[ppml] HD Ratio changes

[William Stucke]

Hi Owen,

> or, it isn't simple enough for me and my math didn't work right

It didn't work quite right ;-)
All the numbers in your last (difference) column, except for the last two,
are off by one, for example.

In Owen's table, ignoring the last two values (/30 & /31), the .966 HD Ratio
figure gives a number of hosts required on average 15.47% higher than the
80% figure, with a range from 12.27% (/3) to 18.75% (/28) However, see
below.

The Excel spreadsheet quoted by Ian Baker at
 	http://www.codecutters.org/temp/HD-Ratio.xls
makes the erroneous assumption that 254 out of every 256 addresses are
available for any size block, when in fact it's 2 addresses (first and last)
out of any size block that are unavailable. (His spreadsheet has a
"*254/256" factor in the number of IP addresses column). He calculates it
as: -
	(2^(32-CIDR))*254/256,
whereas I believe if should simply be: -
	(2^(32-CIDR))-2,

where CIDR is the number of bits in the prefix.

Unless I misunderstand what's meant by what one author calls "N Hosts" and
the other calls "IP Addresses", both are incorrect as they have used them -
and are not equivalent.

If the prefix length = CIDR  is "n", then: -
Number of IP addresses = 2^(32-n) [Which Owen called "Hosts"]
Number of "useful" IP addresses = maximum possible Number of Hosts =
2^(32-n)-2 [Which Ian called "IP Addresses!]

After that, the PERL script figures differ widely from the Excel numbers ...

Here's a new table for you: (I didn't bother to round correctly, so figures
might be off by 1)

+------+-----------+-----------+-----------+-------------+---------+
|Prefix| N Hosts   | .996 HD   | 80% HD    | .996 HD - 80| Percent |
+------+-----------+-----------+-----------+-------------+---------+
| /3   |536,870,910|271,053,050|429,496,728| -158,443,678|  -58.45%|
| /4   |268,435,454|138,758,412|214,748,363|  -75,989,951|  -54.76%|
| /5   |134,217,726| 71,033,685|107,374,181|  -36,340,496|  -51.16%|
| /6   | 67,108,862| 36,363,809| 53,687,090|  -17,323,281|  -47.64%|
| /7   | 33,554,430| 18,615,486| 26,843,544|   -8,228,058|  -44.20%|
| /8   | 16,777,214|  9,529,704| 13,421,771|   -3,892,067|  -40.84%|
| /9   |  8,388,606|  4,878,478|  6,710,885|   -1,832,407|  -37.56%|
|/10   |  4,194,302|  2,497,407|  3,355,442|     -858,035|  -34.36%|
|/11   |  2,097,150|  1,278,481|  1,677,720|     -399,239|  -31.23%|
|/12   |  1,048,574|    654,484|    838,859|     -184,375|  -28.17%|
|/13   |    524,286|    335,045|    419,429|      -84,384|  -25.19%|
|/14   |    262,142|    171,517|    209,714|      -38,197|  -22.27%|
|/15   |    131,070|     87,803|    104,856|      -17,053|  -19.42%|
|/16   |     65,534|     44,948|     52,427|       -7,479|  -16.64%|
|/17   |     32,766|     23,010|     26,213|       -3,203|  -13.92%|
|/18   |     16,382|     11,779|     13,106|       -1,327|  -11.26%|
|/19   |      8,190|      6,029|      6,552|         -523|   -8.67%|
|/20   |      4,094|      3,086|      3,275|         -189|   -6.13%|
|/21   |      2,046|      1,579|      1,637|          -58|   -3.66%|
|/22   |      1,022|        808|        818|          -10|   -1.19%|
|/23   |        510|        413|        408|            5|    1.21%|
|/24   |        254|        211|        203|            8|    3.70%|
|/25   |        126|        107|        101|            6|    5.79%|
|/26   |         62|         54|         50|            4|    8.15%|
|/27   |         30|         27|         24|            3|   11.11%|
|/28   |         14|         13|         11|            2|   13.85%|
|/29   |          6|          6|          5|            1|   20.00%|
|/30   |          2|          2|          2|            0|   20.00%|
+------+-----------+-----------+-----------+-------------+---------+

> The table here
shows that in all cases, a .996 HD ratio is a larger number than the
80% requirement, and, that the more space you have, the worse it gets.

Different numbers allow one to draw very different conclusions!

The HD method requires far FEWER hosts for larger networks, as expected, but
more hosts for networks smaller than a /23 - up to 20% more.

I'm going to bed, it's after 2 am here!


Regards,

William Stucke
ZAnet Internet Services (Pty) Ltd
+27 11 465 0700
William at zanet.co.za