Modelling lateral vehicle arrivals in lane-free, heterogeneous traffic using a stochastic approach

Understanding how road users position themselves laterally on the roadway is critical for improving traffic capacity and safety in heterogeneous, lane-free environments. Unlike lane-based conditions, where trajectories are largely constrained, lane-free traffic requires drivers to make continuous decisions about their placement across the road cross-section. These lateral arrival patterns determine how different vehicle types interact, self-organize, and ultimately shape roadway performance. Traditional lane-based arrival models cannot capture this spatial decision-making or the stochastic nature of mixed traffic, limiting their usefulness in many developing-country contexts. This paper develops a stochastic lateral arrival model grounded in empirical evidence. Data were extracted using a computer-vision-based system from three typical streets in Hanoi, Vietnam, where motorcycles, passenger cars, buses, and trucks operate in shared space without strict lane discipline. The lateral distributions of vehicles were modelled using a three-parameter Weibull distribution, which successfully captured the variability and clustering tendencies of different vehicle classes. Results show systematic patterns: motorcycles concentrate near the curbs, while larger vehicles (passenger cars, buses, trucks) position themselves closer to the centerline. These self-organizing tendencies have direct implications for traffic capacity, safety assessment, and the design of intelligent mobility systems. Beyond its analytical value, the proposed lateral arrival model provides a critical behavioral component for both microscopic traffic simulation, autonomous driving, and digital twins, enabling more realistic representation and decision-making in non-lane-based traffic environments.