Dynamics of a Simulated Demonstration March: An Efficient Sensitivity Analysis

Protest demonstrations are a manifestation of fundamental rights. Authorities are responsible for guiding protesters safely along predefined routes, typically set in an urban built environment. Microscopic crowd simulations support decision-makers in finding sustainable crowd management strategies. Planning routes usually requires knowledge about the length of the demonstration march. This case study quantifies the impact of two uncertain parameters, the number of protesters and the standard deviation of their free-flow speeds, on the length of a protest march through Kaiserslautern, Germany. Over 1000 participants walking through more than 100,000 m2 lead to a computationally demanding model that cannot be analyzed with a standard Monte Carlo ansatz. We select and apply analysis methods that are efficient for large topographies. This combination constitutes the main novelty of this paper: We compute Sobol’ indices with two different methods, based on polynomial chaos expansions, for a down-scaled version of the original set-up and compare them to Monte Carlo computations. We employ the more accurate of the approaches for the full-scale scenario. The global sensitivity analysis reveals a shift in the governing parameter from the number of protesters to the standard deviation of their free-flow speeds over time, stressing the benefits of a time-dependent analysis. We discuss typical actions, for example floats that reduce the variation of the free-flow speed, and their effectiveness in view of the findings.

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

[2]  Daichi Yanagisawa,et al.  Traffic flow in a crowd of pedestrians walking at different speeds. , 2019, Physical review. E.

[3]  Gerta Köster,et al.  APPLYING BAYESIAN INVERSION WITH MARKOV CHAIN MONTE CARLO TO PEDESTRIAN DYNAMICS , 2019 .

[4]  Nikolai Bode.  Parameter Calibration in Crowd Simulation Models using Approximate Bayesian Computation , 2020, ArXiv.

[5]  Dongbin Xiu,et al.  Stochastic collocation methods: A survey , 2017 .

[6]  Paola Annoni,et al.  Variance based sensitivity analysis of model output. Design and estimator for the total sensitivity index , 2010, Comput. Phys. Commun..

[7]  Gerta Köster,et al.  Sensitivity Analysis for Resilient Safety Design: Application to a Bottleneck Scenario , 2021 .

[8]  A. Saltelli,et al.  Making best use of model evaluations to compute sensitivity indices , 2002 .

[9]  A. Saltelli,et al.  Importance measures in global sensitivity analysis of nonlinear models , 1996 .

[10]  Federico Toschi,et al.  Parameter Estimation of Social Forces in Crowd Dynamics Models via a Probabilistic Method , 2014, Mathematical biosciences and engineering : MBE.

[11]  Eric Bonabeau,et al.  Agent-based modeling: Methods and techniques for simulating human systems , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[12]  Bruno Sudret,et al.  Global sensitivity analysis using polynomial chaos expansions , 2008, Reliab. Eng. Syst. Saf..

[13]  Marion Gödel,et al.  Sensitivity Analysis for Microscopic Crowd Simulation , 2020, Algorithms.

[14]  Will Usher,et al.  SALib: An open-source Python library for Sensitivity Analysis , 2017, J. Open Source Softw..

[15]  Hans-Joachim Bungartz,et al.  FAST AND FLEXIBLE UNCERTAINTY QUANTIFICATION THROUGH A DATA-DRIVEN SURROGATE MODEL , 2018 .

[16]  Benedikt Zönnchen,et al.  Vadere: An open-source simulation framework to promote interdisciplinary understanding , 2019, Collective Dynamics.

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

[18]  D. Xiu.  Fast numerical methods for stochastic computations: A review , 2009 .

[19]  Ilya M. Sobol,et al.  Sensitivity Estimates for Nonlinear Mathematical Models , 1993 .

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

[21]  L. Macía,et al.  A Charter of Fundamental Rights for the European Union , 2000 .

[22]  Hans-Joachim Bungartz,et al.  Modelling social identification and helping in evacuation simulation , 2016, ArXiv.

[23]  Hans Petter Langtangen,et al.  Chaospy: An open source tool for designing methods of uncertainty quantification , 2015, J. Comput. Sci..