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 [email protected] 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.

  * The globally-connected physics/space science DECnet (Phase IV)
    stopped growing at about 15K nodes (i.e. new nodes were hidden)
    which in a 16 bit space gives a ratio of 0.26

  * There are about 200 million IEEE 802 nodes in a 46 bit space, which
    gives a ratio of 0.18. That number space, however, is not
    saturated.

  From these examples, we can assert that the efficiency ratio usually
  lies between 0.14 and 0.26.

3. Evaluating proposed address plans

  Using a reverse computation, we get the following population counts
  in the network:

                   Pessimistic (0.14)     Optimistic (0.26)

     32 bits             3 E+4 (!)           2 E+8
     64 bits             9 E+8               4 E+16
     80 bits           1.6 E+11            2.6 E+27
    128 bits             8 E+17              2 E+33

  I guess that the figure explains well why some feel that 64 bits is
  "not enough" while other feel it is "sufficient by a large margin":
  depending of the assignment efficiency, we are either well below the
  target or well above. But there is no question, in my view, that 128
  bits is "more than enough". Even if we presume the lowest efficiency,
  we are still way above the hyperbolic estimate of 1.E+15 Internet
  hosts.

  It is also interesting to note that if we devote 80 bits to the
  "network" and use 48 bits for "server less autoconfiguration", we can
  number more that E.11 networks in the pessimistic case - it would
  only take an efficiency of 0.15 to reach the E+12 networks hyperbole.

  I guess this explains well why I feel that 128 bits is entirely safe
  for the next 30 year. The level of constraints that we will have to
  incorporate in the address assignment appears very much in line with
  what we know how to do, today.




Huitema                                                         [Page 3]

RFC 1715                        H Ratio                    November 1994


4.  Security Considerations

  Security issues are not discussed in this memo.

5. Author's Address

  Christian Huitema
  INRIA, Sophia-Antipolis
  2004 Route des Lucioles
  BP 109
  F-06561 Valbonne Cedex
  France

  Phone: +33 93 65 77 15
  EMail: [email protected]




































Huitema                                                         [Page 4]


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