Effect of Response Time Distribution in Weak Lane Discipline on Linear Stability

The increase in mixed traffic with weak lane discipline (2D mixed traffic) has attracted significant research attention. To better replicate and understand traffic with weak lane discipline, this study examined the variation in response time relative to the position of the leading vehicle, including lateral shifts. Through experiments conducted using a driving simulator and functional fitting, we demonstrated that changes in response time due to longitudinal and lateral locational shifts are well represented by linear and exponential functions, respectively. Additionally, we proposed an extended formulation of the 2D optimal velocity model (2D OVM) that incorporates variable response times, termed the 2D OVM with varying sensitivities (2D OVMVS). The stability condition was derived using a linear approximation. A comparative analysis of the phase diagrams of the 2D OVM and 2D OVMVS, along with a sensitivity analysis, revealed that the proposed 2D OVMVS exhibited a larger unstable region in the phase diagram and lower stability in stable regions than the 2D OVM. As a result, in 2D traffic with weak lane discipline, the equilibrium formation of vehicles was more susceptible to disruption. Our findings indicate that variable response times, as observed in this study, substantially influence the stability of no-lane traffic. Unlike fixed-response models, incorporating response time variability accentuates unstable tendencies. This underscores the necessity of accounting for non-uniform response time distributions in future traffic models.