

Static floor field construction and fine discrete cellular automaton model: Algorithms, simulations and insights

While cellular automaton (CA) models have a broad range of applications in the field of pedestrian dynamics, there are still three significant issues (the efficient and accurate construction of the static floor field (SFF), the insufficient simulation accuracy, and the discretization effect) that have not been resolved or fully clarified yet. This work aims to tackle these challenges. First, a novel approximate algorithm that resolves the dilemma between accuracy and efficiency is proposed to construct the SFF, based on which the static navigation field is created by the proposed method. Then, a novel fine discrete CA model based on the desired direction is developed to capture the locomotion movement behaviour. The novel SFF construction algorithm and locomotion movement model are (theoretically and/or numerically) validated and compared to the state-of-the-art approaches in manifold scenarios. Later on, systematic simulation analyses are conducted to investigate the discretization effect at the micro and macro levels. The assessment metrics show that the performance of the proposed algorithm and model is superior over that of the state-of-the-art approaches. The proposed model can resolve the well-known diagonal movement artefact in the existing CA models and reproduce crowd movement and self-organized lane formation observed empirically. It is found that the non-isotropic SFF results in significantly biased and unrealistic evacuation movement. Moreover, the discretization degree is found to significantly affect the individual and crowd movement simulation outcomes, and the magnitude and direction of its effect depend on the used model and the setup of the scenarios. The proposed algorithm and model are promising tools in pedestrian modelling and simulation. The findings provide fresh insights into the development and application of CA models.