Development and Validation of a Probabilistic Fundamental Traffic-Flow Model Using UAV Observations from Representative Motorway and Expressway Segments

Abstract

Reliable traffic-flow models are important for traffic analysis, simulation and intelligent transport management, yet fundamental traffic-flow relationships are frequently transferred between countries despite differences in road design, traffic composition and driver behavior. This study developed and validated probabilistic speed–density and flow–density models for Croatian motorways and expressways. Sixteen representative road segments were selected through traffic and spatial analysis, clustering and stratified sampling. Traffic was recorded using an unmanned aerial vehicle, producing 25,634 individual vehicle observations and 5994 valid one-minute records. Seven deterministic functions and more than 60 probability distributions were examined. A negative exponential function achieved the highest overall performance score for the deterministic component. Speed variation was represented by a Generalized Extreme Value distribution whose scale and shape parameters changed across four density groups. Probabilistic flow values were derived from generated speed values to preserve the relationship q = gV. Fivefold cross-validation produced an average MAE of 15.75 km/h, RMSE of 19.45 km/h and MAPE of 14.37%. The deterministic component also produced the lowest MAE and MAPE among 11 comparison models for both speed and flow. By providing empirically derived relationships that capture both typical traffic conditions and the observed variability in traffic flow, the proposed model can support traffic simulation, traffic-state assessment, and the development of smart mobility and traffic-management applications. The findings contribute to a more reliable representation and assessment of traffic-flow conditions on motorways and expressways, with potential applicability to comparable road environments. Further observations under high-density conditions and validation at independent locations are required before the model is applied more widely or transferred to other road environments.