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An aging population is bringing new challenges to the management of escape routes and facility design in many countries. This paper investigates pedestrian movement properties of crowd with different age compositions. Three pedestrian groups are considered: young student group, old people group and mixed group. It is found that traffic jams occur more frequently in mixed group due to the great differences of mobilities and self-adaptive abilities among pedestrians. The jams propagate backward with a velocity 0.4 m/s for global density around 1.75 m-1 and 0.3 m/s for higher than 2.3 m-1. The fundamental diagrams of the three groups are obviously different from each other and cannot be unified into one diagram by direct non-dimensionalization. Unlike previous studies, three linear regimes in mixed group but only two regimes in young student group are observed in the headway-velocity relation, which is also verified in the fundamental diagram. Different ages and mobilities of pedestrians in a crowd cause the heterogeneity of system and influence the properties of pedestrian dynamics significantly. It indicates that the density is not the only factor leading to jams in pedestrian traffic. The composition of crowd has to be considered in understanding pedestrian dynamics and facility design.

Pedestrian crowds often include social groups, i.e. pedestrians that walk together because of social relationships. They show characteristic configurations and influence the dynamics of the entire crowd. In order to investigate the impact of social groups on evacuations we performed an empirical study with pupils. Several evacuation runs with groups of different sizes and different interactions were performed. New group parameters are introduced which allow to describe the dynamics of the groups and the configuration of the group members quantitatively. The analysis shows a possible decrease of evacuation times for large groups due to self-ordering effects. Social groups can be approximated as ellipses that orientate along their direction of motion. Furthermore, explicitly cooperative behaviour among group members leads to a stronger aggregation of group members and an intermittent way of evacuation.

We propose and document the evidence for an analogy between the dynamics of granular counter-flows in the presence of bottlenecks or restrictions and financial price formation processes. Using extensive simulations, we find that the counter-flows of simulated pedestrians through a door display many stylized facts observed in financial markets when the density around the door is compared with the logarithm of the price. The stylized properties are present already when the agents in the pedestrian model are assumed to display a zero-intelligent behavior. If agents are given decision-making capacity and adapt to partially follow the majority, periods of herding behavior may additionally occur. This generates the very slow decay of the autocorrelation of absolute return due to an intermittent dynamics. Our finding suggest that the stylized facts in the fluctuations of the financial prices result from a competition of two groups with opposite interests in the presence of a constraint funneling the flow of transactions to a narrow band of prices.

We present simulations of evacuation processes using a recently introduced cellular automaton model for pedestrian dynamics. This model applies a bionics approach to describe the interaction between the pedestrians using ideas from chemotaxis. Here we study a rather simple situation, namely the evacuation from a large room with one or two doors. It is shown that the variation of the model parameters allows to describe different types of behaviour, from regular to panic. We find a non-monotonic dependence of the evacuation times on the coupling constants. These times depend on the strength of the herding behaviour, with minimal evacuation times for some intermediate values of the couplings, i.e. a proper combination of herding and use of knowledge about the shortest way to the exit.

Understanding the complex behavior of pedestrians walking in crowds is a challenge for both science and technology. In particular, obtaining reliable models for crowd dynamics, capable of exhibiting qualitatively and quantitatively the observed emergent features of pedestrian flows, may have a remarkable impact for matters as security, comfort and structural serviceability. Aiming at a quantitative understanding of basic aspects of pedestrian dynamics, extensive and high-accuracy measurements of pedestrian trajectories have been performed. More than 100.000 real-life, time-resolved trajectories of people walking along a trafficked corridor in a building of the Eindhoven University of Technology, The Netherlands, have been recorded. A measurement strategy based on Microsoft Kinect\texttrademark has been used; the trajectories of pedestrians have been analyzed as ensemble data. The main result consists of a statistical descriptions of pedestrian characteristic kinematic quantities such as positions and fundamental diagrams, possibly conditioned to local crowding status (e.g., one or more pedestrian(s) walking, presence of co-flows and counter-flows).

We extend the class of pedestrian crowd models introduced by Lachapelle and Wolfram (2011) to allow for nonlocal congestion and arbitrarily but finitely many interacting crowds. The new congestion feature grants pedestrians a personal space where crowding is undesirable. We treat the model as a mean-field type game which we derive from a particle picture. Solutions to the mean-field type game are characterized via a Pontryagin-type Maximum Principle. The behavior of a crowd acting under nonlocal congestion is illustrated by a numerical simulation.

In this work we propose a model to describe the statistical fluctuations of the self-driven objects (species A) walking against an opposite crowd (species B) in order to simulate the regime characterized by stop-and-go waves in the context of pedestrian dynamics. By using the concept of single-biased random walks (SBRW), this setup is modeled both via partial differential equations and by Monte-Carlo simulations. The problem is non-interacting until the opposite particles visit the same cell of the considered particle. In this situation, delays on the residence time of the particles per cell depends on the concentration of particles of opposite species. We analyzed the fluctuations on the position of particles and our results show a non-regular diffusion characterized by long-tailed and asymmetric distributions which is better fitted by some chromatograph distributions found in the literature. We also show that effects of the reverse crowd particles is able to enlarge the dispersion of target particles in relation to the non-biased case ($\alpha =0$) after observing a small decrease of this dispersion

This paper presents a new approach to behavioral-social dynamics of pedestrian crowds by suitable development of methods of the kinetic theory. It is shown how heterogeneous individual behaviors can modify the collective dynamics, as well as how local unusual behaviors can propagate in the crowd. The main feature of this approach is a detailed analysis of the interactions between dynamics and social behaviors.

When two pedestrians travelling in opposite directions approach one another, each must decide on which side (the left or the right) they will attempt to pass. If both make the same choice then passing can be completed with ease, while if they make opposite choices an embarrassing stand-off or collision can occur. Pedestrians who encounter each other frequently can establish "social norms" that bias this decision. In this study we investigate the effect of binary decision-making by pedestrians when passing on the dynamics of pedestrian flows in order to study the emergence of a social norm in crowds with a mixture of individual biases. Such a situation may arise, for instance, when individuals from different communities mix at a large sporting event or at transport hubs. We construct a phase diagram that shows that a social norm can still emerge provided pedestrians are sufficiently attentive to the choices of others in the crowd. We show that this collective behaviour has the potential to greatly influence the dynamics of pedestrians, including the breaking of symmetry by the formation of lanes.

Experimental results for congested pedestrian traffic are presented. For data analysis we apply a method providing measurements on an individual scale. The resulting velocity-density relation shows a coexistence of moving and stopping states revealing the complex structure of pedestrian fundamental diagrams and supporting new insights into the characteristics of pedestrian congestions. Furthermore we introduce a model similar to event driven approaches. The velocity-density relation as well as the phase separation is reproduced. Variation of the parameter distribution indicates that the diversity of pedestrians is crucial for phase separation.

Many agent based simulation approaches have been proposed for pedestrian flow. As such models are applied e.g.\ in evacuation studies, the quality and reliability of such models is of vital interest. Pedestrian trajectories are functional data and thus functional principal component analysis is a natural tool to asses the quality of pedestrian flow models beyond average properties. In this article we conduct functional PCA for the trajectories of pedestrians passing through a bottleneck. We benchmark two agent based models of pedestrian flow against the experimental data using PCA average and stochastic features. Functional PCA proves to be an efficient tool to detect deviation between simulation and experiment and to asses quality of pedestrian models.

We developed a machine vision system to automatically capture the dynamics of pedestrians under four different traffic scenarios. By considering the overhead view of each pedestrian as a digital object, the system processes the image sequences to track the pedestrians. Considering the perspective effect of the camera lens and the projected area of the hallway at the top-view scene, the distance of each tracked object from its original position to its current position is approximated every video frame. Using the approximated distance and the video frame rate (30 frames per second), the respective velocity and acceleration of each tracked object are later derived. The quantified motion characteristics of the pedestrians are displayed by the system through 2-dimensional graphs of the kinematics of motion. The system also outputs video images of the pedestrians with superimposed markers for tracking. These visual markers were used to visually describe and quantify the behavior of the pedestrians under different traffic scenarios.

Stop-and-go waves in single-file movement are a phenomenon that is ob- served empirically in pedestrian dynamics. It manifests itself by the co-existence of two phases: moving and stopping pedestrians. We show analytically based on a simplified one-dimensional scenario that under some conditions the system can have instable homogeneous solutions. Hence, oscillations in the trajectories and in- stabilities emerge during simulations. To our knowledge there exists no force-based model which is collision- and oscillation-free and meanwhile can reproduce phase separation. We develop a new force-based model for pedestrian dynamics able to reproduce qualitatively the phenomenon of phase separation. We investigate analytically the stability condition of the model and define regimes of parameter values where phase separation can be observed. We show by means of simulations that the predefined conditions lead in fact to the expected behavior and validate our model with respect to empirical findings.

Stop-and-go waves in single-file movement are a phenomenon that is ob- served empirically in pedestrian dynamics. It manifests itself by the co-existence of two phases: moving and stopping pedestrians. We show analytically based on a simplified one-dimensional scenario that under some conditions the system can have instable homogeneous solutions. Hence, oscillations in the trajectories and in- stabilities emerge during simulations. To our knowledge there exists no force-based model which is collision- and oscillation-free and meanwhile can reproduce phase separation. We develop a new force-based model for pedestrian dynamics able to reproduce qualitatively the phenomenon of phase separation. We investigate analytically the stability condition of the model and define regimes of parameter values where phase separation can be observed. We show by means of simulations that the predefined conditions lead in fact to the expected behavior and validate our model with respect to empirical findings.

We investigate via extensive experimental data the dynamics of pedestrians walking in a corridor-shaped landing in a building at Eindhoven University of Technology. With year-long automatic measurements employing a Microsoft KinectTM 3D-range sensor and ad hoc tracking techniques, we acquired few hundreds of thousands pedestrian trajectories in real-life conditions. Here we discuss the asymmetric features of the dynamics in the two walking directions with respect to the flights of stairs (i.e. ascending or descending). We provide a detailed analysis of position and speed fields for the cases of pedestrians walking alone undisturbed and for couple of pedestrians in counter-flow. Then, we show average walking velocities exploring all the observed combinations in terms of numbers of pedestrians and walking directions.

Pedestrian and Evacuation Dynamics dumped with WikiTeam tools.

Being determined by human social behaviour, pedestrian group dynamics depends on "intrinsic properties" of the group such as the purpose of the pedestrians, their personal relation, their gender, age, and body size. In this work we quantitatively study the dynamical properties of pedestrian dyads by analysing a large data set of automatically tracked pedestrian trajectories in an unconstrained "ecological" setting (a shopping mall), whose relational group properties have been coded by three different human observers. We observed that females walk slower and closer than males, that workers walk faster, at a larger distance and more abreast than leisure oriented people, and that inter group relation has a strong effect on group structure, with couples walking very close and abreast, colleagues walking at a larger distance, and friends walking more abreast than family members. Pedestrian height (obtained automatically through our tracking system) influences velocity and abreast distance, both growing functions of the average group height. Results regarding pedestrian age show as expected that elderly people walk slowly, while active age adults walk at the maximum velocity. Groups with children have a strong tendency to walk in a non abreast formation, with a large distance (despite a low abreast distance). A cross-analysis of the interplay between these intrinsic features, taking in account also the effect of extrinsic crowd density, confirms these major effects but reveals also a richer structure. An interesting and unexpected result, for example, is that the velocity of groups with children {\it increases} with density, at least in the low-medium density range found under normal conditions in shopping malls. Children also appear to behave differently according to the gender of the parent.

This article considers execution and analysis of laboratory experiments of pedestrians moving in a quasi-one-dimensional system with periodic boundary conditions. To analyze characteristics of jams in the system we aim to use the whole experimental setup as the measurement area. Thus the trajectories are transformed to a new coordinate system. We show that the trajectory data from the straight and curved parts are comparable and assume that the distributions of the residuals come from the same continuous distribution. Regarding the trajectories of the entire setup, the creation of stop-and-go waves in pedestrian traffic can be investigated and described.

This paper introduces a space-continuous force-based model for simulating pedestrian dynamics. The main interest of this work is the quantitative description of pedestrian movement through a bottleneck. Measurements of flow and density will be presented and compared with empirical data. The results of the proposed model show a good agreement with empirical data. Furthermore, we emphasize the importance of volume exclusion in force-based models.

We introduce an enhanced model based on the generalized centrifugal force model. Furthermore, the desired direction of pedestrians is investigated. A new approach leaning on the well-known concept of static and dynamic floor-fields in cellular automata is presented. Numerical results of the model are presented and compared with empirical data.

Richard D. Peacock, Erica D. Kuligowski, Jason D. Averill - Pedestrian and Evacuation Dynamics

Several spatially continuous pedestrian dynamics models have been validated against empirical data. We try to reproduce the experimental fundamental diagram (velocity versus density) with simulations. In addition to this quantitative criterion, we tried to reproduce stop-and-go waves as a qualitative criterion. Stop-and-go waves are a characteristic phenomenon for the single file movement. Only one of three investigated models satisfies both criteria.

The social-force model is systematically modified to achieve a satisfying agreement with the fundamental diagram. Furthermore, our modification allows an efficient computation of the simulation. Finally, different simulation-results will be compared to empirical data.

The social-force model is systematically modified to achieve a satisfying agreement with the fundamental diagram. Furthermore, our modification allows an efficient computation of the simulation. Finally, different simulation-results will be compared to empirical data.

In this paper we present a numerical study of some variations of the Hughes model for pedestrian flow under different types of congestion effects. The general model consists of a coupled non-linear PDE system involving an eikonal equation and a first order conservation law, and it intends to approximate the flow of a large pedestrian group aiming to reach a target as fast as possible, while taking into account the congestion of the crowd. We propose an efficient semi-Lagrangian scheme (SL) to approximate the solution of the PDE system and we investigate the macroscopic effects of different penalization functions modelling the congestion phenomena.

This paper introduces a spatially continuous force-based model for simulating pedestrian dynamics. The main intention of this work is the quantitative description of pedestrian movement through bottlenecks and in corridors. Measurements of flow and density at bottlenecks will be presented and compared with empirical data. Furthermore the fundamental diagram for the movement in a corridor is reproduced. The results of the proposed model show a good agreement with empirical data.

We show that keeping a constant lower limit on the net-time headway is the key mechanism behind the dynamics of pedestrian streams. There is a large variety in flow and speed as functions of density for empirical data of pedestrian streams, obtained from studies in different countries. The net-time headway however, stays approximately constant over all these different data sets. By using this fact, we demonstrate how the underlying dynamics of pedestrian crowds, naturally follows from local interactions. This means that there is no need to come up with an arbitrary fit function (with arbitrary fit parameters) as has traditionally been done. Further, by using not only the average density values, but the variance as well, we show how the recently reported stop-and-go waves [Helbing et al., Physical Review E, 75, 046109] emerge when local density variations take values exceeding a certain maximum global (average) density, which makes pedestrians stop.

We investigate the role of conflicts in pedestrian traffic, i.e. situations where two or more people try to enter the same space. Therefore a recently introduced cellular automaton model for pedestrian dynamics is extended by a friction parameter $\mu$. This parameter controls the probability that the movement of all particles involved in a conflict is denied at one time step. It is shown that these conflicts are not an undesirable artefact of the parallel update scheme, but are important for a correct description of the dynamics. The friction parameter $\mu$ can be interpreted as a kind of internal local pressure between the pedestrians which becomes important in regions of high density, ocurring e.g. in panic situations. We present simulations of the evacuation of a large room with one door. It is found that friction has not only quantitative effects, but can also lead to qualitative changes, e.g. of the dependence of the evacuation time on the system parameters. We also observe similarities to the flow of granular materials, e.g. arching effects.

We propose a 2-dimensional cellular automaton model to simulate pedestrian traffic. It is a vmax=1 model with exclusion statistics and parallel dynamics. Long-range interactions between the pedestrians are mediated by a so called floor field which modifies the transition rates to neighbouring cells. This field, which can be discrete or continuous, is subject to diffusion and decay. Furthermore it can be modified by the motion of the pedestrians. Therefore the model uses an idea similar to chemotaxis, but with pedestrians following a virtual rather than a chemical trace. Our main goal is to show that the introduction of such a floor field is sufficient to model collective effects and self-organization encountered in pedestrian dynamics, e.g. lane formation in counterflow through a large corridor. As an application we also present simulations of the evacuation of a large room with reduced visibility, e.g. due to failure of lights or smoke.

A spatially continuous force-based model for simulating pedestrian dynamics is introduced which includes an elliptical volume exclusion of pedestrians. We discuss the phenomena of oscillations and overlapping which occur for certain choices of the forces. The main intention of this work is the quantitative description of pedestrian movement in several geometries. Measurements of the fundamental diagram in narrow and wide corridors are performed. The results of the proposed model show good agreement with empirical data obtained in controlled experiments.

In this paper we present an optimal control approach modeling fast exit scenarios in pedestrian crowds. In particular we consider the case of a large human crowd trying to exit a room as fast as possible. The motion of every pedestrian is determined by minimizing a cost functional, which depends on his/her position, velocity, exit time and the overall density of people. This microscopic setup leads in the mean-field limit to a parabolic optimal control problem. We discuss the modeling of the macroscopic optimal control approach and show how the optimal conditions relate to Hughes model for pedestrian flow. Furthermore we provide results on the existence and uniqueness of minimizers and illustrate the behavior of the model with various numerical results.

We propose and analyze extended floor field cellular automaton models for evacuation dynamics of inhomogeneous pedestrian pairs which are coupled by asymmetric group interactions. Such pairs consist of a leader, who mainly determines the couple's motion and a follower, who has a defined tendency to follow the leader. Examples for such pairs are mother and child or two siblings of different age. We examine the system properties and compare them to the case of a homogeneous crowd. We find a strong impact on evacuation times for the regime of strong pair coupling due to the occurrence of a clogging phenomenon. In addition we obtain a non-trivial dependence of evacuation times on the followers' coupling to the static floor field, which carries the information of the shortest way to the exit location. In particular we find that systems with fully passive followers, who are solely coupled to their leaders, show lower evacuation times than homogeneous systems where all pedestrians have an equal tendency to move towards the exit. We compare the results of computer simulations with recently performed experiments.

A simulation model for the dynamic behaviour of pedestrian crowds is mathematically formulated in terms of a social force model, that means, pedestrians behave in a way as if they would be subject to an acceleration force and to repulsive forces describing the reaction to borders and other pedestrians. The computational simulations presented yield many realistic results that can be compared with video films of pedestrian crowds. Especially, they show the self-organization of collective behavioural patterns. By assuming that pedestrians tend to choose routes that are frequently taken the above model can be extended to an active walker model of trail formation. The topological structure of the evolving trail network will depend on the disadvantage of building new trails and the durability of existing trails. Computer simulations of trail formation indicate to be a valuable tool for designing systems of ways which satisfy the needs of pedestrians best. An example is given for a non-directed trail network.

A stochastic cellular automata (CA) model for pedestrian dynamics is presented. Our goal is to simulate different types of pedestrian movement, from regular to panic. But here we emphasize regular situations which imply that pedestrians analyze environment and choose their route more carefully. And transition probabilities have to depict such effect. The potentials of floor fields and environment analysis are combined in the model obtained. People patience is included in the model. This makes simulation of pedestrians movement more realistic. Some simulation results are presented and comparison with basic FF-model is made.

We present a new microscopic ODE-based model for pedestrian dynamics: the Gradient Navigation Model. The model uses a superposition of gradients of distance functions to directly change the direction of the velocity vector. The velocity is then integrated to obtain the location. The approach differs fundamentally from force based models needing only three equations to derive the ODE system, as opposed to four in, e.g., the Social Force Model. Also, as a result, pedestrians are no longer subject to inertia. Several other advantages ensue: Model induced oscillations are avoided completely since no actual forces are present. The derivatives in the equations of motion are smooth and therefore allow the use of fast and accurate high order numerical integrators. At the same time, existence and uniqueness of the solution to the ODE system follow almost directly from the smoothness properties. In addition, we introduce a method to calibrate parameters by theoretical arguments based on empirically validated assumptions rather than by numerical tests. These parameters, combined with the accurate integration, yield simulation results with no collisions of pedestrians. Several empirically observed system phenomena emerge without the need to recalibrate the parameter set for each scenario: obstacle avoidance, lane formation, stop-and-go waves and congestion at bottlenecks. The density evolution in the latter is shown to be quantitatively close to controlled experiments. Likewise, we observe a dependence of the crowd velocity on the local density that compares well with benchmark fundamental diagrams.

We propose in this paper a minimal speed-based pedestrian model for which particle dynamics are intrinsically collision-free. The speed model is an optimal velocity function depending on the agent length (i.e.\ particle diameter), maximum speed and time gap parameters. The direction model is a weighted sum of exponential repulsion from the neighbors, calibrated by the repulsion rate and distance. The model's main features like the reproduction of empirical phenomena are analysed by simulation. We point out that phenomena of self-organisation observable in force-based models and field studies can be reproduced by the collision-free model with low computational effort.

It is suggested that the motion of pedestrians can be described as if they would be subject to `social forces'. These `forces' are not directly exerted by the pedestrians' personal environment, but they are a measure for the internal motivations of the individuals to perform certain actions (movements). The corresponding force concept is discussed in more detail and can be also applied to the description of other behaviors. In the presented model of pedestrian behavior several force terms are essential: First, a term describing the acceleration towards the desired velocity of motion. Second, terms reflecting that a pedestrian keeps a certain distance to other pedestrians and borders. Third, a term modeling attractive effects. The resulting equations of motion are nonlinearly coupled Langevin equations. Computer simulations of crowds of interacting pedestrians show that the social force model is capable of describing the self-organization of several observed collective effects of pedestrian behavior very realistically.

We construct a two dimensional Cellular Automata based model for the description of pedestrian dynamics. Wide range of complicated pattern formation phenomena in pedestrian dynamics are described in the model, e.g. lane formation, jams in a counterflow and egress behavior. Mean-field solution of the densely populated case and numerical solution of the sparsely populated case are provided. This model has the potential to describe more flow phenomena.

We study discretisation effects in cellular automata models for pedestrian dynamics by reducing the cell size. Then a particle occupies more than one cell which leads to subtle effects in the dynamics, e.g. non-local conflict situations. Results from computer simulations of the floor field model are compared with empirical findings. Furthermore the influence of increasing the maximal walking speed $v_{{\rm max}}$ is investigated by increasing the interaction range beyond nearest neighbour interactions. The extension of the model to $v_{{\rm max}}>1$ turns out to be a severe challenge which can be solved in different ways. Four major variants are discussed that take into account different dynamical aspects. The variation of $v_{{\rm max}}$ has strong influence on the shape of the flow-density relation. We show that walking speeds $v_{{\rm max}}>1$ lead to results which are in very good agreement with empirical data.

We study the dynamics of pedestrian evacuations through a narrow doorway by means of controlled experiments. The influence of the pedestrians' behaviours is investigated by prescribing a selfish attitude to a fraction c\_s of the participants, while the others behave politely. Thanks to an original setup enabling the re-injection of egressed participants into the room, the analysis is conducted in a (macroscopically) quasi-stationary regime. We find that, as c\_s is increased, the flow rate J rises, interpolating between published values for egresses in normal conditions and measurements for competitive evacuations. The dependence of several flow properties on the pedestrian density $\rho$ at the door, independently of c\_s , suggests that macroscopically the behavioural aspects could be subsumed under the density, at least in our specific settings with limited crowd pressure. In particular, under these conditions, J grows monotonically with $\rho$ up to "close-packing" ($\rho$ $\approx$ 9 pers/m${}^2$). The flow is then characterised microscopically. Among other quantities, the time lapses between successive escapes, the pedestrians' waiting times in front of the door, and their angles of incidence are analysed statistically. In a nutshell, our main results show that the flow is orderly for polite crowds, with narrowly distributed time lapses between egresses, while for larger c\_s the flow gets disorderly and vanishing time lapses emerge. For all c\_s , we find an alternation between short and long time lapses, which we ascribe to a generalised zipper effect. The average waiting time in the exit zone increases with its occupancy. The disorder in the flow and the pressure felt by participants are also assessed.

We study the dynamics of pedestrian evacuations through a narrow doorway by means of controlled experiments. The influence of the pedestrians' behaviours is investigated by prescribing a selfish attitude to a fraction c\_s of the participants, while the others behave politely. Thanks to an original setup enabling the re-injection of egressed participants into the room, the analysis is conducted in a (macroscopically) quasi-stationary regime. We find that, as c\_s is increased, the flow rate J rises, interpolating between published values for egresses in normal conditions and measurements for competitive evacuations. The dependence of several flow properties on the pedestrian density $\rho$ at the door, independently of c\_s , suggests that macroscopically the behavioural aspects could be subsumed under the density, at least in our specific settings with limited crowd pressure. In particular, under these conditions, J grows monotonically with $\rho$ up to "close-packing" ($\rho$ $\approx$ 9 pers/m${}^2$). The flow is then characterised microscopically. Among other quantities, the time lapses between successive escapes, the pedestrians' waiting times in front of the door, and their angles of incidence are analysed statistically. In a nutshell, our main results show that the flow is orderly for polite crowds, with narrowly distributed time lapses between egresses, while for larger c\_s the flow gets disorderly and vanishing time lapses emerge. For all c\_s , we find an alternation between short and long time lapses, which we ascribe to a generalised zipper effect. The average waiting time in the exit zone increases with its occupancy. The disorder in the flow and the pressure felt by participants are also assessed.

This paper deals with a mathematical model of a pedestrian movement. A stochastic cellular automata (CA) approach is used here. The Floor Field (FF) model is a basis model. FF models imply that virtual people follow the shortest path strategy. But people are followed by a strategy of the shortest time as well. This paper is focused on how to mathematically formalize and implement to a model these features of the pedestrian movement. Some results of a simulation are presented.

Force-based models describe pedestrian dynamics in analogy to classical mechanics by a system of second order ordinary differential equations. By investigating the linear stability of two main classes of forces, parameter regions with unstable homogeneous states are identified. In this unstable regime it is then checked whether phase transitions or stop-and-go waves occur. Results based on numerical simulations show, however, that the investigated models lead to unrealistic behavior in form of backwards moving pedestrians and overlapping. This is one reason why stop-and-go waves have not been observed in these models. The unrealistic behavior is not related to the numerical treatment of the dynamic equations but rather indicates an intrinsic problem of this model class. Identifying the underlying generic problems gives indications how to define models that do not show such unrealistic behavior. As an example we introduce a new force-based model which produces realistic jam dynamics without the appearance of unrealistic negative speeds for empirical desired walking speeds.

The results of a systematic quantitative validation of PEDFLOW based on the experimental data from FZJ are presented. Unidirectional flow experiments, totaling 28 different combinations with varying entry, corridor and exit widths, were considered. The condition imposed on PEDFLOW was that all the cases should be run with the same input parameters. The exit times and fundamental diagrams for the measuring region were evaluated and compared. This validation process led to modifications and enhancements of the model underlying PEDFLOW. The preliminary conclusions indicate that the results agree well for densities smaller than 3 m-2 and a good agreement is observed even at high densities for the corridors with bcor = 2.4 m, and bcor = 3.0 m. For densities between 1 and 2 m-2 the specific flow and velocities are underpredicted by PEDFLOW.

This report results from a contract tasking Bar Ilan University as follows: Accounting for Culture in Agent-Based Pedestrian Crowd Simulation. Accurate models of crowd dynamics are an important challenge in multi-agent systems and agent-based social simulation. Crowd models are able to predict the resulting macro level behavior from micro level interactions. However, many existing crowd models do not yet account for cultural factors in crowd behavior, and even more so, for crowds composed of members of different cultures. In this paper we examine the impact of cultural differences on the crowd dynamics in pedestrian and evacuation domains. In the pedestrian domain we relate to recorded pedestrian data in five different countries: Iraq, Israel, England, Canada and France and characterize these cultures based on cultural attributes at the individual level: personal spaces, speed, avoidance side and group formations. We use an agent-based simulation to investigate the impact on the resulting macro level behavior, such as pedestrian flow, number of collisions, etc. We also examine the impact of mixed-culture pedestrians on the resulting macro-level behavior. We quantitatively validate the simulation against data from movies of human crowds, in different countries. In the evacuation domain, we use an established simulation system to investigate cultural differences reported in the literature, and additionally explore the resulting macro level behavior.