The H-Density Ratio for Address Assignment Efficiency An Update on the H ratio
RFC 3194

Document Type RFC - Informational (November 2001; No errata)
Updates RFC 1715
Last updated 2013-03-02
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Network Working Group                                          A. Durand
Request for Comments: 3194                              SUN Microsystems
Updates: 1715                                                 C. Huitema
Category: Informational                                        Microsoft
                                                           November 2001

       The Host-Density Ratio for Address Assignment Efficiency:
                        An update on the H ratio

Status of this Memo

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

Copyright Notice

   Copyright (C) The Internet Society (2001).  All Rights Reserved.


   This document provides an update on the "H ratio" defined in RFC
   1715.  It defines a new ratio which the authors claim is easier to

1. Evaluating the efficiency of address allocation

   A naive observer might assume that the number of addressable objects
   in an addressing plan is a linear function of the size of the
   address.  If this were true, a telephone numbering plan based on 10
   digits would be able to number 10 billion telephones, and the IPv4 32
   bit addresses would be adequate for numbering 4 billion computers
   (using the American English definition of a billion, i.e. one
   thousand millions.) We all know that this is not correct: the 10
   digit plan is stressed today, and it handles only a few hundred
   million telephones in North America; the Internet registries have
   started to implement increasingly restrictive allocation policies
   when there were only a few tens of million computers on the Internet.

   Addressing plans are typically organized as a hierarchy: in
   telephony, the first digits will designate a region, the next digits
   will designate an exchange, and the last digits will designate a
   subscriber within this exchange; in computer networks, the most
   significant bits will designate an address range allocated to a
   network provider, the next bits will designate the network of an
   organization served by that provider, and then the subnet to which
   the individual computers are connected.  At each level of the

Durand & Huitema             Informational                      [Page 1]
RFC 3194                An update on the H ratio           November 2001

   hierarchy, one has to provide some margins:  one has to allocate more
   digits to the region code than the current number of regions would
   necessitate, and more bits in a subnet than strictly required by the
   number of computers.  The number of elements in any given level of
   the   hierarchy will change over time, due to growth and mobility.
   If the current allocation is exceeded, one has to engage in
   renumbering, which is painful and expensive.  In short, trying to
   squeeze too many objects into a hierarchical address space increases
   the level of pain endured by operators and subscribers.

   Back in 1993, when we were debating the revision of the Internet
   Protocol, we wondered what the acceptable ratio of utilization was of
   a given addressing plan.  Coming out with such a ratio was useful to
   assess how many computers could be connected to the Internet with the
   current 32-bit addresses, as well as to decide the size of the next
   generation addresses.  The second point is now decided, with 128-bits
   addresses for IPv6, but the first question is still relevant:
   knowing the capacity of the current address plan will help us predict
   the date at which this capacity will be exceeded.

   Participants in the IPNG debates initially measured the efficiency of
   address allocation by simply dividing the number of allocated
   addresses by the size of the address space.  This is a simple
   measure, but it is largely dependent on the size of the address
   space.  Loss of efficiency at each level of a hierarchical plan has a
   multiplicative effect; for example, 50% efficiency at each stage of a
   three level hierarchy results in a overall efficiency of 12.5%.  If
   we want a "pain level indicator", we have to use a ratio that takes
   into account these multiplicative effects.

   The "H-Ratio" defined in RFC 1715 proposed to measure the efficiency
   of address allocation as the ratio of the base 10 logarithm of the
   number of allocated addresses to the size of the address in bits.
   This provides an address size independent ratio, but the definition
   of the H ratio results in values in the range of 0.0 to 0.30103, with
   typical values ranging from 0.20 to 0.28.  Experience has shown that
   these numbers are difficult to explain to others; it would be easier
   to say that "your address bits are used to 83% of their H-Density",
   and then explain what the H-Density is, than to say "you are hitting
   a H ratio of 0.25" and then explain what exactly the range is.

   This memo introduces the Host Density ratio or "HD-Ratio", a proposed
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