Linear and nonlinear stability analysis of an extended car-following model considering pedestrians on adjacent lane

This paper presents an extended car-following model, which can be used to describe the dynamic characteristics of mixed traffic with pedestrians walking on adjacent lane. The proposed model is based on the optimal velocity function by taking into account two additional stimuli generated by adjacent pedestrians, i.e., the lateral and longitudinal headways between the observed car and the preceding pedestrian. By using the linear stability theory, this paper first derives the stability condition and plots the neutral stability curves with the model-related parameters. Then through the reductive perturbation method, we obtain the soliton solution of the modified Korteweg–de Vries equation near the critical point and depict the coexisting curve which divides the traffic flow state into three types (i.e., stable, metastable and unstable state) along with the corresponding neutral stability curve. Numerical results demonstrate that the proposed model can effectively characterize traffic following behaviors under the mixed-pedestrian–vehicle situation.