Floor Field Cellular Automaton Model Research Articles

Modeling heterogenous crowd evacuation on stairs in high-rise buildings using a fine discrete floor field cellular automaton model: Accounting for speed and boundary layer variations

The article investigates the impact of crowd heterogeneities on stair evacuation dynamics in high-rise building. Using a fine discrete floor field cellular automaton (FFCA) model, the study explores the often-overlooked influence of crowd variations in mobility and behaviors. The simulation, set in a 21-story staircase, incorporates variations in speeds and boundary layer widths to replicate the heterogenous crowd dynamics. Key findings reveal that the heterogenous group, considering speed variations, exhibit prolonged stair evacuation time, with children and elderly individuals finishing last. Interactions among individuals with different mobilities lead to a 24.1% blocking effect on young adults' evacuation, while young adults enhance the evacuation of children and elderly by 19.0% and 23.8%, respectively. Children on the inner side of stairs lag behind due to the boundary layer, and the entire heterogeneous crowd's evacuation time decreases by 7.0%, highlighting the efficiency boost from boundary layers. A robust linear correlation is identified between specific outflow and the average desired speed for the heterogeneous group, with a consistent density of 0.46ped/m2 near the exit. The proposed model's validity is supported by trajectories consistent with prior observations and empirical data from homogenous crowd evacuation. The study advances our understanding of evacuation behaviors in heterogenous crowds within high-rise buildings during emergencies.

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.

A refined simulation method of building earthquake evacuation processes considering multi-exits and time-variant velocities

This study proposes a refined method for effectively simulating the evacuation processes of multi-story buildings during earthquakes. The method is developed by combining the exit-option algorithm and multi-velocity field model with the previously developed probabilistic network-based floor-field cellular automaton (PN-FFCA) model. Besides, the formula is also proposed for calculating the time-variant moving velocities of evacuees in the buildings subjected to the earthquake loads. Consequently, the refined method can fully consider the effect of multi-exits and time-variant velocities on the random evacuation processes of multi-story buildings during earthquakes. The recorded evacuation process of a school classroom during the 2022 Luding earthquake in China is reproduced using the refined method, which verifies its validity. In addition, the evacuation processes of an actual three-story office building subjected to random earthquake loads are simulated using the refined method. The simulated results are compared with those obtained from the PN-FFCA to demonstrate the advantages and utility of the refined method.

A fine discrete floor field cellular automaton model with natural step length for pedestrian dynamics

This paper proposes an extended floor field cellular automaton (FFCA) model for evacuation simulations, which integrates the natural step length into pedestrian movement. The model enables pedestrians to occupy multiple grids and extends the interaction area to a disk with a radius determined by the natural step length. These modifications facilitate pedestrian movement in various directions, limited only by the chosen numerical resolution. The model is calibrated to reproduce known density-velocity relations by simulating different evacuation scenarios. The flow rate through the bottleneck scenario matches the experimental results very well. Interestingly, the evacuation time, crowd shape near the exit and average conflict frequency are found to be independent of the discretisation degree, which is different from previous work. Compared with the traditional FFCA model, the proposed model yields larger and more reasonable velocity variation and evacuation path. The main parameters have a similar influence on the evacuation time, indicating that the proposed model retains the robustness of the traditional FFCA model.

Modeling Pedestrian Tactical and Operational Decisions Under Risk and Uncertainty: A Two-Layer Model Framework

Pedestrian tactical choices and operational movement in evacuations essentially pertain to decision-making under risk and uncertainty. However, in microscopic evacuation models, this attribute has been greatly overlooked, even lacking a methodology to delineate the related decision characteristics (bounded rationality and risk attitudes), let alone their effects on evacuation processes. This work presents an innovative two-layer floor field cellular automaton model framework, where three intertwined sub-modules respectively dedicated to modelling the exit choice, the locomotion movement and the exit-choice changing behaviours are proposed and integrated as an entity. By introducing various decision-making elements computed by the proposed algorithm, Cumulative Prospect Theory (CPT) is proposed for the first time to model the exit choice and locomotion decision-making under risk and uncertainty. In the exit-choice changing module, attractive and repulsive forces are invented to jointly describe the tendency to revisit the routing decision. Each sub-module and the whole framework are validated in manifold indoor environments. The simulation results of the modules with CPT accord with the empirics from the evacuation experiments and are superior over those from the state-of-the-art models. The degree of rationality and risk attitudes are proven to have significant impacts on tactical and operational decisions. Furthermore, irrational behaviour in decision-making is not variably detrimental to locomotion efficiency of pedestrians. The proposed framework can serve as an elegant tool to predict pedestrian dynamics. The behavioural findings shed new light on understanding and modelling the tactical and operational decisions in evacuations.

Pedestrian counterflow in a floor field cellular automaton model coupled with an evolutionary game

We study the bidirectional pedestrian flow in a straight corridor using a floor field cellular automaton model, where a game-theoretical framework is exclusively introduced to deal with conflicts that multiple pedestrians are trying to move to the same target position. The pedestrians can behave as either cooperators or defectors, depending on whether they show gentle or aggressive in face of conflicts, respectively. When competing with cooperators, a defector always obtains a relatively greater payoff, characterizing the advantage of occupying the preferred vacant cell, while a reduced payoff factor δ is introduced for mutual defection due to the possible injuries by aggressiveness. We study how the pedestrian counterflow dynamics depends on δ, the corridor width W and the anticipation floor field parameter k A. It is found that the average separation time of the pedestrians displays a resonance-like behavior as a function of δ, irrespective of the width of the corridor as long as jam does not happen. The way of dealing with conflicts has no qualitative effect on the lane formation, where the jam probability mainly depends on the parameters W and k A as well as the pedestrian density. A large value of k A means a strong tendency to avoid potential future collisions and suppress the overtaking motivation, but, at a cost, increases the average separation time of the two groups of pedestrians when the width of the corridor is not so narrow. Our results provide a meaningful perspective on the understanding of the process of lane formation and jam dissolution in the bidirectional pedestrian flow, and may shed light on designing policies to improve the efficiency of passing through.

The Negative Dependence of Evacuation Time on Group Size Under a Binding Mechanism

This paper initiates the analysis of the relation between evacuation time and group size by applying an extended floor-field cellular automaton model. Multi-speed-agents, a group structure containing leaders and followers, and a local-density-dependent dynamic field are implemented all together in the model. Most importantly, a complete binding mechanism which includes leaders waiting for followers is brought up for the first time. A counterintuitive negative relation between evacuation time and group size is discovered in one-group-type simulations, which corresponds to a previous experimental finding. An entropy-like quantity, namely the mixing index, is constructed to analyze the cause of that relation. It is found that under the binding mechanism, the higher degree of group mixing, the longer the evacuation time will be. Moreover, through a constant scale transformation, it is shown that the mixing index can be a key indicator that contains useful information about the evacuation system.

Simulation of crowd dynamics in pedestrian evacuation concerning panic contagion: A cellular automaton approach

The study of the panic evacuation process is of great significance to emergency management. Panic not only causes negative emotions such as irritability and anxiety, but also affects the pedestrians decision-making process, thereby inducing the abnormal crowd behavior. Prompted by the epidemiological SIR model, an extended floor field cellular automaton model was proposed to investigate the pedestrian dynamics under the threat of hazard resulting from the panic contagion. In the model, the conception of panic transmission status (PTS) was put forward to describe pedestrians’ behavior who could transmit panic emotions to others. The model also indicated the pedestrian movement was governed by the static and hazard threat floor field. Then rules that panic could influence decision-making process were set up based on the floor field theory. The simulation results show that the stronger the pedestrian panic, the more sensitive pedestrians are to hazards, and the less able to rationally find safe exits. However, when the crowd density is high, the panic contagion has a less impact on the evacuation process of pedestrians. It is also found that when the hazard position is closer to the exit, the panic will propagate for a longer time and have a greater impact on the evacuation. The results also suggest that as the extent of pedestrian’s familiarity with the environment increases, pedestrians spend less time to escape from the room and are less sensitive to the hazard. In addition, it is essential to point out that, compared with the impact of panic contagion, the pedestrian’s familiarity with environment has a more significant influence on the evacuation.

Incorporating genetic algorithm to optimise initial condition of pedestrian evacuation based on agent aggressiveness

In the study of pedestrian evacuation dynamics, pedestrian aggressiveness is important to consider as it potentially impacts evacuation efficiency. A representative example is the ‘faster-is-slower’ phenomenon. In reality, a crowd is a mixture of patient and impatient pedestrians, rather than a collection of like individuals. The impact of such heterogeneity has been reported in previous studies; however, these studies are all based on handcrafted solutions. In this study, we propose a heuristic approach for incorporating a genetic algorithm into the floor field cellular automata model to investigate the optimal initial pedestrian evacuation condition. Pedestrian aggressiveness is represented by two different approaches: the revised friction function and the persisting probability. To verify our genetic algorithm approach, we compared the results with the theoretical analysis and simulation results based on handcrafted solutions. The first contribution of this study is that the initial condition, a mixture of patient and impatient pedestrians, affects evacuation efficiency. Another contribution of this study is the heuristic approach incorporating a genetic algorithm. Our approach exerts the computational efficiency advantage of the floor field cellular automata model.

A continuous floor field cellular automata model with interaction area for crowd evacuation

Discrete and continuous models are generally used to study the evacuation dynamics. Considering the low accuracy of the discrete model such as floor field cellular automata model (FFCA) and the high time complexity of the continuous model such as social force model (SFM), a continuous FFCA (CFFCA) model is proposed. Pedestrians no longer occupy cells but are treated as particles in continuous space. To reduce the time complexity caused by continuity, the social force is replaced by interactions by drawing on SFM from different perspectives. The obstacle and pedestrian interaction area are proposed to simulate the repulsion, friction and attraction between pedestrians and obstacles, and between pedestrians. By simulating different evacuation scenarios, it is found that the simulation results are close to the experiments data. CFFCA evacuation path is more reasonable than that of FFCA and the execution time is shorter than that of SFM. Because of the superiority of interaction area used in CFFCA, pedestrians can move freely without being restricted by the spatial scale of cells, and the complex psychology of pedestrians can be simulated under lower time complexity. Our study may be useful to find the trade-off between model realism and tractability.

An extended model for crowd evacuation considering pedestrian panic in artificial attack

An extended floor field cellular automata model considering pedestrian panic was proposed to investigate pedestrian dynamics under the threat of artificial attack. In the model, a new parameter D was introduced to reflect quantitatively the extent of the impact of panic on pedestrian evacuation. Besides, pedestrian movement is governed by the static, attack threat and herding floor field. And some modifications were made to introduce the influence of panic on the decision-making of the individual. Further, the motion and assault of the artificial attacker and the death of pedestrians were taken into account simultaneously. The simulation results show that the proposed model can reproduce some real characteristic features of escape panics, such as (1) Pedestrians become less rational. (2) At exits, arching and clogging are observed. (3) People show a tendency towards mass behavior, i.e., pedestrian herding. (4) Alternative exits are overlooked or not efficiently used. As the extent of the panic increases, pedestrians spend more time to escape from the room and are more sensitive to the movement of the crowd and the action of the attacker. The phenomenon of pedestrian herding and jamming can be clearly observed as D increases. And the results also indicate that the tension caused by moderate panic can help reduce casualties, whereas excessive panic will increase casualties. Besides, enhancing pedestrian initiative, i.e., the ability that pedestrian finds the exit independently in panic, is beneficial to the evacuation. In addition, more pedestrians would lose their lives due to attack and the evacuation efficiency would be reduced if the attacker starts the attack from the positions of the exits, so the security forces near the exits should be strengthened.

Revealing the hidden rules of bidirectional pedestrian flow based on an improved floor field cellular automata model

The floor field cellular automaton model (FFCA) has been widely adopted to simulate pedestrian and evacuation dynamics. Many self-organized phenomena could be reproduced with the FFCA model, such as the lane formation in bidirectional pedestrian flow. However, as presented in this study, when we tried to use the FFCA model to simulate an experiment on bidirectional pedestrian flows performed in discrete space and time, we found the model failed to agree with the empirical results. The gridlock formation (not observed in the experiment) was unavoidable in the FFCA model and the clearance time in simulation was much larger than that of the experiment. From the experiments, we observed that people would like to stop if they would foresee a benefit in the near feature and consequently give way to people coming from the opposite direction. This inspired us to incorporate such behavioral rules for modeling pedestrian movements in bidirectional flows. To this end, we introduced a waiting time rule to the original FFCA model. Results showed the performance of the model could be significantly improved. The gridlock probability could be reduced to zero, with clearance time agreeing well with the experimental outcome. Findings from this study can provide meaningful insights for researchers into understanding the pedestrian behavior in bidirectional flow and help develop more reliable simulation software.

Experiment and simulation of pedestrian’s behaviors during evacuation in an office

Pedestrian evacuation in an office is a critical problem that has not been fully explored and understood, which is investigated in this paper, through conducting an evacuation experiment under emergency and developing an extended Floor Field cellular automaton (FFCA) model. The video recordings have revealed several typical patterns of pedestrian behaviors related to the distance to exit, internal layout of the office, living habits of pedestrians. Herding behavior, pedestrians’ response time, living habits, and two abnormal behaviors – backtracking and choosing farther exit – are observed from experiment video. To reproduce the evacuation process in the experiment and research pedestrian evacuation dynamics, an extended FFCA model is proposed considering the behaviors observed in the video. Through numerical simulations, proper values of sensitive parameters are obtained, which can make the simulation in line with the evacuation process in experiment. Simulation results show that living habit of pedestrians has a positive impact on evacuation efficiency while abnormal behaviors play a negative role in evacuation procedure but have little impact on total evacuation time in this experiment. Meanwhile, personal response time is a significant factor to determine total evacuation time, which cannot be ignored. This study is expected to give some advice in planning emergency evacuation schemes of such buildings, such as office, classroom, assembly room and so on.

Modeling the effect of visibility on upstairs crowd evacuation by a stochastic FFCA model with finer discretization

In recent years, deep underground buildings appear more often than ever, and stairs are the main facilities for the upward evacuation of crowds from these buildings. As one of the most essential factors, the visibility might play a dominant role in the upward evacuation on stairs. To ensure the safety of the crowd in underground spaces, a finer discrete and stochastic floor field cellular automaton (FFCA) model integrating the visibility influence is established for the simulation of the crowd upward evacuation from a 21-storey staircase. By comparison, the simulation fits well with the observation and experiment, which implies that the model captures the main features of upward evacuations on stairs. Then, from the predicted results, it is found that the visibility reduction has a significant negative impact on the temporal–spatial distribution of pedestrians, especially on the inflow and outflow, while the entrance flow rate shows little impact as long as it is higher than 1.0 ped⋅m−1⋅s−1.

Modeling fatigue of ascending stair evacuation with modified fine discrete floor field cellular automata

Fatigue even increases the complexity of the pedestrian dynamics which is regarded as a kind of nonlinear system, and might have a significant negative impact on the crowd evacuation. However, it has never been investigated completely and properly. Thus, the fine discrete floor field cellular automata model is modified by integrating the fatigue function to explore the influence of fatigue on the crowd ascending evacuation. The simulation fits well with the empirical data and the observations quantitatively and qualitatively, indicating the model captures the main features of evacuation considering fatigue impact. As a prediction, without merging streams, compared with the case of walking in constant speed, when fatigue is considered, it takes 71.4% longer for all persons to enter the stairs and 87.2% longer to evacuate. With merging streams, fatigue has little impact on the inflow, while it makes the total evacuation time 84.2% longer.

Experimental features and mathematical model of pedestrian evacuation with asymmetrical pedestrian distribution

Pedestrian’s movement is a complex dynamic process because of the diversity in their psychological characteristics, such as cognitive, emotion, attitude and demand, etc. Simulation of pedestrian flow evacuation from a room with asymmetrical pedestrian distribution is presented based on the improved floor field cellular automata model in this paper. This model aims to define the direction fuzzy visual field to describe the difference of pedestrian’s behavior in different environments, and present the region of pedestrian distribution in an exit to achieve the simulation of pedestrian flow evacuation with asymmetrical pedestrian distribution. When a pedestrian chooses the next target position, his behavior is affected by the repulsive force and the attractive force between pedestrians in direction fuzzy visual field, pedestrian’s distribution in exits, and the shortest distance from a pedestrian to his target position. It simulates the scenes of a single exit and four exits in the condition of asymmetrical pedestrian distribution, and observes the self-organization phenomena in the process of simulation in order to reveal the inherent law of pedestrian flow evacuation with asymmetrical pedestrian distribution. Moreover, the simulation results of the improved and original models are compared and analyzed. The results indicate that the modified model can achieve the dynamic evacuation balance in the process of movement with asymmetrical pedestrian distribution. The improved model does not have to rely on the influence coefficient of every factor. Therefore, it avoids the subjectivity and the limitations of evacuation system in the process of making these factors. Evacuation time is related to radii of the direction fuzzy visual field and the region of pedestrian distribution in exits. If pedestrians can keep a lager radius of view in the direction fuzzy visual field and real-time master a moderate pedestrian’s distribution of exits, these should effectively improve the evacuation efficiency of pedestrian flow. The present study is helpful for devising evacuation strategies and schemes in buildings that are similar to this pedestrian flow.

Simulation study of overtaking in pedestrian flow using floor field cellular automaton model

Properties of pedestrian may change along the moving path, for example, as a result of fatigue or injury, which has never been properly investigated in the past research. The paper attempts to study tactical overtaking in pedestrian flow. That is difficult to be modeled using a microscopic discrete model because of the complexity of the detailed overtaking behavior, and crossing/overlaps of pedestrian routes. Thus, a multi-velocity floor field cellular automaton model explaining the detailed psychical process of overtaking decision was proposed. Pedestrian can be either in normal state or in tactical overtaking state. Without tactical decision, pedestrians in normal state are driven by the floor field. Pedestrians make their tactical overtaking decisions by evaluating the walking environment around the overtaking route (the average velocity and density around the route, visual field of pedestrian) and obstructing conditions (the distance and velocity difference between the overtaking pedestrian and the obstructing pedestrian). The effects of tactical overtaking ratio, free velocity dispersion, and visual range on fundamental diagram, conflict density, and successful overtaking ratio were explored. Besides, the sensitivity analysis of the route factor relative intensity was performed.

A Cellular Automaton model for pedestrian counterflow with swapping

In this paper, we propose a new floor field Cellular Automaton (CA) model with considering the swapping behaviors of pedestrians. The neighboring pedestrians in opposite directions take swapping in a probability decided by the linear density of pedestrian flow. The swapping which happens simultaneously with the normal movement is introduced to eliminate the gridlock in low density region. Numerical results show that the fundamental diagram is in good agreement with the measured data. Then the model is applied to investigate the counterflow and four typical states such as free flow, lane, intermediate and congestion states are found. More attention is paid on the intermediate state which lane-formation and local congestions switch in an irregular manner. The swapping plays a vital role in reducing the gridlock. Furthermore, the influence of the corridor size and individual’s eyesight on counterflow are discussed in detail.

A study of pedestrian group behaviors in crowd evacuation based on an extended floor field cellular automaton model

In the study of pedestrian movements, a consideration of group behaviors is important because of their potential impacts on pedestrian flow dynamics. In this paper, we investigate the group behaviors during emergency evacuation, which is a critical case for emergency crowd management but has not been fully explored and understood. It has been well recognized that in evacuation situations, some people within a crowd, especially those who are with families and friends, often move in small groups and act in particular patterns distinct from individuals. As a result, the crowd is a mixture of individuals and groups rather than a pure collection of individuals. To capture and evaluate the influence of group behaviors on crowd evacuation, we propose an extended floor field cellular automaton (CA) model that takes into account such phenomena. Our model is formulated by leveraging the leader-follower behavior rule that is evident in pedestrian group behaviors. To calibrate and validate the proposed model, a few field experiments of crowd evacuation were conducted in a university building. Through a representative case study, it is demonstrated that the proposed extended floor field CA model can replicate the well-known phenomena in crowd evacuation such as collective arch-like clogging at the exit as well as other commonly observed group behaviors in evacuation. Moreover, it is found that the total crowd evacuation time significantly increases with the presence of pedestrian groups in the crowd. The results also show that such negative effects of group behaviors in crowd evacuation intensify when the density of the crowd is higher. Subsequently, sensitivity analyses are performed to further explore how pedestrian group behaviors are influenced by model parameters that reflect the pedestrian flow dynamics in evacuation scenarios. With its capability of realistically replicating the field pedestrian evacuation, the proposed model can serve as a valuable tool for predicting crowd evacuation time and designing guidelines for pedestrian evacuation in emergency situations, in particular when group behaviors are salient.

A floor field cellular automaton for crowd evacuation considering different walking abilities

It has been hard to model a crowd evacuation process considering different walking abilities using a synchronous cellular automaton. That is because the cross and the overlaps of routes have to be taken into consideration and the conflicts resolution between pedestrians is more complex. However, the desired velocities of evacuees might be quite different due to the discrepancies of the physiological function, including age, gender, physical state, and the psychological behavior, such as the perception and reflection to the dangers. Additionally, an evacuee might change his desired velocity constantly to adapt to the changing evacuation environment. Thus, a multi-velocities floor field cellular automaton model was established in this paper. Using little CPU time, a dense crowd evacuation simulation with tiny varied velocity can be conducted very well. Significant discrepancies between the single-velocity evacuation and the multi-velocities evacuation were observed. The plateaus, where the exit flow rate is rather low, can be well predicted by a dimensionless parameter describing the congestion level of the evacuation system. The crowd evacuation time almost depends on the low desired velocity evacuees, though the proportion is not high. We also observed that faster evacuees make the evacuation system easily approaching to the jam.