Module 3 : Microscopic Traffic Flow Modeling

Lecture 14 : Car Following Models

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	The earliest car-following models considered the difference in speeds between the leader and the follower as the stimulus. It was assumed that every driver tends to move with the same speed as that of the corresponding leading vehicle so that $${a_n^t} =\frac{1}{\tau}{(v_n^{t+1}-v_{n+1}^t})$$ (1) where $\tau$ is a parameter that sets the time scale of the model and $\frac{1}{\tau}$ can be considered as a measure of the sensitivity of the driver. According to such models, the driving strategy is to follow the leader and, therefore, such car-following models are collectively referred to as the follow the leader model. Efforts to develop this stimulus function led to five generations of car-following models, and the most general model is expressed mathematically as follows. $$a_{n+1}^{t+{\Delta{T}}}={\frac{\alpha_{l,m}~[{v_{n+1}^{t-\Delta{T... ...}-{x_{n+1}^{t-\Delta{T}}}]^l}}{({v_{n}^{t-\Delta{T}}}-{v_{n+1}^{t-\Delta{T}}})}$$ (2) 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.