Characteristics and a Simulation Model of Self-organizing Behavior of Pedestrian Flow at Crosswalk under Rainy Condition

To enhance traffic safety and efficiency of urban street-crossing facilities during rainfall, the self-organizing behavior of pedestrian flows crossing streets in the rain is investigated. A corresponding simulation model is also developed. More specifically, the crossing trajectory data of pedestrian flows in both sunny and rainy conditions are collected through on-site observation. Next, a comparative analysis is employed to determine pedestrian flow's distribution of speed, displacement offset for avoidance, and magnitude of spatial overflow with moderate and light rainfalls. Based on these findings, a pedestrian flow movement model for rainy conditions is proposed by modifying the social force model. The model parameters are calibrated and simulation verification is performed using the collected data. The results of the characteristic analysis reveal that: Due to rainfalls, the proportion of pedestrian's speeds ranging between 0.5 and 1.25 m/s increases by 58.80%; while it decreases by 24.37% in the range of 1.25 to 2.0 m/s. This indicates a significant shift of speed towards a lower range (p < 0.001). However, there are 8.05% of the pedestrians, without umbrellas or in an overflow situation, crossing streets at higher speeds in the range of 2.0 to 2.5 m/s. A notable increase (46.8%) in displacement offset is observed when pedestrians encounter each other in rainy conditions, a change that is statistically significant (p < 0.001). The thresholds of the number and flow rate of waiting pedestrians triggering overflow situations decreases by 7 people and 3 people/min, respectively, and the corresponding overflow magnitude ranges from 5.07% to 24.80%. The simulation results indicate that: The proposed model exhibits an accuracy in rainy condition that is comparable to that in sunny conditions. Specifically, the root mean square errors of forward movement in one direction and avoidance movement in opposite directions for sunny conditions are 0.245 and 0.483 respectively, while those for rainy conditions are 0.329 and 0.702 respectively. No significant difference between the simulated speed distribution and the measured one is observed (p =0.620 for sunny conditions, p =0.649 for rainy conditions). The model is able to reproduce the urgent behavior of crossing streets of pedestrians without umbrellas or in an overflow situation. The absolute error of overflow magnitude of pedestrian flows between the simulated and measured situations is 2.08% in typical rainy conditions, while no overflow situations are observed in sunny conditions, which aligns with the empirical findings.