Capturing Stochastic Variabilities in Pedestrian Flows: A Dynamic Continuum Modeling Approach

Stochastic phenomena are commonly observed in pedestrian flow. However, the existing models for pedestrian dynamics rely on averaged inputs and yield deterministic outputs only, and thereby fail to capture the stochastic variabilities inherent in pedestrian dynamics. This study builds upon Hughes’ dynamic continuum model to develop mathematical models for stochastic pedestrian dynamics that explicitly consider two types of stochastic characteristics: demand stochasticity and behavioral stochasticity. The proposed system, represented as a set of time-dependent stochastic partial differential equations, is solved using a combination of the Monte Carlo (MC) method or Quasi Monte Carlo (QMC) method and efficient numerical schemes, such as a fifth-order weighted essentially non-oscillatory finite difference scheme and the fast sweeping method. Benchmarking scenarios are designed and simulated, and the numerical results demonstrate the convergence and computational performance of the MC and QMC methods. The advantage of stochastic modeling is evident given the significant differences between the averaged stochastic outputs and deterministic outputs, attributable to the strength of stochasticity and extent of stochastic dimensions. Moreover, based on stochastic data inputs, the proposed stochastic models and numerical solutions can clarify the probabilistic distributions of key indicators, such as density, which are valuable for the design and improvement of pedestrian facilities.