The HADES seminar on Tuesday, **May 9th** will be at **3:30 pm** in **Room 740**.

**Speaker:** Nadim Saad

**Abstract:** In this talk, first, we start with the traditional Lighthill-Whitham-Richards (LWR) model for unidirectional traffic on a single road and present a novel traffic model which incorporates realistic driver behaviors through a non-linear velocity function. We develop a particle-based traffic model to inform the choice of velocity functions for the PDE model. We incorporate various driver behaviors in the particle-based model to generate realistic velocity functions. We explore various impacts of numerous driving behaviors on different traffic situations using both the PDE model and the particle-based model, and compare the traffic distributions and throughput of cars on the road obtained by both models. Second, we extend the one-lane model to a multi-lane traffic model and incorporate source functions representing lanes exchanges. We derive desirable mathematical conditions for source functions to ensure $L^1$ contractivity for the system of PDEs. We build a multi-lane particle-based model to inform the choice of source functions for the PDE model. We study various driver behaviors in the particle-based model to develop realistic source functions. We explore various impacts of different driving scenarios using both models.