Module 3 : Microscopic Traffic Flow Modeling

Lecture 14 : Car Following Models

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	Follow-the-leader model The car following model proposed by General motors is based on follow-the leader concept. This is based on two assumptions; (a) higher the speed of the vehicle, higher will be the spacing between the vehicles and (b) to avoid collision, driver must maintain a safe distance with the vehicle ahead. Let $\Delta x^{t}_{n+1}$ is the gap available for $(n+1)^{th}$ vehicle, and let $\Delta x_{safe}$ is the safe distance, $v^t_{n+1}$ and $v^t_{n}$ are the velocities, the gap required is given by, $$\Delta x^{t}_{n+1}= \Delta{x}_{safe} + \tau v^{t}_{n+1}$$ (1) where $\tau$ is a sensitivity coefficient. The above equation can be written as $$x_n - x^{t}_{n+1} = \Delta{x}_{safe} + \tau v^t_{n+1}$$ (2) Differentiating the above equation with respect to time, we get $$v_n^{t}-v_{n+1}^t = \tau.a_{n+1}^t$$ $$a^t_{n+1} = \frac{1}{\tau}[v^t_{n}-v^t_{n+1}]$$ General Motors has proposed various forms of sensitivity coefficient term resulting in five generations of models. The most general model has the form, $$a^t_{n+1} = \left[\frac{\alpha_{l,m}{(v^t_{n+1}})^m}{{(x^t_n-x^t_{n+1}})^{l}}\right]\left[v_n^{t}-v^t_{n+1}\right]$$ (3) where $l$ is a distance headway exponent and can take values from +4 to -1, $m$ is a speed exponent and can take values from -2 to +2, and $\alpha$ is a sensitivity coefficient. These parameters are to be calibrated using field data. This equation is the core of traffic simulation models.