The Superposition Principle: A Conceptual Perspective on Pedestrian Stream Simulations

Models using a superposition of scalar fields for navigation are prevalent in microscopic pedestrian stream simulations. However, classifications, differences, and similarities of models are not clear at the conceptual level of navigation mechanisms. In this paper, we describe the superposition of scalar fields as an approach to microscopic crowd modelling and corresponding motion schemes. We use this background discussion to focus on the similarities and differences of models, and find that many models make use of similar mechanisms for the navigation of virtual agents. In some cases, the differences between models can be reduced to differences between discretisation schemes. The interpretation of scalar fields varies across models, but most of the time this variation does not have a large impact on simulation outcomes. The conceptual analysis of different models of pedestrian dynamics allows for a better understanding of their capabilities and limitations and may lead to better model development and validation.

[1]  Gerd Gigerenzer,et al.  Why Heuristics Work , 2008, Perspectives on psychological science : a journal of the Association for Psychological Science.

[2]  Celso Leandro Palma,et al.  Simulation: The Practice of Model Development and Use , 2016 .

[3]  Craig W. Reynolds.  Steering Behaviors For Autonomous Characters , 1999 .

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

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

[6]  E. Mcmullin,et al.  What do Physical Models Tell us , 1968 .

[7]  Armin Seyfried,et al.  Collision-free nonuniform dynamics within continuous optimal velocity models. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  G. Strube.  Generative Theories in Cognitive Psychology , 2000 .

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

[10]  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.

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

[12]  K. Lewin,et al.  Field Theory in Social Science: Selected Theoretical Papers , 1951 .

[13]  P G Gipps,et al.  A micro simulation model for pedestrian flows , 1985 .

[14]  Yoshihiro Ishibashi,et al.  Self-Organized Phase Transitions in Cellular Automaton Models for Pedestrians , 1999 .

[15]  Norris R. Johnson,et al.  Panic and the Breakdown of Social Order: Popular Myth, Social Theory, Empirical Evidence , 1987 .

[16]  Benigno E. Aguirre,et al.  Commentary on "Understanding Mass Panic and Other Collective Responses to Threat and Disaster" Emergency Evacuations, Panic, and Social Psychology , 2005 .

[17]  P. Holmes,et al.  Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields , 1983, Applied Mathematical Sciences.

[18]  Clifford Stott,et al.  Representing crowd behaviour in emergency planning guidance: ‘mass panic’ or collective resilience? , 2013 .

[19]  A. R. Humphries,et al.  Dynamical Systems And Numerical Analysis , 1996 .

[20]  Stefania Bandini,et al.  Heterogeneous Speed Profiles in Discrete Models for Pedestrian Simulation , 2014, ArXiv.

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

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

[23]  Alex M. Andrew,et al.  Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science (2nd edition) , 2000 .

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

[25]  Mark J. Embrechts,et al.  Cellular automata modeling of pedestrian movements , 1997, 1997 IEEE International Conference on Systems, Man, and Cybernetics. Computational Cybernetics and Simulation.

[26]  Peter Vortisch,et al.  Comparison of Various Methods for the Calculation of the Distance Potential Field , 2008, ArXiv.

[27]  Stefania Bandini,et al.  Heterogeneous Speed Profiles in Discrete Models for , 2014 .

[28]  Benedikt Zönnchen,et al.  Queuing at Bottlenecks Using a Dynamic Floor Field for Navigation , 2014 .

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

[30]  Victor J. Blue,et al.  Cellular automata microsimulation for modeling bi-directional pedestrian walkways , 2001 .

[31]  Yūki Sugiyama,et al.  Optimal velocity model for traffic flow , 1999 .

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

[33]  Paul H. Rubin.  Gerd Gigerenzer, Peter M. Todd & the ABC [Center for Adaptive Behavior and Cognition] Research Group. Simple Heuristics That Make Us Smart , 2000 .

[34]  André Borrmann,et al.  Generation and use of sparse navigation graphs for microscopic pedestrian simulation models , 2012, Adv. Eng. Informatics.

[35]  Isabella von Sivers,et al.  How Stride Adaptation in Pedestrian Models Improves Navigation , 2014, ArXiv.

[36]  Tobias Kretz,et al.  Pedestrian traffic: on the quickest path , 2009, ArXiv.

[37]  George Yannis,et al.  A critical assessment of pedestrian behaviour models , 2009 .

[38]  S. Dai,et al.  Centrifugal force model for pedestrian dynamics. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

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

[41]  M. Smith.  Field Theory in Social Science: Selected Theoretical Papers. , 1951 .

[42]  Jonathan D. Nelson,et al.  Simple Heuristics and the Modelling of Crowd Behaviours , 2014 .

[43]  Serge P. Hoogendoorn,et al.  State-of-the-art crowd motion simulation models , 2013 .

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

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

[46]  D. Helbing,et al.  The Walking Behaviour of Pedestrian Social Groups and Its Impact on Crowd Dynamics , 2010, PloS one.

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

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

[49]  Felix Dietrich,et al.  The effect of stepping on pedestrian trajectories , 2015 .

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

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

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

[53]  Andreas Schadschneider,et al.  Extended Floor Field CA Model for Evacuation Dynamics , 2004, IEICE Trans. Inf. Syst..