Microscopic traffic flow model

Microscopic traffic flow models are a class of scientific models of vehicular traffic dynamics.

In contrast to macroscopic models, microscopic traffic flow models simulate single vehicle-driver units, so the dynamic variables of the models represent microscopic properties like the position and velocity of single vehicles.

Also known as time-continuous models, all car-following models have in common that they are defined by ordinary differential equations describing the complete dynamics of the vehicles' positions ${\displaystyle x_{\alpha }}$ and velocities ${\displaystyle v_{\alpha }}$. It is assumed that the input stimuli of the drivers are restricted to their own velocity ${\displaystyle v_{\alpha }}$, the net distance (bumper-to-bumper distance) ${\displaystyle s_{\alpha }=x_{\alpha -1}-x_{\alpha }-l_{\alpha -1}}$ to the leading vehicle ${\displaystyle \alpha -1}$ (where ${\displaystyle l_{\alpha -1}}$ denotes the vehicle length), and the velocity ${\displaystyle v_{\alpha -1}}$ of the leading vehicle. The equation of motion of each vehicle is characterized by an acceleration function that depends on those input stimuli:

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