Unidirectional Pedestrian Flow Research Articles

Single-file pedestrian flow experiments under high-density conditions

In order to investigate the mechanism of uni-directional pedestrian flow, we organize one single-file flow experiment on a ring corridor. With 203 participants, the maximum global density reaches 4ped/m. The fundamental diagrams are given, and compared with that of the single-file experiments held in other countries. We find the pedestrians’ velocities in our experiment are close to the Indian results, and larger than German results. In the time-headway distributions, the peak gradually disappears with the increase of density. At medium densities, the upstream propagation of stop-and-go waves can be observed. The calculated propagation velocity is about 0.4∼0.5 m/s. At extremely high densities, the transition between stopping state and moving state can occur, which is similar to that found in uni-directional experiments with wider system width. In these phenomena, we find there exists one critical density, which is about 3ped/m. All these results can help to learn more about the essence of single-file pedestrian flow.

Characterization of Collision Avoidance in Pedestrian Crowds

The avoidance behavior of pedestrians was characterized in the present paper by simulating the movement of crowds in both unidirectional and bidirectional pedestrian flow. A phase change of alternative lane formation observed in real bidirectional pedestrian flows has been studied, where pedestrians tended to evade individuals in counterflow and simultaneously keep a certain distance from each other in the uniform pedestrian flow when the counterflow disappeared. What is more, the comparison between the effect of evading and pushing behavior on evacuation has been investigated in the room egress scenario. Additionally, the evading and overtaking behavior of fast pedestrians have also been simulated in heterogeneous crowds. The performance of the proposed model was compared to the experimental data and the results obtained using other evacuation models. Numerical results showed that both the phase change of alternative lane formation in bidirectional pedestrian flow and the effective evading behavior in unidirectional pedestrian flow were conductive to reduce the evacuation time of pedestrian crowds. Even though pushing behavior of fast pedestrians seemed to improve the flow through the wide exit, it might lead to the panic and other negative effect on the crowds, such as crowds trample. The proposed model in this paper could provide a theoretical basis for the pedestrian crowd management during emergency evacuation.

An optimization-based overtaking model for unidirectional pedestrian flow

We propose an optimization-based model for simulating the overtaking behaviour in the unidirectional pedestrian flow. A ‘visual area’ is introduced so that agents could receive the information regarding their surroundings and react by choosing one of three options: to move straight on, to dodge to the left, or to dodge to the right. And a side preference of each pedestrian for evading and overtaking is implemented based on traffic ‘social norms’. The model was validated by reproducing the experimentally obtained pedestrian flow patterns. The effects of the initial pedestrian formation on overtaking behaviour and the evacuation time have been analysed in different geometries. The results show that pedestrian flow patterns after overtaking are obviously influenced by both the initial positions and density of the slow pedestrians in the front. Phase changes of pedestrian formation are observed in both experiment and simulations. On the other hand, for sparse pedestrian crowds, the egress time of the fast individuals is mainly impacted by the horizontal distance between the initial positions of the slow pedestrians in the front, especially in the geometry with a bottleneck.

Microscopic events under high-density condition in uni-directional pedestrian flow experiment

In order to investigate the pedestrian behaviors under high-density condition, we organize one experiment with 278 pedestrians, and the global density as high as 9 ped/(m̂2) is reached. The experiment is filmed by one unmanned aerial vehicle (UAV). In the experimental video, we find many interesting microscopic events. They can be categorized into two types: the interactions with the boundaries (Type A) and the absentmindedness (Type B). Among them, ”the staffs arrange the stools” (Event A1) and ”the pedestrians play with mobile phones” (Event B1) can be measured and evaluated. We find the time series data of Event A1 and B1 have strong relationship with the evolution of pedestrian flow. The results in hyper-congested state and that in over-congested state are qualitatively different, and the critical density is about 8 ped/(m̂2). At the same time, the averaged results of both Event A1 and B1 qualitatively change at about 6 ped/(m̂2), which is the critical density between over-congested state and congested state. Why different pedestrian flow data have different maximum densities also can be explained by this critical value. Therefore, the bridge between pedestrian dynamics and individual pedestrian’s behaviors is built in this study.

A least-effort principle based model for heterogeneous pedestrian flow considering overtaking behavior

In the context of global aging, how to design traffic facilities for a population with a different age composition is of high importance. For this purpose, we propose a model based on the least effort principle to simulate heterogeneous pedestrian flow. In the model, the pedestrian is represented by a three-disc shaped agent. We add a new parameter to realize pedestrians' preference to avoid changing their direction of movement too quickly. The model is validated with numerous experimental data on unidirectional pedestrian flow. In addition, we investigate the influence of corridor width and velocity distribution of crowds on unidirectional heterogeneous pedestrian flow. The simulation results reflect that widening corridors could increase the specific flow for the crowd composed of two kinds of pedestrians with significantly different free velocities. Moreover, compared with a unified crowd, the crowd composed of pedestrians with great mobility differences requires a wider corridor to attain the same traffic efficiency. This study could be beneficial in providing a better understanding of heterogeneous pedestrian flow, and quantified outcomes could be applied in traffic facility design.

Simulating the special features of fundamental diagrams observed by Mori-Tsukaguchi and Helbing et al in uni-directional pedestrian flow

The pedestrian flow dynamics are very complex. Even the fundamental diagrams of uni-directional pedestrian flow exhibit diversity. In the empirical data of Mori-Tsukaguchi and Helbing et al, the flows drop drastically with medium densities and nearly keep constant with high densities, which is different from many other empirical and experimental results. To simulate these special phenomena with cellular automaton (CA) models, we use the new configuration, in which the occupied area of each pedestrian is 0.4 m * 0.2 m. The modeling framework is based on the ITP model, which is a two-process CA model presented in our previous paper, and one new rule is added: when the local density behind is below a threshold, pedestrians prefer to keep a certain front gap. With the simple rule, the new fundamental diagrams can qualitatively coincide with the empirical facts of Mori-Tsukaguchi and Helbing et al. Some other results, including simulation patterns and velocities of pedestrians can further confirm the validity of the new rule, and give some explanations for the diversity of different empirical data. These results are useful contributions for pedestrian flow modeling.

Modeling and simulation of pedestrian dynamical behavior based on a fuzzy logic approach

This study proposes a fuzzy logic approach to model and simulate pedestrian dynamical behaviors, which takes full advantage of human experience and knowledge and perceptual information obtained from interactions with surrounding environments. First, the radial-based method is adopted to represent the physical space. A pedestrian’s visual field, defined as a fan-shaped area with a certain visual distance and visual angle, is divided into five sectors. Then, the motion states of a pedestrian are determined by the integration of recommendations of local obstacle-avoiding behavior, regional path-searching behavior and global goal-seeking behavior with mutable weighting factors at three different scopes. These elementary behaviors and weighting’s assignment principle are modeled as fuzzy inference systems with the input information of a pedestrian’s perception toward surrounding environments. A pedestrian is guided to avoid the front obstacles and select the lowest negative energy path by local obstacle-avoiding behavior and regional path-searching behavior, respectively. The global goal-seeking behavior makes a pedestrian has a tendency of moving in direction of his/her goal regardless of external environments. The magnitudes of weighting factors are adjusted automatically to coordinate three elementary behaviors and resolve potential conflicts. At last, the effectiveness of the proposed model is validated by simulations of crowd evacuation, unidirectional and bidirectional pedestrian flows. The simulation results are analyzed from both qualitative and quantitative aspects, which indicate that the fuzzy logic based pedestrian model can get true reappearance of self-organization phenomena such as ‘arching and clogging’, ‘faster-is-slower effect’ and ‘lane formation’, and the fundamental diagrams are in matching with a large variety of empirical and experimental data. A further study finds that walking habits have negligible influence on the fundamental diagrams of bidirectional pedestrian flow at least for densities of ρ < 3p/m2.

Modeling lane formation in pedestrian counter flow and its effect on capacity

For the development of a sustainable transportation system, a modal shift from automobiles to walking or transit is encouraged. In order to design a more convenient and comfortable walking environment, a sound modeling of pedestrian flow is necessary. Most of the previously developed pedestrian flow models well described the macroscopic features of unidirectional pedestrian flow. However, in pedestrian counter-flow, interactions among conflicting pedestrians are so complicated and existing flow models fall short in explaining some features of pedestrian behaviors. A spontaneous lane formation, which helps to reduce conflicts and increase travel speeds, is a commonly observed feature of a crowded pedestrian flow. This paper develops a social-force based pedestrian model, which can explain the lane formation phenomenon. From the simulation results, it turns out that the ‘following effect' and ‘evasive effect' mainly contribute to the lane formation. Higher capacity and travel speed are obtained when pedestrians are more congregated.

Modeling Unidirectional Pedestrian Movement: An Investigation of Diffusion Behavior in the Built Environment

Unidirectional pedestrian movement is a special phenomenon in the evacuation process of large public buildings and urban environments at pedestrian scale. Several macroscopic models for collective behaviors have been built to predict pedestrian flow. However, current models do not explain the diffusion behavior in pedestrian crowd movement, which can be important in representing spatial-temporal crowd density differentiation in the movement process. This study builds a macroscopic model for describing crowd diffusion behavior and evaluating unidirectional pedestrian flow. The proposed model employs discretization of time and walking speed in geometric distribution to calculate downstream pedestrian crowd flow and analyze movement process based on upstream number of pedestrians and average walking speed. The simulated results are calibrated with video observation data in a baseball stadium to verify the model precision. Statistical results have verified that the proposed pedestrian diffusion model could accurately describe pedestrian macromovement behavior within the margin of error.

Modeling and Simulation on Unidirectional Pedestrian Flow Based on Cellular Automata

The CA-based Model of unidirectional pedestrian flow simulation is established. Model takes into account pedestrian forward, change lanes , side forward, backward , away from the dense crowd behavior. Simulation research and analyzed the relationship between pedestrian flow speed ,flow speed, flow , without moving the proportion of pedestrians and the pedestrian density in different pedestrian density. The results showed that: unidirectional pedestrian flow with the pedestrian density increases, there will be two thresholds K1 and K2. Pedestrian flow velocity will appear slight and obvious decrease after these two thresholds. Pedestrian flow traffic reaches its maximum value at K2. The proportion of unmoving pedestrians will increase and the increased amplitude increases when it reaches at the two thresholds K1 and K2.

A Two-Dimensional Optimal Velocity Model for Unidirectional Pedestrian Flow Based on Pedestrian's Visual Hindrance Field

Modeling and simulation of pedestrian movement is a feasible and effective way to evaluate evacuation facilities and risk. Inspired by the visual field and movement characteristic of pedestrians, we developed a 2-D continuous model that integrates a self-slowing, local direction-changing mechanism, and visual hindrance information. The model allows for the movement in continuous space and time, only controlled by simple kinematic equations and visual hindrance distribution. In order to get the parameters of the kinematic equations, we conducted controlled experiments, collected empirical data, and obtained velocity-changing and direction-changing relations. We then validate the model by simulating three experimental scenarios, i.e., passage, bottleneck, and classroom evacuation. It is found that some typical phenomena such as the stop-and-go waves in the passage and lane formation in the bottleneck can be reproduced. The obtained fundamental diagram and specific flow agree with classic conclusions and experimental measures very well. It is hoped that the idea of this study may be helpful in promoting the modeling and simulation study of pedestrian flow.

Effect of Aspiration and Mean Gain on the Emergence of Cooperation in Unidirectional Pedestrian Flow

When more than one pedestrian want to move to the same site, conflicts appear and thus the involved pedestrians play a motion game. In order to describe the emergence of cooperation during the conflict resolving process, an evolutionary cellular automation model is established considering the effect of aspiration and mean gain. In each game, pedestrian may be gentle cooperator or aggressive defector. We propose a set of win-stay-lose-shrift (WSLS) like rules for updating pedestrian's strategy. These rules prescribe that if the mean gain of current strategy between some given steps is larger than aspiration the strategy keeps, otherwise the strategy changes. The simulation results show that a high level aspiration will lead to more cooperation. With the increment of the statistic length, pedestrians will be more rational in decision making. It is also found that when the aspiration level is small enough and the statistic length is large enough all the pedestrian will turn to defectors. We use the prisoner's dilemma model to explain it. At last we discuss the effect of aspiration on fundamental diagram.

The effect of overtaking behavior on unidirectional pedestrian flow

We present a model of overtaking behavior that can be used to simulate unidirectional pedestrian flow in routine. All pedestrians have the ability to determine whether or not to overtake other pedestrians according to their desired velocity and position. Although existing models such as cellular automata models, lattice gas models, social force models, etc., can be used to predict evacuation performance, most of these models are either computationally inefficient or do not account for some crucial elements of human behavior in a moving crowd. Furthermore, these models use either empirical equations developed from experiments or mechanical system analogies to determine movement decisions. The pedestrian flow patterns simulated by these models may deviate significantly from reality. In reality, pedestrians walk at different velocities and pedestrians with a higher walking velocity are accustomed to overtaking other pedestrians with a lower walking velocity and this paper aims to mimic this behavior as the original social force model developed by Helbing et al. does not reflect this pattern of collective pedestrian behavior. In this paper, we propose modifications of the social force model that reflects how overtaking behavior operates in routine. The comparison of the pedestrian flow pattern between the original social force model and the modified social force models with the real data collected by the camcorder is also performed in order to demonstrate our modified social force model can be used to achieve reasonable simulations of overtaking behavior among pedestrians.

Pedestrian flow dynamics in a lattice gas model coupled with an evolutionary game

This paper studies unidirectional pedestrian flow by using a lattice gas model with parallel update rules. Game theory is introduced to deal with conflicts that two or three pedestrians want to move into the same site. Pedestrians are either cooperators or defectors. The cooperators are gentle and the defectors are aggressive. Moreover, pedestrians could change their strategy. The fundamental diagram and the cooperator fraction at different system width W have been investigated in detail. It is found that a two-lane system exhibits a first-order phase transition while a multilane system does not. A microscopic mechanism behind the transition has been provided. Mean-field analysis is carried out to calculate the critical density of the transition as well as the probability of games at large value of W. The spatial distribution of pedestrians is investigated, which is found to be dependent (independent) on the initial cooperator fraction when W is small (large). Finally, the influence of the evolutionary game rule has been discussed.

Macroscopic Simulation of Pedestrian Flow through a Bottleneck

The paper deals with the macroscopic type modelling of the unidirectional pedestrian flow moving through a corridor with a bottleneck. The macroscopic model of pedestrian flow is the two-dimensional Lighthill-Whitham-Richards model described as a mass conservation equation. The characteristic feature of pedestrian route choice is that pedestrians in the corridor try to minimize the instantaneous travel time and improve the comfort level. The model equation is solved numerically by the discontinuous Galerkin method. Numerical results visualize the ability of the model to predict macroscopic characteristics of pedestrian flow through bottlenecks, i.e. the spatial distribution of the flow speed and density, as well as the formation and dissipation of traffic congestion in the corridor. They also validate that congestion is caused by the limited capacity of the bottleneck.

Pedestrian flow in a lattice gas model with parallel update

This paper studies unidirectional pedestrian flow in a channel using the lattice gas model with parallel update rule. The conflict (i.e., several pedestrians intend to move to the same site) is solved by introducing probabilities as in floor field models. The fundamental diagram (FD) is investigated and it is found that when the drift strength D≲0.5, the FD is a concave curve. With the further increase in drift strength, a turning point appears on FD. The empirical findings show that both concave FD and FD with a turning point exist. Thus, the model might be able to reproduce both by tuning drift strength. It is also shown that in the special case D=1, two congested branches exist in the FD. We have carried out mean-field analysis of the FD and the mean-field results are in approximate agreement with simulations when the drift strength D is small. A comparison with random sequential update rule model is also made.

New Insights into Pedestrian Flow Through Bottlenecks

Capacity estimation is an important tool for the design and dimensioning of pedestrian facilities. The literature contains different procedures and specifications that show considerable differences with respect to the estimated flow values. Moreover, new experimental data indicate a stepwise growth of capacity with width and thus challenge the validity of the specific flow concept. To resolve these differences, we experimentally studied the unidirectional pedestrian flow through bottlenecks under laboratory conditions. The time development of quantities such as individual velocities, density, and individual time gaps in bottlenecks of different widths is presented. The data show a linear growth of flow with width. The comparison of the results with experimental data from other authors indicates that the basic assumption of the capacity estimation for bottlenecks has to be revised. In contrast to most planning guidelines, our main result is that a jam occurs even if the incoming flow does not overstep the capacity defined by the maximum flow according to the fundamental diagram.

EXPERIMENTAL VALIDATION OF MOTOR SCHEMA-BASED CELLULAR AUTOMATON MODEL FOR PEDESTRIAN DYNAMICS

In this paper, experiments were carried out to validate the motor schema-based cellular automaton model for pedestrian dynamics presented by Weng et al. [Int. J. Mod. Phys. C17, 853 (2006)]. Unidirectional pedestrian flow with different walk velocities is studied by means of simulations and experiments. The lower walk velocity was provided by the young people with special equipment, which made them walk slowly, to imitate the elderly people. Travel time of each pedestrian from start line to goal line with different initial distribution patterns and obstacles in the way was measured to compare with simulation results. The comparison results indicate that the experimental observations can be well reproduced with the motor schema-based cellular automaton model. And the simulation results of the mean travel time agree well with the experimental data.

Variation of Walking Speeds on a Unidirectional Walkway and on a Bidirectional Stairway

The variation of walking speeds for passengers passing through a facility within a congested underground station is known to be an important factor influencing pedestrian route choices. This paper describes a study of walking speed variation under unidirectional and bidirectional pedestrian flow conditions in Hong Kong, China, mass transit railway stations. The studied facilities selected for data collection and analysis include a unidirectional walkway and a bidirectional stairway. The variation in walking speed is due to increased passenger demand in the station when trains arrive. A study of the distribution of walking speed variation and relationships between average walking speed and variations of that speed was conducted based on data collected from an observation survey. For uncongested sections, when the mean walking speed decreased, the walking speed variation also decreased under both unidirectional and bidirectional pedestrian flow conditions. In addition, the walking speed variation was smallest when pedestrian flow approached capacity. However, in congested sections, when the mean walking speed decreased, the walking speed variation increased under both unidirectional and bidirectional pedestrian flow conditions. All walking time data were empirically proved to present a normal distribution. This paper presents newly developed walking speed variation models for three selected pedestrian facilities. These models can be further considered in connection with pedestrian simulation models to assess alternative improvement schemes at urban railway stations.

Variation of Walking Speeds on a Unidirectional Walkway and on a Bidirectional Stairway

The variation of walking speeds for passengers passing through a facility within a congested underground station is known to be an important factor influencing pedestrian route choices. This paper describes a study of walking speed variation under unidirectional and bidirectional pedestrian flow conditions in Hong Kong, China, mass transit railway stations. The studied facilities selected for data collection and analysis include a unidirectional walkway and a bidirectional stairway. The variation in walking speed is due to increased passenger demand in the station when trains arrive. A study of the distribution of walking speed variation and relationships between average walking speed and variations of that speed was conducted based on data collected from an observation survey. For uncongested sections, when the mean walking speed decreased, the walking speed variation also decreased under both unidirectional and bidirectional pedestrian flow conditions. In addition, the walking speed variation was smallest when pedestrian flow approached capacity. However, in congested sections, when the mean walking speed decreased, the walking speed variation increased under both unidirectional and bidirectional pedestrian flow conditions. All walking time data were empirically proved to present a normal distribution. This paper presents newly developed walking speed variation models for three selected pedestrian facilities. These models can be further considered in connection with pedestrian simulation models to assess alternative improvement schemes at urban railway stations.