Bridging the gap: From cellular automata to differential equation models for pedestrian dynamics

Abstract Cellular automata (CA) and ordinary differential equation (ODE) models compete for dominance in microscopic pedestrian dynamics. There are two major differences: movement in a CA is restricted to a grid and navigation is achieved by moving directly in the desired direction. Force based ODE models operate in continuous space and navigation is computed indirectly through the acceleration vector. We present the Optimal Steps Model and the Gradient Navigation Model, which produce trajectories similar to each other. Both are grid-free and free of oscillations, leading to the conclusion that the two major differences are also the two major weaknesses of the older models.

[1]  Mohcine Chraibi,et al.  Force-based models of pedestrian dynamics , 2011, Networks Heterog. Media.

[2]  Edward Lester,et al.  Modelling contra-flow in crowd dynamics DEM simulation. , 2009 .

[3]  Dirk Hartmann,et al.  Adaptive pedestrian dynamics based on geodesics , 2010 .

[4]  Michel Bierlaire,et al.  Discrete Choice Models for Pedestrian Walking Behavior , 2006 .

[5]  Mohcine Chraibi,et al.  On Force-Based Modeling of Pedestrian Dynamics , 2013, Modeling, Simulation and Visual Analysis of Crowds.

[6]  Daichi Yanagisawa,et al.  Simulation of space acquisition process of pedestrians using Proxemic Floor Field Model , 2012 .

[7]  M. Schreckenberg,et al.  Experimental study of pedestrian flow through a bottleneck , 2006, physics/0610077.

[8]  Dirk Helbing,et al.  How simple rules determine pedestrian behavior and crowd disasters , 2011, Proceedings of the National Academy of Sciences.

[9]  Felix Dietrich,et al.  Gradient navigation model for pedestrian dynamics. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  D. Manocha,et al.  Pedestrian Simulation Using Geometric Reasoning in Velocity Space , 2014 .

[11]  A. Schadschneider,et al.  Simulation of pedestrian dynamics using a two dimensional cellular automaton , 2001 .

[12]  Armin Seyfried,et al.  Empirical data for pedestrian flow through bottlenecks , 2009 .

[13]  Wolfram Klein,et al.  Microscopic Pedestrian Simulations: From Passenger Exchange Times to Regional Evacuation , 2010, OR.

[14]  Tony White,et al.  Macroscopic effects of microscopic forces between agents in crowd models , 2007 .

[15]  Dirk Helbing,et al.  Experimental study of the behavioural mechanisms underlying self-organization in human crowds , 2009, Proceedings of the Royal Society B: Biological Sciences.

[16]  Gerta Köster,et al.  Avoiding numerical pitfalls in social force models. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[17]  Dirk Helbing,et al.  Simulating dynamical features of escape panic , 2000, Nature.

[18]  Zvi Shiller,et al.  Motion planning in dynamic environments: obstacles moving along arbitrary trajectories , 2001, Proceedings 2001 ICRA. IEEE International Conference on Robotics and Automation (Cat. No.01CH37164).

[19]  Paolo Fiorini,et al.  Motion Planning in Dynamic Environments Using Velocity Obstacles , 1998, Int. J. Robotics Res..

[20]  James A. Sethian,et al.  Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid , 2012 .

[21]  Jaroslaw Was,et al.  Adapting Social Distances Model for Mass Evacuation Simulation , 2013, Journal of Cellular Automata.

[22]  Mohcine Chraibi,et al.  Generalized centrifugal-force model for pedestrian dynamics. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  Xiaoping Zheng,et al.  Modeling crowd evacuation of a building based on seven methodological approaches , 2009 .

[24]  Michael Schreckenberg,et al.  Simulation of competitive egress behavior: comparison with aircraft evacuation data , 2003 .

[25]  J A Sethian,et al.  A fast marching level set method for monotonically advancing fronts. , 1996, Proceedings of the National Academy of Sciences of the United States of America.

[26]  Adrien Treuille,et al.  Continuum crowds , 2006, SIGGRAPH 2006.

[27]  S. Wong,et al.  Potential field cellular automata model for pedestrian flow. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[28]  Ulrich Weidmann,et al.  Transporttechnik der Fussgänger , 1992 .

[29]  Armin Seyfried,et al.  Microscopic insights into pedestrian motion through a bottleneck, resolving spatial and temporal variations , 2011, Collective Dynamics.

[30]  Wolfram Klein,et al.  On modelling the influence of group formations in a crowd , 2011 .

[31]  Andreas Schadschneider,et al.  Empirical results for pedestrian dynamics and their implications for modeling , 2011, Networks Heterog. Media.

[32]  Dinesh Manocha,et al.  Reciprocal n-Body Collision Avoidance , 2011, ISRR.

[33]  Andreas Schadschneider,et al.  A stochastic cellular automaton model for traffic flow with multiple metastable states , 2004 .

[34]  Gerta Köster,et al.  Natural discretization of pedestrian movement in continuous space. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[35]  A. Johansson,et al.  Constant-net-time headway as a key mechanism behind pedestrian flow dynamics. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[36]  Helbing,et al.  Social force model for pedestrian dynamics. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[37]  Mohcine Chraibi,et al.  Validated force-based modeling of pedestrian dynamics , 2012 .