Does your "reading" part work without the call to fork?

Personally, I would just use a pipe from bzcat to read the file instead:

open my $fh, "bzcat '$file' |"
    or die "Couldn't spawn [bzcat '$file']: $! / $?";
while (<$fh>) {
    $number_of_lines++
};
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Once that works, look at either using Dominus' runN script or re-wrap your script with the routine doing the "fork" calls. Alternatively, you can also look at Parallel::ForkManager to rate-limit your child programs.