Macroscopic Modelling of Pedestrian Flows Based on Conservation Law

Abstract

Overcrowded of sidewalks can reduce the level of satisfaction of pedestrians. The large crowd on the sidewalks results in slowing down time of the pedestrian to arrive in their destination. This studt, focuses on pedestrian flows modelling using the macroscopic model. Numerical approximation of the macroscopic model is formulated as scalar hyperbolic conservation laws. The Lax-Wendroff scheme is used to discretize the equation of conservation laws. The simulation results show that the numerical approximation in term of density confirms the exact solution. In this simulation, the velocity function is obtained by curve fitting of observation data using linear regression method. The observation data, which are consist of velocity-density relation, are obtained from observation of pedestrian flows. The study case of this research conducts on the sidewalks of Braga Street, Bandung, Indonesia. There are two velocity functions used in the simulation, i.e. c 1 = 0.58206 + −0.94476ρ and c 2 = 0.59926 + −0.78052ρ, respectively. In performing the velocity function c 2, the pedestrian leader position is approximately 1 meter in front of the pedestrian leader using the velocity function c 1 at final time T = 20 seconds and T = 30 seconds. Overall, the numerical experiment shows that the pedestrian leader using the velocity functions c 2 is faster than by using c 1.