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            <title xml:lang="en">From Microscopic Driver Models to Macroscopic PDEs in Ring Road Traffic Dynamics</title>
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              <p>In this paper, using a continuation method [22], we provide a simple procedure to derive macroscopic models from second order ordinary differential equations modeling individual vehicles moving on a ring. In particular, the result is applied to classical traffic models such as the optimal velocity follow the leader (OV-FTL) models, the intelligent driver model (IDM) or delayed driver models and we are able to modelize the macroscopic behavior of the drivers through a 2 × 2 partial differential equations whose variables are the density of the traffic and the speed of the vehicles. The paper concludes with open questions regarding stability and microscopic control design.</p>
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