Comparison study of the reactive and predictive dynamic models for pedestrian flow

This paper formulates the reactive and predictive dynamic models for pedestrian flow and presents a comparison of the two models. The path-choice behavior of pedestrians in the reactive dynamic model is described that pedestrians tend to walk along a path with the lowest instantaneous cost. The desired walking direction of pedestrians in the predictive dynamic model is chosen to minimize the actual cost based on predictive traffic conditions. An algorithm used to solve the two models encompasses a cell-centered finite volume method for a hyperbolic system of conservation laws and a time-dependent Hamilton–Jacobi equation, a fast sweeping method for an Eikonal-type equation, and a self-adaptive method of successive averages for an arisen discrete fixed point problem. The two models and their algorithm are applied to investigate the spatio-temporal patterns of flux or density and path-choice behaviors of pedestrian flow marching in a facility scattered with an obstacle. Numerical results show that the two models are able to capture macroscopic features of pedestrian flow, traffic instability and other complex nonlinear phenomena in pedestrian traffic, such as the formation of stop-and-go waves and clogging at bottlenecks. Different path-choice strategies of pedestrians cause different spatial distributions of pedestrian density specially in the high-density regions (near the obstacle and exits).

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

[2]  Renyong Guo.  New insights into discretization effects in cellular automata models for pedestrian evacuation , 2014 .

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

[4]  Adrian Muntean,et al.  Dynamics of pedestrians in regions with no visibility:a lattice model without exclusion , 2012, 1203.4852.

[5]  P. Degond,et al.  A Hierarchy of Heuristic-Based Models of Crowd Dynamics , 2013, 1304.1927.

[6]  Serge P. Hoogendoorn,et al.  Pedestrian route-choice and activity scheduling theory and models , 2004 .

[7]  N. Bellomo,et al.  ON THE MODELLING CROWD DYNAMICS FROM SCALING TO HYPERBOLIC MACROSCOPIC MODELS , 2008 .

[8]  Paola Goatin,et al.  Macroscopic modeling and simulations of room evacuation , 2013, 1308.1770.

[9]  Bing-Hong Wang,et al.  The escape of pedestrians with view radius , 2013 .

[10]  S. Wong,et al.  A higher-order macroscopic model for pedestrian flows , 2010 .

[11]  Hongkai Zhao,et al.  Fixed-point iterative sweeping methods for static hamilton-Jacobi Equations , 2006 .

[12]  Serge P. Hoogendoorn,et al.  DYNAMIC USER-OPTIMAL ASSIGNMENT IN CONTINUOUS TIME AND SPACE , 2004 .

[13]  D. Knopoff,et al.  A kinetic theory approach to the dynamics of crowd evacuation from bounded domains , 2015 .

[14]  Roger L. Hughes,et al.  A continuum theory for the flow of pedestrians , 2002 .

[15]  Yanqun Jiang,et al.  Numerical simulation of a continuum model for bi-directional pedestrian flow , 2011, Appl. Math. Comput..

[16]  R. Alizadeh,et al.  A dynamic cellular automaton model for evacuation process with obstacles , 2011 .

[17]  Chi-Wang Shu,et al.  Revisiting Jiang’s dynamic continuum model for urban cities , 2013 .

[18]  Dirk Helbing,et al.  From Crowd Dynamics to Crowd Safety: a Video-Based Analysis , 2008, Adv. Complex Syst..

[19]  Chi-Wang Shu,et al.  Dynamic continuum pedestrian flow model with memory effect. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[20]  Hai-Jun Huang,et al.  A mobile lattice gas model for simulating pedestrian evacuation , 2008 .

[21]  Chi-Wang Shu,et al.  A REACTIVE DYNAMIC CONTINUUM USER EQUILIBRIUM MODEL FOR BI-DIRECTIONAL PEDESTRIAN FLOWS ∗ , 2009 .

[22]  N. Bellomo,et al.  On the multiscale modeling of vehicular traffic: From kinetic to hydrodynamics , 2014 .

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

[24]  Xiwei Guo,et al.  Modeling of pedestrian evacuation under fire emergency based on an extended heterogeneous lattice gas model , 2013 .

[25]  E. Toro.  Riemann Solvers and Numerical Methods for Fluid Dynamics , 1997 .

[26]  D. Helbing,et al.  Lattice gas simulation of experimentally studied evacuation dynamics. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[27]  Eric Wai Ming Lee,et al.  The effect of overtaking behavior on unidirectional pedestrian flow , 2012 .

[28]  Luisa Fermo,et al.  TOWARDS THE MODELING OF VEHICULAR TRAFFIC AS A COMPLEX SYSTEM: A KINETIC THEORY APPROACH , 2012 .

[29]  Sze Chun Wong,et al.  Perceived cost potential field cellular automata model with an aggregated force field for pedestrian dynamics , 2014 .

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

[31]  Sze Chun Wong,et al.  A macroscopic approach to the lane formation phenomenon in pedestrian counterflow , 2011 .

[32]  Nicola Bellomo,et al.  On the Modeling of Traffic and Crowds: A Survey of Models, Speculations, and Perspectives , 2011, SIAM Rev..

[33]  Chi-Wang Shu,et al.  Revisiting Hughes’ dynamic continuum model for pedestrian flow and the development of an efficient solution algorithm , 2009 .

[34]  Nicola Bellomo,et al.  From the Microscale to Collective Crowd Dynamics , 2013, Multiscale Model. Simul..

[35]  Andreas Schadschneider,et al.  Simulation of evacuation processes using a bionics-inspired cellular automaton model for pedestrian dynamics , 2002 .

[36]  Serge P. Hoogendoorn,et al.  Pedestrian Behavior at Bottlenecks , 2005, Transp. Sci..