Katsuhiro Nishinari

Friction effects and clogging in a cellular automaton model for pedestrian dynamics

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 artifact 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 an internal local pressure between the pedestrians which becomes important in regions of high density, occurring, 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.

Discretization effects and the influence of walking speed in cellular automata models for pedestrian dynamics

We study discretization 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 vmax is investigated by increasing the interaction range beyond nearest neighbour interactions. The extension of the model to vmax>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 vmax has a strong influence on the shape of the flow–density relation. We show that walking speeds vmax>1 lead to results which are in very good agreement with empirical data.

Simulation of competitive egress behavior: comparison with aircraft evacuation data

We report new results obtained using cellular automata for pedestrian dynamics with friction. Monte-Carlo simulations of evacuation processes are compared with experimental results on competitive behavior in emergency egress from an aircraft. In the model, the recently introduced concept of a friction parameter μ is used to distinguish between competitive and cooperative movement. However, an additional influence in competition is increased walking speed. Empirical results show that a critical door width wc separates two regimes: for wwc it leads to a decrease. This result is reproduced in the simulation only if both influences, walking speed and friction, are taken into account.

Intracellular transport of single-headed molecular motors KIF1A.

Motivated by experiments on single-headed kinesin KIF1A, we develop a model of intracellular transport by interacting molecular motors. It captures explicitly not only the effects of adenosine triphosphate hydrolysis, but also the ratchet mechanism which drives individual motors. Our model accounts for the experimentally observed single-molecule properties in the low-density limit and also predicts a phase diagram that shows the influence of hydrolysis and Langmuir kinetics on the collective spatiotemporal organization of the motors. Finally, we provide experimental evidence for the existence of domain walls in our in vitro experiment with fluorescently labeled KIF1A.

Cluster formation and anomalous fundamental diagram in an ant-trail model

A recently proposed stochastic cellular automaton model [J. Phys. A 35, L573 (2002)], motivated by the motions of ants in a trail, is investigated in detail in this paper. The flux of ants in this model is sensitive to the probability of evaporation of pheromone, and the average speed of the ants varies nonmonotonically with their density. This remarkable property is analyzed here using phenomenological and microscopic approximations thereby elucidating the nature of the spatiotemporal organization of the ants. We find that the observations can be understood by the formation of loose clusters, i.e., space regions of enhanced, but not maximal, density.

Introduction of frictional and turning function for pedestrian outflow with an obstacle

In this paper, two important factors which affect the pedestrian outflow at a bottleneck significantly are studied in detail to analyze the effect of an obstacle setup in front of an exit. One is a conflict at an exit when pedestrians evacuate from a room. We use floor field model for simulating such behavior, which is a well-studied pedestrian model using cellular automata. The conflicts have been taken into account by the friction parameter. However, the friction parameter so far is a constant and does not depend on the number of the pedestrians conflicting at the same time. Thus, we have improved the friction parameter by the frictional function, which is a function of the number of the pedestrians involved in the conflict. Second, we have presented the cost of turning of pedestrians at the exit. Since pedestrians have inertia, their walking speeds decrease when they turn and the pedestrian outflow decreases. The validity of the extended model, which includes the frictional function and the turning function, is supported by the comparison of a mean-field theory and real experiments. We have observed that the pedestrian flow increases when we put an obstacle in front of an exit in our real experiments. The analytical results clearly explains the mechanism of the effect of the obstacle, i.e., the obstacle blocks pedestrians moving to the exit and decreases the average number of pedestrians involved in the conflict. We have also found that an obstacle works more effectively when we shift it from the center since pedestrians go through the exit with less turning.

CA Approach to Collective Phenomena in Pedestrian Dynamics

Pedestrian dynamics exhibits a variety of fascinating and surprising collective phenomena (lane formation, flow oscillations at doors etc.). A 2-dimensional cellular automaton model is presented which is able to reproduce these effects. Inspired by the principles of chemotaxis the interactions between the pedestrians are mediated by a so-called floor field. This field has a similar effect as the chemical trace created e.g. by ants to guide other individuals to food places. Due to its simplicity the model allows for faster than real time simulations of large crowds.

Modelling of self-driven particles : Foraging ants and pedestrians

Models for the behavior of ants and pedestrians are studied in a unified way in this paper. Each ant follows pheromone put by preceding ants, hence creating a trail on the ground, while pedestrians also try to follow others in a crowd for efficient and safe walking. These following behaviors are incorporated in our stochastic models by using only local update rules for computational efficiency. It is demonstrated that the ant trail model shows a unusual non-monotonic dependence of the average speed of the ants on their density, which can be well analyzed by the zero-range process. We also show that this anomalous behavior is clearly observed in an experiment of multiple robots. Next, the relation between the ant trail model and the floor field model for studying evacuation dynamics of pedestrians is discussed. The latter is regarded as a two-dimensional generalization of the ant trail model, where the pheromone is replaced by footprints. It is shown from simulations that small perturbations to pedestrians will sometimes avoid congestion and hence allow safe evacuation.

Analytical properties of ultradiscrete Burgers equation and rule-184 cellular automaton

In this paper, we propose an ultradiscrete Burgers equation of which all the variables are discrete. The equation is derived from a discrete Burgers equation under an ultradiscrete limit and reduces to an ultradiscrete diffusion equation through the Cole-Hopf transformation. Moreover, it becomes a cellular automaton (CA) under appropriate conditions and is identical to rule-184 CA in a specific case. We show shock wave solutions and asymptotic behaviours of the CA exactly via the diffusion equation. Finally, we propose a particle model expressed by the CA and discuss a mean flux of particles.

Multi-value cellular automaton models and metastable states in a congested phase

In this paper, a family of multi-value cellular automaton (CA) associated with traffic flow is presented. The family is obtained by extending the rule-184 CA, which is an ultradiscrete analogue to the Burgers equation. CA models in the family show both metastable states and stop-and-go waves, which are often observed in real traffic flow. Metastable states in the models exist not only on a prominent part of a free phase but also in a congested phase.