Continuous and Discrete-Time Optimal Controls for an Isolated Signalized Intersection

Algorithm 1

The adjusting algorithm for the discretized approximate solution in Case  I(a).

() Set as the discretized approximate solution. Calculate by Eq. (15)-(16);

() if then

()  Set and set ;

()  Update by Eq. (16) and set ;

()  if   then

()    and update and by Eq. (15) and (16);

  end

  end

  while do;

  . Update such that stream is cleared exactly in cycle ;

  Update by Eq. (15);

  if then

   1. Find the minimum such that ;

   Update such that stream is cleared exactly in cycle ;

   Set ;

  end

 if then

     and update and by Eq. (15) and (16);

 end

  end

  while do

  . Update such that stream is cleared exactly in cycle ;

  Update by Eq. (15);

  if then

    . Find the maximum such that ;

    Update such that stream is cleared exactly in cycle ;

  else if and then

     break;

  end

  if   then

(31)      and update and by Eq. (15)-(16);

(32)  end

(33) end

(34) if and then

(35)  Calculate , by Eq. (2)-Eq. (3);

(36)  Set ;

(37)  for do  ;

(38) end