Results 1 to 3 of 3

Math Help - Matrix Street Traffic Problem

  1. #1
    Member
    Joined
    Sep 2008
    Posts
    79

    Matrix Street Traffic Problem




    The question asks 'What is the solution vector for the unknown number of cars per day in this network of one-way streets?' I know that the number of cars going in equals the number going out, but I do not know how to approach setting up the matrix. I should be able to solve it from there on my own, but I just have no idea how to go about setting it up. Thank you.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Opalg's Avatar
    Joined
    Aug 2007
    From
    Leeds, UK
    Posts
    4,041
    Thanks
    7
    For each of the four intersections, write down the equation which says that the number of cars entering the intersection per day is equal to the number of cars leaving the intersection. For example, the equation for the northeast corner (intersection of College and High) is x_1+x_2 = N_2+N_3.

    The matrix form of these four equations should look like \begin{bmatrix}1&1&0&0&N_2+N_3\\ 0&1&1&0&N_4+N_5\\ 0&0&1&1&N_6+N_7\\ 1&0&0&1&N_1+N_8\end{bmatrix}. Now solve the equations by the usual process of reducing the matrix to diagonal form.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Sep 2008
    Posts
    79
    Thank you very much!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. 1D Traffic Flow Problem
    Posted in the Differential Equations Forum
    Replies: 0
    Last Post: May 17th 2011, 09:39 AM
  2. traffic flow
    Posted in the Calculus Forum
    Replies: 2
    Last Post: December 3rd 2008, 05:25 PM
  3. Traffic Intersection Probability
    Posted in the Statistics Forum
    Replies: 2
    Last Post: September 29th 2008, 09:42 PM
  4. Unbelievable traffic on this site...why?
    Posted in the Math Forum
    Replies: 14
    Last Post: August 22nd 2008, 05:47 AM
  5. traffic flow - strange problem!
    Posted in the Calculus Forum
    Replies: 0
    Last Post: March 27th 2008, 10:06 AM

Search Tags


/mathhelpforum @mathhelpforum