use Thread::Queue;

my $q = Thread::Queue->new;

# Later, in producer thread(s) ($first and $second
# represent the 2 dimensional tuple you wish to enqueue)
$q->enqueue( [ $first, $second ] ); # Anonymous array ref

# Later still, to signal the end of all elements:
$q->enqueue(undef);

# In the consumer thread(s):
while (defined (my $ref = $q->dequeue)) {
    my ($first, $second) = @$ref;   # Dereference array
    # ... Process $first and $second
}