A Study of Pedestrian Movement on Crosswalks Based on Chaos Theory

Walking, as an important transportation mode, plays a large part in urban transportation systems. This mode is of great importance for planners and decision-makers because of its impact on environmental and health aspects of communities. However, this mode is so complex in nature that makes it difficult to study or model. On the other hand, chaos theory studies complex dynamical nonlinear systems that are sensitive to their initial conditions. A small change in initial conditions and/or parameters, may cause a big variation in the results. That is the situation that could happen in many fields of transportation. In the current study, the pedestrian behavior in crosswalks was studied in terms of chaos theory. The well-known social force model was chosen to model pedestrian movement in crosswalks, and based on the model, sensitivity analysis with respect to its parameters was carried out. Pedestrian road crossing behavior based on Helbing social force model was simulated in Matlab codes. Then pedestrian crossing behavior was investigated to detect the chaotic behavior. It was concluded that the speed of a pedestrian when the other pedestrians are closer than 100 cm and when the number of crossing pedestrians is more than 6 is chaotic. Moreover, increasing the number of pedestrians or decreasing the distance between pedestrians increase the occurrence of chaos. Chaotic behavior of speed causes turbulence in pedestrian crossing path, and that makes the path longer. Finally, some solutions for taking the system out of chaos, and consequently making its performance better, were proposed.