A macroscopic loading model for dynamic, anisotropic and congested pedestrian flows

Abstract

A dynamic network loading model applicable to anisotropic, time-varying and congested pedestrian flows is proposed. The model is formulated at the aggregate level with respect to time, space and pedestrians. Space is partitioned into cells, each associated with a set of prevalent walking directions. These uni-directional pedestrian streams are represented by links that interact unless pedestrian density is low. The mathematical formulation of the model is based on a generalization of the cell-transmission model and the underlying LWR theory for traffic flow. It makes use of a recently proposed stream-based pedestrian fundamental diagram that empirically relates density and walking speed for multi-directional pedestrian flows. *Transport and Mobility Laboratory, School of Architecture, Civil and Environmental Engineering, Ecole Polytechnique Fédérale de Lausanne, Switzerland tDepartment of Civil and Environmental Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, China

Besides presenting and motivating the proposed loading model, several test cases are discussed that illustrate the behavior of the model in different situations'. Particular emphasis is thereby given to the study of test cases involving multi-directional flow. A comparison to a related isotropic loading model allows to assess the advantages of the multi-directional formulation in terms of accuracy and realism. Moreover, a real test case is considered to calibrate the model and to assess its ability to reproduce empirical results.