Why not create three worker threads. Whenever a new file arrives, add it to the queue. The workers pick stuff off the queue as they become idle.

use strict;
use warnings;

use threads;
use Thread::Queue qw( );

my $num_workers = 3;

sub process_file {
   my ($file) = @_;
   ...
}

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

for (1..$num_workers) {
   async {
      while (defined(my $file = $q->dequeue())) {
         process_file($file);
      }
   };   
}

for (;;) {
   ... wait for new files ...
   $q->enqueue(@new_files);
}

$q->enqueue() for 1..$num_workers;
$_->join() for threads->list();
[download]

Adding use forks; should make the above use processes instead of threads.