Bidirectional pedestrian fundamental diagram

• Bidirectional pedestrian fundamental diagram derived from first principles.
• Minimal number of parameters.
• Desirable mathematical properties (non-negative, continuous, closed-form).
• Empirical validation; reproduction of many phenomena from the literature.

This article presents a new model of stationary bidirectional pedestrian flow. Starting out from microscopic first principles, a bidirectional fundamental diagram (FD) is derived that defines direction-specific flow rates as functions of direction-specific densities. The FD yields non-negative and bounded flows and guarantees that the instantaneous density changes that would result from these flows stay bounded between zero and jam density. In its minimal configuration, it uses just as many parameters as a unidirectional triangular FD: maximum walking speed, jam density, a collision avoidance parameter (from which the backward wave speed can be derived). A one-on-one mapping between the parameters guiding uni- and bidirectional pedestrian flows is proposed and both conceptually and empirically justified. Generalizations of the FD that maintain its desirable properties turn out to be straightforward by making its parameters density-dependent. The FD performs very well in comparisons against simulated and real data.