Exploring jamming transitions and density waves in bidirectional pedestrian traffic

In this paper we propose a two-dimensional lattice hydrodynamic model considering path change in the bidirectional flow of pedestrians on the road. The stability condition and the mKdV equation describing the density wave of pedestrian traffic jamming are obtained by linear stability and nonlinear analyses. The phase diagram produced from these analyses indicates that the phase transition occurs amongst the freely moving phase, the coexisting phase and the uniformly congested phase below the critical point a c . Additionally the results reveal the existence of a critical magnitude of path change (γ c ). Once the magnitude of path change exceeds the critical value, it gives rise to unstable density waves. Moreover, numerical simulations are performed and the results are in accordance with the theoretical analyses.