displaying posts by tag from a specific subcategory

I am using this code to display all posts by tag:

<?php query_posts('cat=20'); ?>

                <?php
//get all terms (e.g. categories or post tags), then display all posts in each term
$taxonomy = 'post_tag';//  e.g. post_tag, category
$param_type = 'tag__in'; //  e.g. tag__in, category__in
$term_args=array(
  'orderby' => 'name',
  'order' => 'ASC'
);
$terms = get_terms($taxonomy,$term_args);
if ($terms) {
  foreach( $terms as $term ) {
    $args=array(
      "$param_type" => array($term->term_id),
      'post_type' => 'post',
      'post_status' => 'publish',
      'posts_per_page' => -1,
      'caller_get_posts'=> 1
      );
    $my_query = null;
    $my_query = new WP_Query($args);
    if( $my_query->have_posts() ) {
      echo '<h2 class="venue-city">' . $term->name . '</h2><ul class="venue-listing">';
      while ($my_query->have_posts()) : $my_query->the_post(); ?>
        <li><a href="<?php the_permalink() ?>" rel="bookmark" title="Permanent Link to <?php the_title_attribute(); ?>"><?php the_title(); ?></a></li>
       <?php
      endwhile;
	  echo '</ul>';
    }
  }
}
wp_reset_query();  // Restore global post data stomped by the_post().
?>

it works beautifully except is pulling from all my categories instead of just one specific category. I need to limit this to a certain category on one page then to a certain subcategory within that category on another page. can someone help?