Single-file pedestrian dynamics: a review of agent-following models

Single-file dynamics has been studied intensively, both experimentally and theoretically. It shows interesting collective effects, such as stop-and-go waves, which are validation cornerstones for any agent-based modeling approach of traffic systems. Many models have been proposed, e.g. in the form of car-following models for vehicular traffic. These approaches can be adapted for pedestrian streams. In this study, we delve deeper into these models, with particular attention on their interconnections. We do this by scrutinizing the influence of different parameters, including relaxation times, anticipation time, and reaction time. Specifically, we analyze the inherent fundamental problems with force-based models, a classical approach in pedestrian dynamics. Furthermore, we categorize car-following models into stimulus-response and optimal velocity models, highlighting their historical and conceptual differences. These classes can further be subdivided considering the conceptual definitions of the models, e.g. first-order vs. second-order models, or stochastic vs. deterministic models with and without noise. Our analysis shows how car-following models originally developed for vehicular traffic can provide new insights into pedestrian behavior. The focus on single-file motion, which is similar to single-lane vehicular traffic, allows for a detailed examination of the relevant interactions between pedestrians.