1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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 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:

    [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!
    Last edited by a moderator: May 3, 2017
  2. jcsd
  3. Jul 3, 2008 #2
    Well, my questions are answered in http://www.easts.info/on-line/journal_06/1354.pdf" [Broken]

    [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,
    Last edited by a moderator: May 3, 2017
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook