Lattice hydrodynamic model of pedestrian flow considering the asymmetric effect

The original lattice hydrodynamic model of traffic flow is extended to single-file pedestrian movement at middle and high density by considering asymmetric interaction (i.e., attractive force and repulsive force). A new optimal velocity function is introduced to depict the complex behaviors of pedestrian movement. The stability condition of this model is obtained by using the linear stability theory. It is shown that the modified optimal velocity function has a remarkable influence on the neutral stability curve and the pedestrian phase transitions. The modified Korteweg-de Vries (mKdV) equation near the critical point is derived by applying the reductive perturbation method, and its kink-antikink soliton solution can better describe the stop-and-go phenomenon of pedestrian flow. From the density profiles, it can be found that the asymmetric interaction is more efficient than the symmetric interaction in suppressing the pedestrian jam. The numerical results are consistent with the theoretical analysis.