Probabilistic Modeling of Inter-Vehicle Spacing on Two-Lane Roads: Implications for Safety-Oriented and Sustainable Traffic Operations

Accurate characterization of inter-vehicle spacing is fundamental for safety assessment and sustainable operation of road networks, particularly on two-lane rural roads where monitoring infrastructure is limited. Unlike temporal headways, vehicle spacing directly reflects physical vehicle interactions and roadway occupancy, making it a more appropriate variable for evaluating collision risk and operational efficiency. This study develops a probabilistic framework for modeling vehicle spacing based on the statistical isomorphism between Event Flows and Linear Fields of Random Points. Using a calibrated microscopic simulation model, spacing distributions are generated for unidirectional traffic over flow rates from 100 to 1300 veh/h. A Pearson Type III distribution is shown to consistently reproduce the observed asymmetry, kurtosis, and non-zero minimum spacing across traffic regimes. Distribution parameters are estimated via maximum likelihood and validated using a heuristic Kolmogorov–Smirnov procedure suitable for large samples. Results demonstrate systematic relationships between spacing distribution parameters and macroscopic traffic variables, enabling estimation of the probability of unsafe spacing conditions from commonly available traffic data. The proposed framework supports sustainability-oriented traffic management by providing a quantitative basis for safety evaluation and operational control without requiring extensive sensing infrastructure.