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Car Following Models

  1. Jul 2, 2008 #1

    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 Jiménez et al. (2000) and
    Treiber et al. (2000)... 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:

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

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

    So my questions: what does [tex]\dot{x}_f^m[/tex] express? Sure, [tex]\dot{x}_f[/tex] is the velocity of vehicle [tex]f[/tex], but what is [tex]m[/tex]? The vehicle's mass? Why would one want to potentiate the velocity by the mass? I'm lost! Further, I interpreted [tex]l[/tex] -- being used as an index in equation 1 -- as the leading car, [tex]f[/tex] denoting the following car. However, in equation 2, [tex]l[/tex] 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:
    [tex]\dot{v}_\alpha ( t+T_r ) = \frac{-\lambda v_\alpha^m \Delta v_\alpha}{s_\alpha^l} \quad (3)[/tex]

    My question: the [tex]\lambda[/tex] in eq. 3 seems to be different to the [tex]\lambda[/tex] 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!
  2. jcsd
  3. Jul 3, 2008 #2
    Well, my questions are answered in Chung et al. (2005)

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

    Thanks anyway,
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