Two dimensional outflows for cellular automata with shuffle updates

In this paper, we explore the two-dimensional behavior of cellular automata with shuffle updates. As a test case, we consider the evacuation of a square room by pedestrians modeled by a cellular automaton model with a static floor field. Shuffle updates are characterized by a variable associated to each particle and called phase, that can be interpreted as the phase in the step cycle in the frame of pedestrian flows. Here we also introduce a dynamics for these phases, in order to modify the properties of the model. We investigate in particular the crossover between low- and high-density regimes that occurs when the density of pedestrians increases, the dependency of the outflow in the strength of the floor field, and the shape of the queue in front of the exit. Eventually we discuss the relevance of these results for pedestrians.

[1]  A. Schadschneider,et al.  Asymmetric exclusion processes with shuffled dynamics , 2005, cond-mat/0509546.

[2]  Anne-Hélène Olivier,et al.  Velocity/curvature relations along a single turn in human locomotion , 2007, Neuroscience Letters.

[3]  A. Schadschneider,et al.  The Asymmetric Exclusion Process: Comparison of Update Procedures , 1997 .

[4]  S Bouzat,et al.  Game theory in models of pedestrian room evacuation. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  Julien Cividini,et al.  Diagonal patterns and chevron effect in intersecting traffic flows , 2013 .

[6]  Michael Schultz,et al.  Stochastic Transition Model for Discrete Agent Movements , 2010, ACRI.

[7]  L. Dai,et al.  NEUTRON REFLECTIVITY STUDY OF END-ADSORBED DIBLOCK COPOLYMERS - CROSS-OVER FROM MUSHROOMS TO BRUSHES , 1992 .

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

[9]  Dirk Helbing,et al.  Dynamics of crowd disasters: an empirical study. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  Cécile Appert-Rolland,et al.  Frozen shuffle update for a deterministic totally asymmetric simple exclusion process with open boundaries , 2011 .

[11]  Serge P. Hoogendoorn,et al.  Self-Organization in Pedestrian Flow , 2005 .

[12]  Rui Jiang,et al.  Pedestrian flow in a lattice gas model with parallel update. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  K. Nishinari,et al.  Introduction of frictional and turning function for pedestrian outflow with an obstacle. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  Andreas Schadschneider,et al.  Friction effects and clogging in a cellular automaton model for pedestrian dynamics. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  Angel Garcimartín,et al.  Silo clogging reduction by the presence of an obstacle. , 2011, Physical review letters.

[16]  A. Schadschneider,et al.  Metastable states in cellular automata for traffic flow , 1998, cond-mat/9804170.

[17]  H. Hilhorst,et al.  Frozen shuffle update for an asymmetric exclusion process on a ring , 2011, 1105.0352.

[18]  Cécile Appert-Rolland,et al.  Traffic Instabilities in Self-Organized Pedestrian Crowds , 2012, PLoS Comput. Biol..

[19]  Andreas Schadschneider,et al.  VALIDATION OF CA MODELS OF PEDESTRIAN DYNAMICS WITH FUNDAMENTAL DIAGRAMS , 2009, Cybern. Syst..

[20]  Gerta Köster,et al.  How update schemes influence crowd simulations , 2014 .

[21]  Lubos Buzna,et al.  Self-Organized Pedestrian Crowd Dynamics: Experiments, Simulations, and Design Solutions , 2005, Transp. Sci..

[22]  L Santen,et al.  Boundary induced phase transitions in driven lattice gases with metastable states. , 2001, Physical review letters.

[23]  T. Chou,et al.  Non-equilibrium statistical mechanics: from a paradigmatic model to biological transport , 2011, 1110.1783.

[24]  J. Zittartz,et al.  Cellular Automaton Approach to Pedestrian Dynamics - Applications , 2001, cond-mat/0112119.

[25]  Dirk Helbing,et al.  Patient and impatient pedestrians in a spatial game for egress congestion. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[27]  Claire Marrison,et al.  Effects of Motivation and Cabin Configuration on Emergency Aircraft Evacuation Behavior and Rates of Egress , 1996 .

[28]  Daniel R. Parisi,et al.  Efficient Egress of Escaping Ants Stressed with Temperature , 2013, PloS one.

[29]  A. Schadschneider,et al.  Discretization effects and the influence of walking speed in cellular automata models for pedestrian dynamics , 2004 .

[30]  A. Schadschneider,et al.  Asymmetric Exclusion Processes with Non-Factorizing Steady States , 2007 .

[31]  Daichi Yanagisawa,et al.  Toward Smooth Movement of Crowds , 2010 .

[32]  Cécile Appert-Rolland,et al.  Shuffle Updates in an Evacuation Problem , 2014 .

[33]  David A. Smith,et al.  Dynamical pair approximation for cellular automata with shuffle update , 2007 .

[34]  Jun Zhang,et al.  Comparison of intersecting pedestrian flows based on experiments , 2013, 1312.2475.

[35]  Aya Hagishima,et al.  Study of bottleneck effect at an emergency evacuation exit using cellular automata model, mean field approximation analysis, and game theory , 2010 .

[36]  W. Daamen.  QUALITATIVE RESULTS FROM PEDESTRIAN LABORATORY EXPERIMENTS , 2003 .

[37]  R. E. Wilson,et al.  Extension of cluster dynamics to cellular automata with shuffle update , 2007 .

[38]  Partha Chakroborty,et al.  Comparison of Pedestrian Fundamental Diagram across Cultures , 2009, Adv. Complex Syst..

[39]  Ludger Santen,et al.  Intracellular transport driven by cytoskeletal motors: General mechanisms and defects , 2015, 1507.06166.

[40]  Angel Garcimartín,et al.  The Conference in Pedestrian and Evacuation Dynamics 2014 ( PED 2014 ) Experimental evidence of the “ Faster Is Slower ” effect , 2014 .

[41]  Ludger Santen,et al.  Single-vehicle data of highway traffic: microscopic description of traffic phases. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[42]  A. Schadschneider,et al.  Statistical physics of vehicular traffic and some related systems , 2000, cond-mat/0007053.

[43]  Gerta Köster,et al.  Bridging the gap: From cellular automata to differential equation models for pedestrian dynamics , 2013, J. Comput. Sci..

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

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

[46]  J. Pettré,et al.  Properties of pedestrians walking in line: fundamental diagrams. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[47]  Majid Sarvi,et al.  Animal dynamics based approach for modeling pedestrian crowd egress under panic conditions , 2011 .

[48]  Michael Schreckenberg,et al.  A cellular automaton model for freeway traffic , 1992 .

[49]  Daniel R. Parisi,et al.  Faster-is-slower effect in escaping ants revisited: Ants do not behave like humans , 2014, 1410.5261.

[50]  A. Seyfried,et al.  The fundamental diagram of pedestrian movement revisited , 2005, physics/0506170.

[51]  Armin Seyfried,et al.  Quantitative comparison of estimations for the density within pedestrian streams , 2015 .

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

[53]  D. Helbing.  Traffic and related self-driven many-particle systems , 2000, cond-mat/0012229.

[54]  Andreas Schadschneider,et al.  Critical bottleneck size for jamless particle flows in two dimensions. , 2014, Physical review letters.

[55]  Hubert Klüpfel,et al.  Evacuation Dynamics: Empirical Results, Modeling and Applications , 2009, Encyclopedia of Complexity and Systems Science.

[56]  Serge P. Hoogendoorn,et al.  Experimental Research of Pedestrian Walking Behavior , 2003 .

[57]  Stefan Holl,et al.  Universal flow-density relation of single-file bicycle, pedestrian and car motion , 2013, 1312.2735.

[58]  A. Schadschneider.  Cellular Automaton Approach to Pedestrian Dynamics - Theory , 2001, cond-mat/0112117.

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