# Car Following Models

1. Jul 2, 2008

### aldous

Hello,

I'm a computer science student in desperate need for help. In the process of writing my master's thesis I've successfully developed a traffic simulation using a model I've found in the traffic research literature, the IDM, to be precise. This model seems straight-forward and is easy to grasp even for a dim mind like mine.

However, I fail to understand older car following models, such as presented by http://www-sop.inria.fr/mascotte/Philippe.Mussi/papers/esm2000.ps" [Broken] and
http://arxiv.org/PS_cache/cond-mat/pdf/0002/0002177v2.pdf" [Broken]... Hopefully just because I simply don't know what some variables mean, which are apparently not introduced.

Jiménez et al. (2000) state that all car following models can be summarized by:

$$\ddot{x}_f ( t+T_r ) = \lambda * [ \dot{x}_{l}(t) - \dot{x}_{f}(t)] \quad (1)$$

$$\lambda = \frac{a_{l,m}* \dot{x}_{f}^m(t+T)}{[x_{l}(t)-x_{f}(t)]^l} \quad (2)$$

So my questions: what does $$\dot{x}_f^m$$ express? Sure, $$\dot{x}_f$$ is the velocity of vehicle $$f$$, but what is $$m$$? The vehicle's mass? Why would one want to potentiate the velocity by the mass? I'm lost! Further, I interpreted $$l$$ -- being used as an index in equation 1 -- as the leading car, $$f$$ denoting the following car. However, in equation 2, $$l$$ is used as a power? How is this to be interpreted?

Similarly, Treiber et al. (2000) state that older car following models can be reduced to that formula:
$$\dot{v}_\alpha ( t+T_r ) = \frac{-\lambda v_\alpha^m \Delta v_\alpha}{s_\alpha^l} \quad (3)$$

My question: the $$\lambda$$ in eq. 3 seems to be different to the $$\lambda$$ in eq. 2. Is it this a variable often used in physics one should just know? (It is not defined in the paper)

Thank you very much in advance for any pointers!
Alexander

Last edited by a moderator: May 3, 2017
2. Jul 3, 2008

### aldous

Well, my questions are answered in http://www.easts.info/on-line/journal_06/1354.pdf" [Broken]

$$m,l$$ are -- when used as powers -- simply parameters influencing the driving behavior, $$\lambda$$ is just any proportionality factor.

Thanks anyway,
Alexander

Last edited by a moderator: May 3, 2017