sub checkReadTime  # call this with just your list of files
{
    my $linecount = 0;
    my $starttime = time;
    for my $file ( @_ ) {
        my $fh = &openLogFile($file) or next;
        while ( <$fh> ) {
            $linecount++;
        }
        close $fh;
    }
    my $endtime = time;
    warn sprintf( "read %d lines from %d files in %d sec\n",
                  $linecount, scalar @_, $endtime - $starttime );
}

##</code><code>##

  filterLogFiles file.list | sort | your_main_app

##</code><code>##

    open( my $logsort, "-|", "filterLogFiles @files | sort" ) or die $!;
    while ( <$logsort> ) {
        ...
    }