Based on experimental traffic data obtained from German and US highways, we propose a novel two-dimensional first-order macroscopic traffic flow model. The goal is to reproduce a detailed description of traffic dynamics for the real road geometry. In our approach both the dynamics along the road and across the lanes is continuous. The closure relations, being necessary to complete the hydrodynamics equation, are obtained by regression on fundamental diagram data. Comparison with prediction of one-dimensional models shows the improvement in performance of the novel model. MSC 90B20; 35L65; 35Q91; 91B74

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The development of surrogate safety measures has drawn significant research interest in the field of traffic safety analysis. Innovative data sources such as video-based traffic surveillance systems have made it possible to collect large amounts of microscopic traffic data. By deriving traffic safety indicators such as the Deceleration Rate to Avoid a Crash (DRAC) statements concerning traffic safety over a determined road section can be made. This work presents the derivation of a novel surrogate safety indicator based on a Constant Initial Acceleration and reaction time assumption which considers the interaction between vehicles and describes the traffic safety of a road section. The evaluation is based on a video-based microscopic traffic data collection. To examine the efficiency, the new developed indicator is compared to the original Deceleration Rate to Avoid a Crash (DRAC) and the modified indicator (MDRAC) which includes the reaction time. The results showed that the new indicator is more sensitive in detecting critical situations than the other indicators and in addition describes the conflict situations more realistically.

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