Modeling bidirectional pedestrian flow with the perceived uncertainty of preceding pedestrian information

Pedestrian flow models contribute to the effective design and operation of pedestrian spaces. In real traffic, pedestrians usually adjust their walking state in the movement procession according to perceptual information. Subject to the human capability, certain errors would exist between the perceptual information and the real traffic information, which can greatly affect the pedestrian flow performance. This paper proposes a bidirectional pedestrian flow model considering the effect of perceived uncertainty of preceding pedestrian information. In the linear and nonlinear stability analysis, we derive the stability criterion and modified Korteweg–de Vries (mKdV) equation of the proposed model. The kink–antikink solitary wave solution can be acquired via solving the above mKdV equations, which provides insight into the essential property of the formation and propagation of traffic jams near the neutral stability curve. Numerical examples demonstrate that the uncertainty terms and the perception time of pedestrians directly affect the pedestrian congestion.