  Understanding pedestrian dynamics is crucial for appropriately designing
pedestrian spaces. The pedestrian fundamental diagram (FD), which describes the
relationship between pedestrian flow and density within a given space,
characterizes these dynamics. Pedestrian FDs are significantly influenced by
the flow type, such as uni-directional, bi-directional, and crossing flows.
However, to the authors' knowledge, generalized pedestrian FDs that are
applicable to various flow types have not been proposed. This may be due to the
difficulty of using statistical methods to characterize the flow types. The
flow types significantly depend on the angles of pedestrian movement; however,
these angles cannot be processed by standard statistics due to their
periodicity. In this study, we propose a comprehensive model for pedestrian FDs
that can describe the pedestrian dynamics for various flow types by applying
Directional Statistics. First, we develop a novel statistic describing the
pedestrian flow type solely from pedestrian trajectory data using Directional
Statistics. Then, we formulate a comprehensive pedestrian FD model that can be
applied to various flow types by incorporating the proposed statistics into a
traditional pedestrian FD model. The proposed model was validated using actual
pedestrian trajectory data. The results confirmed that the model effectively
represents the essential nature of pedestrian dynamics, such as the capacity
reduction due to conflict of crossing flows and the capacity improvement due to
the lane formation in bi-directional flows.
