my $pm = Parallel::ForkManager->new(NUM_CHILDREN);

for (1..NUM_CHILDREN) {
   $pm->start and next;

   my $client_sock = $server_sock->accept
      or die $!;

   ...

   $pm->finish;
}
[download]

Note: It'll use a new process for each request, but the process will be created as soon as the previous request is complete (even if no requests are pending).