[ppml] HD Ratio Applied to IPv4

Alec H. Peterson ahp at hilander.com
Tue Aug 12 14:52:45 EDT 2003

Greetings all,

APNIC is looking at applying the HD Ratio system to IPv4 allocations. 
Attached is their draft document discussing the idea.  I'm curious what 
people in the ARIN region think of the idea.

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Discussion Document

Application of the HD-Ratio to IPv4

Prepared by: Paul Wilson, APNIC Secretariat
Version: 1.0
Date: 7 August 2003

1    Summary

Internet address space is managed hierarchically, by
allocation from IANA to RIRs and from RIRs to LIRs (ISPs),
and by assignment from LIRs to infrastructure components and
customer networks.  Within each level of allocation or
assignment some address space is generally reserved for
future expansion and/or efficient aggregation.  As more
hierarchical levels are introduced into any address space,
the overall efficiency of utilisation of that space (in
terms of the total number of individual addresses actually
used) will inevitably decrease.

The HD Ratio (Host-Density Ratio) has been proposed as a
practical mechanism for measuring the utilisation of
addresses within hierarchically-managed Internet address
blocks [RFC 3194].  A given HD Ratio value corresponds to a
percentage utilisation which decreases as the size of the
address space grows, thus allowing for the decreasing
overall address management efficiency which is described

The HD Ratio is currently used as the utilisation metric for
IPv6 address space, under the current IPv6 management policy
[ipv6-address-policy].  According to this policy, a block of
IPv6 address space is considered to be effectively utilised
when its HD-Ratio reaches 0.80.  This value is said to
represent a conservative but manageable figure ("values of
80% or less correspond to comfortable trade-offs between
pain and efficiency" [RFC 3194]).

This document explores the possible use of the HD Ratio for
measurement of IPv4 utilisation, for the same purpose of
determining when a given block of address space should be
considered as fully utilised.

2    Background and problem

The current management framework for IPv4 address space
relies on policies developed within each RIR community [ipv4-
address-policy].  These policies dictate, effectively, that
a given block of IPv4 addresses should be considered
"utilised" when at least 80% of the addresses within the
block have been allocated or assigned. This measure is
applied equally for address blocks held by small or large
LIRs, regardless of their size.  In any case, it is deemed
that once 80% of the space held by an LIR has been allocated
or assigned, that LIR may request more address space from
its appropriate RIR.

Current policies assume a hierarchical system of address
space delegation (from IANA to RIRs to LIRs to customers, as
described above), but they make no allowance for
hierarchical address management within an organisation's own
address space. For LIRs in particular, a hierarchical
approach is often required for assignment of address space
to service elements such as customer networks, individual
POPs, regionalised topologies, and even distinct ISP
products. Small network infrastructures may require simple
hierarchies, but large infrastructures can require several
levels of address space subdivision. These levels of
hierarchy are "hidden" in terms of recognition by the
current RIR policy framework, and highly constrained by the
80% utilisation requirement.  As a result, management of
large blocks is often extremely difficult, requiring large
internal routing tables and/or frequent renumbering of
internal address blocks.

One of the goals of the RIR system is to avoid unnecessary
depletion of IPv4 address space, and the 80% utilisation
requirement may be justifiable on that basis.  However
address management policies must also be practical in terms
of management overhead imposed.  It may be argued that when
large address spaces are involved, the "80% rule" imposes
unreasonable management overheads on an LIR.

A more reasonable approach should attempt to impose a
uniform degree of management overhead, rather than
penalising the holders of large address blocks.  This may be
achievable to some degree by basing utilisation requirements
on the HD ratio rather than the fixed percentage-based
measure which is in use today.

3    A Proposal

In recognition of the problems outlined above, it is now
proposed to consider replacing the current fixed percentage
based utilisation requirement for IPv4 address space with an
"HD Ratio" based requirement, referred to as the AD Ratio.

3.1  The HD Ratio

According to RFC3194, The HD-Ratio is calculated as follows:

     HD = log(U)/log(S)

          S is the size of the address block concerned, and
          U is the number of site addresses (/48s) which are

In order to calculate the HD-Ratio for a given IPv6 block,
it is necessary to know the size of that block, and number
of host addresses which are in use.  The current IPv6
policies allow for this by requiring registration of address
assignments to the /48 level, however this degree of
registration is not appropriate under IPv4 management

3.2  Definition - the AD Ratio

IPv4 address space utilisation is measured in terms of the
number of allocations or assignments which have been made
from a given address block, rather than the number of host
addresses which are in use within the block.  We therefore
use the term "Allocation Density" for the measure of address
space utilisation within an IPv4 block, rather than the term
"Host Density" which represents host-address utilisation in

Consequently, we refer propose a new utilisation metric for
IPv4, to be known as the "AD Ratio" (for Allocation or
Assignment Density Ratio). The AD Ratio measures the number
of addresses allocated or assigned from a given block of
address space, as follows:

     AD = log(A)/log(S)

          S is the size of the of the address block, and
          A is the number of addresses allocated or assigned
          from that block.

3.3  Selection of AD Ratio value

The appropriate AD Ratio value for the purposes of this
proposal should be decided on a rational basis. In order to
do this, we make certain assumptions about the depth of
"hidden" hierarchy involved in managing address blocks of
various sizes.  We then assume that at each level of this
assumed hierarchy, the currently accepted 80% utilisation
requirement is achieved, in order for the entire address
space to be considered as fully utilised.

The following table proposes a set of assumed hierarchical
depths which may be reasonably expected within
hierarchically-managed address spaces of certain sizes. At
each delegation level an allocation density of 80% is
assumed, so that within a hierarchy of "n" levels, the
overall address space utilisation is calculated as 0.80 to
the power of "n".

     Size range        Depth     Util        AD Ratio
     (prefix)          (n)       (0.80**n)   (calculated)

     /24 to /20        1         80%         .960 to .973
     /20 to /16        1.5       72%         .961 to .970
     /16 to /12        2         64%         .960 to .968
     /12 to /8         2.5       57.2%       .960 to .966
     /8 to /4          3         51.20%      .960 to .966

     Note:  the above AD Ratio values are derived directly
     from the formula above.  For instance, a /20 block
     contains 4096 addresses, and 80% utilisation
     corresponds to 3276.8 addresses; therefore the
     corresponding AD Ratio is calculated as
     log(3276.8)/log(4096) = 0.973

The depths of address hierarchy listed above are notional
approximations only, based on general assumptions about the
likely size and structure of LIRs holding address blocks in
the respective size ranges.  From the table, a rational
common AD ratio value may be determined as 0.966 (chosen as
the most conservative value which is common to all of the
listed ranges).  For this value, the following table gives
the percentage utilisation requirement for the full range of
IPv4 address blocks (this is also derived directly from the
AD ratio formula shown above).

     IPv4        Addresses        Addresses      Util%
  Prefix            Total         Utilised

      32                1                1     100.00%
      31                2                2      97.67%
      30                4                4      95.40%
      29                8                7      93.17%
      28               16               15      91.00%
      27               32               28      88.88%
      26               64               56      86.81%
      25              128              109      84.79%
      24              256              212      82.82%
      23              512              414      80.89%
      22             1024              809      79.00%
      21             2048             1580      77.16%
      20             4096             3087      75.37%
      19             8192             6030      73.61%
      18            16384            11780      71.90%
      17            32768            23010      70.22%
      16            65536            44949      68.59%
      15           131072            87804      66.99%
      14           262144           171518      65.43%
      13           524288           335046      63.90%
      12          1048576           654485      62.42%
      11          2097152          1278482      60.96%
      10          4194304          2497408      59.54%
       9          8388608          4878479      58.16%
       8         16777216          9529704      56.80%
       7         33554432         18615487      55.48%
       6         67108864         36363809      54.19%
       5        134217728         71033685      52.92%
       4        268435456        138758413      51.69%
       3        536870912        271053050      50.49%
       2       1073741824        529479652      49.31%
       1       2147483648       1034294583      48.16%
       0       4294967296       2020408681      47.04%

   Note: This table provides values for CIDR blocks only,
   however for non-CIDR blocks the same calculations can be
   applied to produce equally meaningful results.

4    Implementation

If implemented at any particular level in the IP address
delegation chain, this proposal would have a number of
impacts on administrative processes at that level.  It is
not currently proposed to apply this proposal to the
relationship between RIRs and IANA, therefore the
implementation of the proposal at the RIR-LIR level is
discussed there.

4.1  RIR-LIR Procedures

The impact of the proposal on the RIR-LIR administrative
procedures would be to replace the current 80% utilisation
requirement, with a 0.966 AD Ratio requirement.

By way of examples, an LIR holding a total address space
equal to a /16 would be able to receive more address space
when they had allocated or assigned 68.59% of that space;
while an LIR holding a /9 would be able to receive more
space when they had allocated or assigned 58.16% of their
address space. For blocks smaller than /22, it is proposed
that the current 80% requirement be used, in order that this
new policy does not impose tighter utilisation requirements
than were previously imposed.

The AD-Ratio calculation is trivial, but certainly more
complex and less intuitive than the existing 80%
calculation.  Some APNIC members may in some circumstances
require extra assistance, however for those using the
MyAPNIC service, the calculation would be automatic and
therefore no additional effort would be involved.

4.2  Assignment procedures

In order to support consistent calculation of an LIR's AD
Ratio, it would be preferable for each LIR to register
infrastructure assignments in the same way as customer
assignments.  This could be done by whois update via email,
or via the MyAPNIC service.  It would not be necessary to
register individual hardware components or subnets, but
rather only the independent infrastructure blocks which are
designated by the LIR, and which can be justified on the
same basis as customer assignments. Such registrations would
be publicly visible as normal whois records, unless database
changes were implemented to specifically hide them.

4.3  Implementation timeline

If implemented, this policy could be effective within 3
months of the implementation date.

5    Impacts

5.1  Administrative Impact

The primary administrative impact of this proposal is to
ease the administrative address management burden
experienced by LIRs, especially those with large address
space holdings. The proposal recognises the need to manage
address space hierarchically within an LIR service
infrastructure, and makes allowance for it through the use
of the AD ratio for assessment of address utilisation.

This proposal would impose a small administrative cost on
LIRs.  In the first place, an LIR's internal systems (manual
or automated) would need to incorporate a new method of
calculating address space utilisation (and especially when
determining the point at which the LIR may request more
space from APNIC).  In the second place, an LIR would need
to register infrastructure assignments in the same way as
customer assignments, which would impose additional
administrative cost.  In both cases, LIRs using the MyAPNIC
service would experience a small extra cost because these
changes can be automated within that system.

The administrative impact on internal systems of the APNIC
Secretariat is also relatively small.  APNIC hostmaster
processes can be tailored easily to accommodate a changed
method of calculating address space utilisation; and the
whois database can certainly accommodate an increased number
of registrations.

5.2  Address Space Consumption

Because this proposal lowers the utilisation requirement for
IPv4 address blocks, it would certainly increase the rate of
deployment of IP addresses.  In analysing this impact, we
can identify two separate factors contributing to increased
consumption: firstly, an initial impact resulting from
increased "wastage" of deployed address space; and secondly,
on ongoing impact as utilisation requirements continue to
fall for individual LIRs' growing address holdings.

5.2.1     Initial impact

The initial impact on address consumption can be estimated
by calculating for each APNIC LIR the difference between the
current 80% utilisation, and the AD-ratio-determined
utilisation requirement. This calculation will indicate the
amount of extra "wasted" address space which would result
from the proposed policy change.

     Total LIRs in sample                788

     Total address space held           4.17  (/8 blocks)
     Utilised addresses (80%)           3.32
     Utilised addresses (AD 0.966)      2.53*
     Extra "wasted" space               0.81
     Extra "wastage" as % of total       19%

     * This figure is calculated from the sample of 788
     LIRs, according to actual address space holdings

These figures show that by reducing the address space
utilisation requirement from 80% to AD 0.966, an additional
0.81 blocks are consumed out of a total 4.17 blocks
allocated. This corresponds to an additional of 19% of the
total allocated address space.

It should be noted that this assessment indicates a
theoretical impact in terms of increased address
consumption, assuming all deployed address space is actually
utilised.  The actual impact will be less than this due to
underutilisation of address space; and furthermore the
impact will not take place at one time, but progressively as
part of ongoing address space allocations.

5.2.2     Ongoing impact

The ongoing impact on address consumption can be estimated
by distributing additional address space to the same set of
LIRs, in proportion to their existing address space
holdings. For the purposes of this analysis, an additional
/8 block is distributed to the same set of 788 LIRs, in
proportion to their existing address holdings.

     Initial address space held         4.17  (/8 blocks)
     Additional space allocated         1.00
     Total address space now held       5.17
     Utilised addresses (AD 0.966)      3.11*
     Additional addresses utilised      0.58*
     Utilised addresses (80%)           0.80
     Extra "wasted" space               0.22
     Extra "wastage" as % of allocation  22%

     * These figures are calculated from the same sample of
     788 LIRs, assuming a proportional distribution of an
     additional /8 block

These figures show that after an additional /8 block is
distributed and utilised, 58% of that block would actually
be utilised, rather than 80%.  Therefore up to 22% of that
block would be "wasted" by the use of AD 0.966 in place of
80% as the utilisation measure, resulting potentially in an
increased consumption rate of up to 22%.

Again, this calculation is theoretical only, and assumes
that all address space which has been distributed will be

5.2.3     Conclusions on address consumption

The above analysis indicates that the adoption of this
proposal would cause an initial additional consumption of up
to 19% of address space allocated.  In APNIC's case, a total
of 8.07 /8 blocks have been allocated (as of 1 July 2003),
so up to an additional 1.53 blocks would eventually be
consumed as a result of the change.

The analysis also indicates that this proposal would cause
an overall 22% increase in the rate of address consumption.
In APNIC's case, a total of 1.90 /8 blocks per year are
currently being allocated (in the 12 months to 1 July 2003),
and this rate would therefore rise to 2.32 blocks per year.

The assumptions on which the above analysis is made include:
firstly, that the 788 LIRs in the sample are representative
of all LIRs in the region; and secondly, that a consistent
rate of growth will be experienced by all LIRs in the

6    References

[RFC 3194] "The Host-Density Ratio for Address Assignment
Efficiency: An update on the H ratio", A. Durand, C.Huitema,
November 2001.

 [ipv6-address-policy] APNIC document: "IPv6 Address
Allocation and Assignment Policy"

[ipv4-address-policy] APNIC document: "Policies for IPv4
address space management in the Asia Pacific region"
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