while(@array1 or @array2) {
    my $i = 0;
    ONE: while(@array1 and $i < $some_large_number/10) {
        $i++;
        my $item = shift @array1;
        # Do various things (as above)
    }
    $i = 0;
    TWO: while(@array2 and $i < $some_large_number) {
        $i++;
        my $item = shift @array2;
        # Do various things (as above)
    }
}