Modeling orderly queuing behavior with bending effects

Orderly queuing behavior in open areas with bending effects is studied in this paper. Models are proposed to simulate such behavior, including a motion state model, bending effect model, leader-follower model, virtual linear obstacle model, and group-shopping model. By comparing a simulated queue with an actual one, the entire processes of a pedestrian walking to a queue tail, joining the queue, orderly moving in the queue, shopping, and leaving the queue can be simulated. Additionally, the "arc bending'' effect with one or multiple obstacles, the "stop-and-go"behavior and its backward propagation along the queue, and the "group shopping'' effect around the shopping point are reproduced, similarly to the behavior observed in actual queues. Moreover, factors affecting queuing efficiency are studied, including the minimum distance between leaders and followers, the shopping duration and its randomness, the time interval for a new pedestrian to appear, and the size of pedestrian groups. Compared with the other factors, shopping duration is the most critical factor. Therefore, measures to shorten shopping duration should be taken to improve queuing efficiency.