The H Ratio for Address Assignment Efficiency
RFC 1715

Document Type RFC - Informational (November 1994; No errata)
Updated by RFC 3194
Last updated 2013-03-02
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Network Working Group                                         C. Huitema
Request for Comments:  1715                                        INRIA
Category: Informational                                    November 1994

             The H Ratio for Address Assignment Efficiency

Status of this Memo

   This memo provides information for the Internet community.  This memo
   does not specify an Internet standard of any kind.  Distribution of
   this memo is unlimited.

Abstract

   This document was submitted to the IETF IPng area in response to RFC
   1550.  Publication of this document does not imply acceptance by the
   IPng area of any ideas expressed within.  Comments should be
   submitted to the author and/or the sipp@sunroof.eng.sun.com mailing
   list.

Table of Contents

   1.   Efficiency of address assignment . . . . . . . . . . . . . . 1
   2.   Estimating reasonable values for the ratio H . . . . . . . . 2
   3.   Evaluating proposed address plans. . . . . . . . . . . . . . 3
   4.   Security Considerations . . . . . . . . . . . . . . . . . .  4
   5.   Author's Address . . . . . . . . . . . . . . . . . . . . . . 4

1. Efficiency of address assignment

   A substantial part of the "IPng" debate was devoted to the choice of
   an address size. A recurring concept was that of "assignment
   efficiency", which most people involved in the discussion expressed
   as a the ratio of the effective number of systems in the network over
   the theoretical maximum. For example, the 32 bits IP addressing plan
   could in theory number over 7 billions of systems; as of today, we
   have about 3.5 millions of addresses reported in the DNS, which would
   translate in an efficiency of 0.05%.

Huitema                                                         [Page 1]
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

Huitema                                                         [Page 2]
RFC 1715                        H Ratio                    November 1994

   * Expending the size of the SITA 7 characters address. According to
     their documentation, they have about 64000 addressed points in
     their network, scattered in 1200 cities, 180 countries. An upper
     case character provides about 5 bits of addressing, which results
     in an efficiency of 0.14. This is an extreme case, as SITA uses
     fixed length tokens in its hierarchy.
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