RFC 1715 (rfc1715) – Page 2 of 4

The H Ratio for Address Assignment Efficiency

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RFC 1715                        H Ratio                    November 1994


   But this classic evaluation is misleading, as it does not take into
   account the number of hierarchical elements. IP addresses, for
   example, have at least three degrees of hierarchy: network, subnet
   and host.  In order to remove these dependencies, I propose to use a
   logarithmic scale for the efficiency ratio:

                             log (number of objects)
                         H = -----------------------
                                  available bits

   The ratio H is not too dependent of the number of hierarchical
   levels. Suppose for example that we have the choice between two
   levels, encoded on 8 bits each, and one single level, encoded in 16
   bits. We will obtain the same efficiency if we allocate in average
   100 elements at each 8 bits level, or simply 10000 elements in the
   single 16 bits level.

   Note that I use base 10 logs in what follows, because they are easier
   to compute mentally. When it comes to large numbers, people tend to
   use "powers of 10", as in "IPng should be capable of numbering 1 E+15
   systems". It follows from this choice of units that H varies between
   0 and a theoretical maximum of 0.30103 (log base 10 of 2).

2. Estimating reasonable values for the ratio H:

   Indeed, we don't expect to achieve a ratio of 0.3 in practice, and
   the interesting question is to assert the values which can be
   reasonably expected. We can try to evaluate them from existing
   numbering plans. What is especially interesting is to consider the
   moment where the plans broke, i.e. when people were forced to add
   digits to phone number, or to add bits to computer addresses. I have
   a number of such figures handy, e.g.:

   * Adding one digit to all French telephone numbers, moving from 8
     digits to 9, when the number of phones reached a threshold of 1.0
     E+7. The log value is 7, the number of bits was about 27 (1 decimal
     digit is about 3.3 bits). The ratio is thus 0.26

   * Expending the number of areas in the US telephone system, making it
     effectively 10 digits long, for about 1.0 E+8 subscribers. The log
     value is 8, the number of bits is 33, the ratio is about 0.24

   * Expending the size of the Internet addresses, from 32 bits to
     something else. There are currently about 3 million hosts on the
     net, for 32 bits. The log of 3.E6 is about 6.5; this gives a ratio
     of 0.20. Indeed, we believe that 32 bits will still be enough for
     some years, e.g. to multiply the number of hosts by 10, in which
     case the ratio would climb to 0.23



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