General Hint:

You can read your data source linewise and process each queue line and store them temporarily in a data structure.

If you encounter a line which starts with BS:, take the data structure and combine it with the data of the current BS: line and clear the temporary data structure.

Example of work:

#!/usr/bin/perl
# vi:ts=4 sw=4 et:
use strict;
use warnings;
use Data::Dumper qw();

my %result;
my %queue;

while ( my $line = <DATA> ) {
    chomp $line;
    
    if ( $line =~ m/^BS:\s+(\S+)/ ) {
        $result{$1} = { %queue };
        %queue = ();
    }
    else {
        my ( $name, $in_percent, $in_num, $out_percent, $out_num ) 
          = split m{ \(| / | of 1024 \| event | of 1024\)}, $line;

        $queue{$name} = {
            in_q_per  => $in_percent,
            in_q_num  => $in_num,
            out_q_per => $out_percent,
            out_q_num => $out_num,
        };
    }
}

# show resulting structure; it's up to you to go on from here ;o)
print Data::Dumper->Dump( [ \%result ], [ '*result' ] );


__DATA__
AAA_AA1_DDD (0% / 0 of 1024 | event 0% / 0 of 1024)
AAA_AA2_DDD (0% / 0 of 1024 | event 0% / 0 of 1024)
BS: 111_DDD, QE: QQQ_DDD (additionnal QE)
BBB_BB1_DDD (0% / 0 of 1024 | event 0% / 0 of 1024)
BBB_BB2_DDD (0% / 0 of 1024 | event 0% / 0 of 1024)
BS: 222_DDD, QE: QQQ_DDD (additionnal QE)
CCC_CC1_DDD (0% / 0 of 1024 | event 0% / 0 of 1024)
CCC_CC2_DDD (0% / 0 of 1024 | event 0% / 0 of 1024)
BS: 333_DDD, QE: QQQ_DDD (additionnal QE)
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