An extended LWR non-lane-based-discipline model for light vehicle traffic flow analysis incorporating driver behavior

Non-lane-based discipline is a common driving behavior in traffic flow, particularly in developing countries such as Iran. Under these conditions, driving behaviors change, affecting overall traffic dynamics and making traffic flow prediction more complex. This complexity leads to inaccurate estimates of lane capacity. To improve flow prediction under non-lane-based traffic conditions, this study first examines the dynamic traffic characteristics of non-lane-based discipline, focusing on microscopic variables such as lateral separation distance (LSD) and time headway on an urban multilane highway in Tehran, Iran. Second, an extended Lighthill-Whitham-Richards (LWR) model is proposed to analyze the effects of LSD on traffic flow characteristics. Numerical simulations are conducted using an adjusted upwind scheme, and a stability analysis is performed for the scheme. The model is validated using field data from Iran, specifically for light vehicles (LVs). The results indicate that, under staggered-following behavior, time headways of LV drivers decrease as LSD values increase. The proposed LWR model effectively simulates smooth transitions in density and speed evolution, capturing shock and rarefaction waves in the middle lane. Under non-lane-based discipline, the model accurately represents the gradual deceleration in the jam phase for shock waves and the gradual acceleration in the free flow condition for rarefaction waves. These transitions reflect the real-world continuous traffic flow, preventing sudden acceleration and deceleration of LVs. Furthermore, under non-lane-based traffic conditions with the maximum LSD parameter, lane capacity and jam density in the middle lane increase by 61% and 60%, respectively, compared to lane-based conditions. The model's simulated results were validated using real-world data, demonstrating its effectiveness in predicting the impact of non-lane-based discipline on traffic flow.