Question 2


We have seen in class that a  norm penalization has the property to provide results with a lot of entries equal to zero. We exploit this property of the  norm to study spatial traffic patterns. For this we study the following optimization problem:


The matrix  represents information on the traffic patterns. For example, we can expect some neighboring links to have the same traffic conditions. In particular, we can encourage neighboring links to have the same speed. We realize that two links  and  with travel times  and  and length  and  have the same speed if and only if


In this section, we will experiment our traffic pattern with different K matrices. K matrix is produced as follows: For every intersection u, there are incoming links  and outgoing links . For every (,) pair, there is a row at index i with value 1/ and at index o with value -1/ .