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Versions: 00 01 02 RFC 4692

Individual Submission                                          G. Huston
Internet-Draft                                                     APNIC
Expires: August 13, 2005                               February 12, 2005


             Considerations on the IPv6 Host density Metric
                     draft-huston-hd-metric-00.txt

Status of this Memo

   This document is an Internet-Draft and is subject to all provisions
   of section 3 of RFC 3667.  By submitting this Internet-Draft, each
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   RFC 3668.

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   This Internet-Draft will expire on August 13, 2005.

Copyright Notice

   Copyright (C) The Internet Society (2005).

Abstract

   This memo provides an analysis of the Host Density metric as
   currently used to guide registry allocations of IPv6 unicast address
   blocks.  This document contrasts the address efficiency as currently
   adopted in the allocation of IPv4 network addresses and that used by
   the IPv6 protocol.  It is noted that for large allocations there are
   very significant variations in the target efficiency metric between
   the two approaches.  The memo notes that the IPv6 address assignment
   efficiency metric would benefit from a detailed technical review,



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   particularly relating to large scale deployments of public
   infrastructure.

Table of Contents

   1.  Introduction . . . . . . . . . . . . . . . . . . . . . . . . .  3
   2.  IPv6 Address Structure . . . . . . . . . . . . . . . . . . . .  3
   3.  The Host Density Ratio . . . . . . . . . . . . . . . . . . . .  4
   4.  The Role of an Address Efficiency Metric . . . . . . . . . . .  5
   5.  Network Structure and Address Efficiency Metric  . . . . . . .  7
   6.  Varying the HD Ratio . . . . . . . . . . . . . . . . . . . . .  8
     6.1   Simulation Results . . . . . . . . . . . . . . . . . . . .  9
   7.  Considerations . . . . . . . . . . . . . . . . . . . . . . . . 11
   8.  Security Considerations  . . . . . . . . . . . . . . . . . . . 12
   9.  Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . 12
   10.   References . . . . . . . . . . . . . . . . . . . . . . . . . 12
   10.1  Normative References . . . . . . . . . . . . . . . . . . . . 12
   10.2  Informative References . . . . . . . . . . . . . . . . . . . 13
       Author's Address . . . . . . . . . . . . . . . . . . . . . . . 13
   A.  Comparison Tables  . . . . . . . . . . . . . . . . . . . . . . 13
   B.  Draft Notes  . . . . . . . . . . . . . . . . . . . . . . . . . 17
       Intellectual Property and Copyright Statements . . . . . . . . 18





























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1.  Introduction

   Metrics of address assignment efficiency are used in the context of
   the public Internet as a part of the address allocation function.
   Through the use of an address assignment efficiency metric individual
   networks can be compared to a target model in an objective fashion.
   The common use of this metric is to form part of the supporting
   material for an address allocation request, demonstrating that the
   network has met the target address efficiency metric and that the
   allocation of a further address block is justified.

   Public IP networks have significant differences in purpose,
   structure, size and technology.  Attempting to impose a single metric
   across this very diverse environment is a challenging task.  Any
   address assignment efficiency metric has to represent a balance
   between stating an achievable metric for any competently designed and
   operated service platform, while not specifying a metric that allows
   for an address usage rate that imperils the protocol's longer term
   viability.  There are a number of views relating to address
   assignment efficiency, both in terms of theoretic analyses of
   assignment efficiency and in terms of practical targets that are part
   of current address assignment practices in today's Internet.

   This document contrasts the address efficiency as currently adopted
   in the allocation of IPv4 network addresses and that used by the IPv6
   protocol.  It is noted that for large allocations there are very
   significant variations in the target efficiency metric.

2.  IPv6 Address Structure

   Before looking at address allocation efficiency metrics it is
   appropriate to summarize the address structure for IPv6 global
   unicast addresses.

   The general format for IPv6 global unicast addresses is defined in
   RFC3513 [RFC3513] as follows (Figure 1).


     |         64 - m bits    |   m bits  |       64 bits              |
     +------------------------+-----------+----------------------------+
     | global routing prefix  | subnet ID |       interface ID         |
     +------------------------+-----------+----------------------------+


   IPv6 Address Structure

                                Figure 1




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   Within the current policy framework for allocation of IPv6 addresses
   in the context of the public Internet, the value for 'm' in the
   figure above is commonly used as a 16 bit value, such that the global
   routing prefix is 48 bits in length, the per-customer subnet ID is 16
   bits in length and the interface ID is 64 bits in length.

   In relating this address structure to the address allocation
   function, the efficiency metric is not intended to refer to the 128
   bit IPv6 address, nor the 64 bit routing prefix, but is limited to
   the 48 bit global routing prefix.  This allocation model assumes that
   each customer is allocated a minimum of a /48 address block, and,
   given that this block allows 2**16 possible subnets, it is also
   assumed that a /48 allocation will be used in the overall majority of
   cases of end-customer address assignment.

   The following discussion makes the assumption that the address
   allocation unit in IPv6 is an address prefix of 48 bits in length,
   and the address assignment efficiency in this context is the
   efficiency of assignment of /48 address allocation units.

3.  The Host Density Ratio

   The "Host Density Ratio" is first described in RFC 1715 [RFC1715],
   and subsequently updated in RFC3194 [RFC3194].

   The "H Ratio", as defined in RFC1715, is:

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

                                Figure 2

   The argument presented in RFC 1715 draws on a number of examples to
   support the assertion that this metric reflected a useful measure of
   address assignment efficiency, and furthermore that the optimal point
   for such a utilization efficiency metric lies between 0.14 and 0.26

      As an aside, the table in RFC1715, indicating a range of addressed
      objects for a 64 bit address range was given as between 9 E+8 and
      4 E+16, while 128 bits yielded values of 8 E+17 through to 2 E+33.
      This data was used to support the argument that 64 bits of address
      space was insufficient.  Given that IPv6 is now operating in a
      mode where the IPv6 address unit is somewhere between 48 and 64
      bits in effective length (as distinct from 128, because of the
      subsequent definition of the interface identifier), there is a
      somewhat ironic twist to this particular definition of address
      density.



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   This metric has a maximal value of log base 10 of 2, or 0.30103.

   The metric was 'normalized' in RFC3194, and a new metric, the
   "HD-Ratio" was introduced, with the definition:

                       log(number of allocated objects)
                 HD = ------------------------------------------
                      log(maximum number of allocatable objects)

                                Figure 3

   HD values are directly proportional to the H ratio, and the values of
   the ratio range from 0 to 1.  The analysis described in RFC 3194 then
   applied this HD-Ratio metric to the examples given in RFC 1715, and
   on the basis of these examples, postulated that HD-Ratios of 0.85 or
   higher forced the network into some form of renumbering, while 0.80
   or lower was considered to be an acceptable network efficiency
   metric.

   The HD ratio is referenced within the IPv6 address allocation
   policies used by the Regional Internet Registries, and the policy
   documents specify that an HD-Ratio metric of 0.8 is an acceptable
   objective in terms of address assignment efficiency for an IPv6
   network.

   By contrast, the generally used address efficiency metric for IPv4 is
   the simple ratio of the number of allocated (or addressed) objects to
   the maximum number of allocatable objects.  For IPv4 the commonly
   applied value for this ratio is 0.8 (or 80%).

   A comparison of these two metrics is given in Table 1 of Attachment
   A.

4.  The Role of an Address Efficiency Metric

   The role of the address efficiency metric is to provide objective
   metrics relating to a network's use of address space than can be used
   by both the allocation entity and the applicant to determine whether
   an address allocation is warranted, and provide some indication of
   the size of the address allocation that should be undertaken.  The
   metric provides a target address utilization levels that indicates at
   what point a network's address resource may be considered to be
   "fully utilized".

   The objective here is to allow the network service provider to deploy
   addresses across both network infrastructure and to customers in a
   manner that does not entail periodic renumbering, and in a manner
   that allows both the internal routing system and inter-domain routing



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   system to operate without excessive fragmentation of the address
   space.  This entails use of an addressing plan where at each level of
   structure within the network there is a pool of address blocks that
   allows expansion of the network at that structure level without
   requiring renumbering of the remainder of the network.

   It is recognized that an address utilization efficiency metric of
   100% is unrealistic in any scenario.  Within a typical address
   structure that address space is exhausted not when all address
   resources have been used, but at the point when one element within
   the structure has exhausted its pool, and augmentation of this pool
   by drawing from the pools of other elements would entail extensive
   renumbering.  While it is not possible to provide a definitive
   threshold of what overall efficiency level is obtainable in all IP
   networks, experience with IPv4 network deployments suggests that it
   is reasonable to observe that at any particular level within a
   hierarchically structured address deployment plan an efficiency level
   of between 60% to 80% is an achievable metric in the general case.

   This IPv4 efficiency threshold is significantly greater than that
   observed in the examples provided in conjunction with the HD-Ratio
   description in RFC 1715.  It is noted that the examples used in the
   HD-Ratio are drawn from, among other sources, the PSTN.  This
   comparison with the PSTN warrants some additional examination.  There
   are a number of differences between public IP network deployments and
   PSTN deployments that may account for this difference.  IP addresses
   are deployed on a per-provider basis with an alignment to network
   topology.  PSTN addresses are, on the whole, deployed using a
   geographical distribution system of "call areas" that share a common
   number prefix.  Within each call area sufficient number blocks from
   the number prefix must be available to allow each operator to draw
   their own number block from the area pool.  Within the IP environment
   service providers do not draw address blocks from a common geographic
   number pool, but receive address blocks from the regional Internet
   registry on a 'whole of network' basis.  This difference in the
   address structure allows an IP environment to achieve an overall
   higher level of address utilization efficiency.

   In terms of considering the number of levels of internal hierarchy in
   IP networks, the interior routing protocol, if uniformly deployed,
   admits a hierarchical network structure that is only two levels deep,
   with a fully connected backbone "core" and a number of satellite
   areas that are directly attached to this "core".  Additional levels
   of routing hierarchy may be obtained using various forms of route
   confederations, but this is not a common deployment technique.  The
   most common form of network structure used in large IP networks is a
   three-level structure using regions, individual Points of Presence
   (POPs), and end-customers.



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   It should also be noted that large scale IP deployments typically use
   a relatively flat routing hierarchy.  In order to improve the dynamic
   performance of the interior routing protocol the number of routes
   carried in the interior routing protocol is commonly restricted to
   the routes corresponding to next hop destinations for iBGP routes,
   and customer routes are carried in the iBGP domain.  This implies
   that per-POP or per-region address aggregations according to some
   fixed address hierarchy is not a common feature of large IP networks.

   [Author's Note:
      It has been suggested that this evaluation of the number of levels
      of hierarchy in deployed IP networks could be supported by
      reference to generic network deployments, and to other sources of
      address deployment data in deployed public IP networks.  This is a
      token holder for inclusion of such data in future revisions of
      this document.
   ]

5.  Network Structure and Address Efficiency Metric

   An address efficiency metric can be expressed using the number of
   levels of structure (n) and the efficiency achieved at each level
   (e).  If the same efficiency threshold is applied at each level of
   structure the resultant efficiency threshold is n**e.  This then
   allows us to make some additional observations about the HD-Ratio
   values.  Table 2 of Appendix A (Figure 8) indicates the number of
   levels of structure that are implied by a given HD-Ratio value of 0.8
   for each address allocation block size, assuming a fixed efficiency
   level at all levels of the structure.  The implication is that for
   large address blocks the HD-Ratio assumes a large number of elements
   in the hierarchical structure, or a very low level of address
   efficiency at the lower levels.  In the case of IP network
   deployments this latter situation is not commonly the case.

   As noted above, the most common form of structure used in IP networks
   is a three level structure.  For larger networks a four level
   structure may be used, where the network is the union of a number of
   distinct operating entities, each of which use a three level internal
   structure.

   Table 3 of Attachment A (Figure 9) shows an example of address
   efficiency outcomes using a per-level efficiency metric of 0.75 and a
   progressively deeper network structure as the address block expands.
   This model (termed here "limited levels"), limits the maximal number
   of levels of internal hierarchy to 6, and uses a model where the
   number of levels of network hierarchy increases by 1 when the network
   increases in size by a factor of a little over one order of
   magnitude.



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   It is illustrative to compare these metrics for a larger network
   deployment.  If, for example, the network is designed to encompass 8
   million end customers, each of which is assigned a 16 bit subnet ID,
   then the following table Figure 4indicates the associated allocation
   size as determined by the address efficiency metric.

      Allocation:  8M Customers

                                Allocation    Relative Ratio

      100% Allocation Efficiency   /25               1
      80% Efficiency (IPv4)        /24               2
      0.8 HD-Ratio                 /19              64
      75% with Limited Levels      /23               4
      0.94HD Ratio                 /23               4

                                Figure 4

   It is noted that the 0.8 HD-Ratio produces a significantly lower
   efficiency level than the other metrics.  The limited level model
   appears to point to a more realistic value for an efficiency value
   for networks of this scale (corresponding to a network with 4 levels
   of internal hierarchy, each with a target utilization efficiency of
   75%).  This limited level model corresponds to an HD Ratio with a
   threshold value of 0.945.

6.  Varying the HD Ratio

   One way to model the range of outcomes of taking a more limited
   approach to the number of levels of aggregateable hierarchy is to
   look at a comparison of various values for the HD Ratio with the
   model of a fixed efficiency and the "Limited Levels" model.  This is
   indicated in Figure 5.


















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     Prefix Length (bits)

          Address Utilization Efficiency Levels
          Methods:
            1       2       3       4        5       6       7

      1   0.750   0.986   0.959   0.933   0.908   0.883   0.871
      4   0.750   0.946   0.847   0.758   0.678   0.607   0.574
      8   0.750   0.895   0.717   0.574   0.460   0.369   0.330
     12   0.563   0.847   0.607   0.435   0.312   0.224   0.189
     16   0.563   0.801   0.514   0.330   0.212   0.136   0.109
     20   0.422   0.758   0.435   0.250   0.144   0.082   0.062
     24   0.422   0.717   0.369   0.189   0.097   0.050   0.036
     28   0.316   0.678   0.312   0.144   0.066   0.030   0.021
     32   0.316   0.642   0.264   0.109   0.045   0.018   0.012
     36   0.237   0.607   0.224   0.082   0.030   0.011   0.007
     40   0.237   0.574   0.189   0.062   0.021   0.007   0.004
     44   0.178   0.543   0.160   0.047   0.014   0.004   0.002
     48   0.178   0.514   0.136   0.036   0.009   0.003   0.001


     Methods: 1 - "Limited Levels" using a base efficiency of 0.75
              2 - HD-Ratio value of 0.98
              3 - HD-Ratio value of 0.94
              4 - HD-Ratio value of 0.90
              5 - HD-Ratio value of 0.86
              6 - HD-Ratio value of 0.82
              7 - HD-Ratio value of 0.80

                                Figure 5

   As shown in this figure it is possible to select an HD-Ratio value
   that models IP level structures in a fashion that behaves more
   consistently for very large deployments.  In this case the choice of
   an HD-Ratio of 0.94 is consistent with a limited level model of up to
   6 levels of hierarchy with a metric of 75% density at each level.
   This correlation is indicated in Table 3 of Attachment A.

6.1  Simulation Results

   In attempting to assess the impact of potentially changing the HD
   ratio to a lower value, it is useful to assess this using actual
   address consumption data.  The results described here use the IPv4
   allocation data as published by the Regional Internet Registries
   [RIR-Data] .  The simulation work assumes that the IPv4 delegation
   data uses an IPv4 /32 for each end customer, and that assignments
   have been made based on an 80% density metric in terms of assumed
   customer count.  The customer count is then used as the basis of an



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   IPv6 address allocation, using the HD Ratio to map from a customer
   count to the size of an address allocation.

   The result presented here is that of a simulation of an IPv6 address
   allocation registry, using IPv4 allocation data as published by the
   RIRs spanning the period from January 1, 1999 until August 31, 2004.
   The aim is to identify the relative level of IPv6 address consumption
   using a IPv6 request size profile based on the application of various
   HD-Ratio values to the derived customer numbers.

   The profile of total address consumption for selected HD-Ratio values
   is indicated in Figure 6.  The simulation results indicate that the
   choice of an HD-Ratio of 0.8 consumes a total of 7 times the address
   space than that consumed when using an HD-Ratio of 0.94.

     HD-Ratio Address Consumption
              Prefix Length   Count of
              Notation        /32 prefixes
     0.80    /14.45          191,901
     0.81    /14.71          160,254
     0.82    /15.04          127,488
     0.83    /15.27          108,701
     0.84    /15.46           95,288
     0.85    /15.73           79,024
     0.86    /15.88           71,220
     0.87    /16.10           61,447
     0.88    /16.29           53,602
     0.89    /16.52           45,703
     0.90    /16.70           40,302
     0.91    /16.77           38,431
     0.92    /16.81           37,381
     0.93    /16.96           33,689
     0.94    /17.26           27,364
     0.95    /17.32           26,249
     0.96    /17.33           26,068
     0.97    /17.33           26,068
     0.98    /17.40           24,834
     0.99    /17.67           20,595

                                Figure 6

   The implication of these results is that it is probable that a IPv6
   address registry will see sufficient distribution of allocation
   request sizes such that the choice of a threshold HD-Ratio will
   impact the registries' total address consumption rates, and the
   variance between an HD-Ratio of 0.8 and an HD-Ratio of 0.99 is a
   factor of one order of magnitude in relative rates over an extended
   period of time.  The simulation also indicates that the overall



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   majority of allocations fall within a /32 minimum allocation size
   (between 74% to 95% of all address allocations), and the selection of
   a particular HD-Ratio value has a significant impact in terms of
   allocation sizes for a small proportion of allocation transactions
   (the remainder of allocations range between a /19 to a /31 for an
   HD-Ratio of 0.8 and between a /26 and a /31 for an HD-Ratio of 0.99).

   The conclusion here is that the choice of the HD-Ratio will have some
   impact on one quarter of all allocations, while the remainder are
   serviced using the minimum allocation unit of a /32 address prefix.
   Of these allocations that are larger than the minimum allocation,
   approximately one tenth of these allocations are 'large' allocations.
   These large allocations have a significant impact on total address
   consumption, and varying the HD-Ratio for these allocations between
   0.8 to 0.99 results in a net difference in total address consumption
   of approximately one order of magnitude.  This is a tail-heavy
   distribution, where a small proportion of large address allocations
   significantly impact the total address consumption rate.  Altering
   the HD Ratio will have little impact on more than 95% of the IPv6
   allocations, but will generate significant variance within the
   largest 2% of these allocations, which, in turn, will have a
   significant impact on total address consumption rates.

7.  Considerations

   The HD-Ratio with a value of 0.8 as a model of network address
   utilization efficiency produces extremely low efficiency outcomes for
   networks spanning of the order of 10**6 end customers and larger.

   The HD-Ratio with a 0.8 value makes the assumption that as the
   address allocation block increases in size the network within which
   the addresses will be deployed adds additional levels of hierarchical
   structure.  This increasing depth of hierarchical structure to
   arbitrarily deep hierarchies is not a commonly observed feature of
   public IP network deployments.

   The fixed efficiency model, as used int eh IPv4 address allocation
   policy, uses the assumption that as the allocation block becomes
   larger the network structure remains at a fixed level of levels, or
   if the number of levels is increased, then efficiency achieved at
   each level increases significantly.  There is little evidence to
   suggest that increasing number of levels in a network hierarchy
   increases the efficiency at each level.

   It is evident that neither of these models accurately encompass IP
   network infrastructure models and the associated requirements of
   address deployment.  The fixed efficiency model places an excessive
   burden on the network operator to achieve very high levels of



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   utilization at each level in the network hierarchy, leading to either
   customer renumbering or deployment of NAT to meet the target
   efficiency value in a hierarchically structure network.  The HD-Ratio
   model using a value of 0.8 specifies an extremely low address
   efficiency target for larger networks, and while this places no
   particular stress on network architects in terms of forced
   renumbering, there is the concern that this represents an extravagant
   use of address resources.  If the objective of IPv6 is to encompass a
   number of decades of deployment, and span a public network that
   ultimately encompasses many billions of end customers, then there is
   legitimate cause for concern that the HD-Ratio value of 0.8 may be
   setting too conservative a target for address efficiency.

   It is recommended that further study of address efficiency metrics
   and the relationship between network structure and address efficiency
   models considered as part of such a study.  Consideration should be
   given to the viability of specifying a higher HD-Ratio value as
   representing a more relevant model of internal network structure,
   internal routing and internal address aggregation structures.

   This document has also noted the common choice of a fixed length of
   16 bits for the subnet ID in the IPv6 unicast address architecture
   for each customer assignment.  While this choice has been used in the
   block of unicast address space spanned by the IPv6 address prefix
   2001::/16, it should not be assumed by vendors or network operators
   that this particular subnet scheme will be used for other unicast
   address blocks.  The IPv6 address architecture allows this subnet
   length to be defined as a variable quantity, and it is considered to
   be a useful exercise to evaluate the effectiveness of a fixed length
   subnet scheme, and compare it to an subnet scheme with a variable
   length and a smaller minimum value.

8.  Security Considerations

   Considerations of various forms of host density metrics creates no
   new threats to the security of the Internet.

9.  Acknowledgements

   The document was reviewed by Kurt Lindqvist, Thomas Narten, Paul
   Wilson, David Kessens, Bob Hinden and Brian Haberman.

10.  References

10.1  Normative References

   [RFC1715]  Huitema, C., "The H Ratio for Address Assignment
              Efficiency", RFC 1715, November 1994.



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   [RFC3194]  Durand, A. and C. Huitema, "The H-Density Ratio for
              Address Assignment Efficiency An Update on the H ratio",
              RFC 3194, November 2001.

   [RFC3513]  Hinden, R. and S. Deering, "Internet Protocol Version 6
              (IPv6) Addressing Architecture", RFC 3513, April 2003.

10.2  Informative References

   [RIR-Data]
              RIRs, "RIR Delegation Records", February 2005,
              <ftp://ftp.apnic.net/pub/stats/>.


Author's Address

   Geoff Huston
   APNIC

   EMail: gih@apnic.net

Appendix A.  Comparison Tables

   The first table compares the threshold number of /48 end user
   allocations that would be performed for a given assigned address
   block in order to consider that the utilization has achieved its
   threshold utilization level.


   Fixed Efficiency Value  0.8
   HD-Ratio Value          0.8

                                     Number of /48 allocations to fill the
                                     address block to the threshold level

   Prefix          Size              Fixed Efficiency HD-Ratio Efficiency Ratio
                                       0.8                 0.8

   /48                 1                 1 100%              1  100%   1
   /47                 2                 2 100%              2   87%   1
   /46                 4                 4 100%              3   76%   1
   /45                 8                 7  88%              5   66%   1
   /44                16                13  81%              9   57%   1
   /43                32                26  81%             16   50%   2
   /42                64                52  81%             28   44%   2
   /41               128               103  80%             49   38%   2
   /40               256               205  80%             84   33%   2
   /39               512               410  80%            147   29%   3



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   /38             1,024               820  80%            256   25%   3
   /37             2,048             1,639  80%            446   22%   4
   /36             4,096             3,277  80%            776   19%   4
   /35             8,192             6,554  80%          1,351   16%   5
   /34            16,384            13,108  80%          2,353   14%   6
   /33            32,768            26,215  80%          4,096   13%   6
   /32            65,536            52,429  80%          7,132   11%   7
   /31           131,072           104,858  80%         12,417    9%   8
   /30           262,144           209,716  80%         21,619    8%  10
   /29           524,288           419,431  80%         37,641    7%  11
   /28         1,048,576           838,861  80%         65,536    6%  13
   /27         2,097,152         1,677,722  80%        114,105    5%  15
   /26         4,194,304         3,355,444  80%        198,668    5%  17
   /25         8,388,608         6,710,887  80%        345,901    4%  19
   /24        16,777,216        13,421,773  80%        602,249    4%  22
   /23        33,554,432        26,843,546  80%      1,048,576    3%  26
   /22        67,108,864        53,687,092  80%      1,825,677    3%  29
   /21       134,217,728       107,374,180  80%      3,178,688    2%  34
   /20       268,435,456       214,748,365  80%      5,534,417    2%  39
   /19       536,870,912       429,496,730  80%      9,635,980    2%  45
   /18     1,073,741,824       858,993,460  80%     16,777,216    2%  51
   /17     2,147,483,648     1,717,986,919  80%     29,210,830    1%  59
   /16     4,294,967,296     3,435,973,837  80%     50,859,008    1%  68
   /15     8,589,934,592     6,871,947,674  80%     88,550,677    1%  78
   /14    17,179,869,184    13,743,895,348  80%    154,175,683    1%  89
   /13    34,359,738,368    27,487,790,695  80%    268,435,456    1% 102
   /12    68,719,476,736    54,975,581,389  80%    467,373,275    1% 118
   /11   137,438,953,472   109,951,162,778  80%    813,744,135    1% 135
   /10   274,877,906,944   219,902,325,556  80%  1,416,810,831    1% 155
   /9    549,755,813,888   439,804,651,111  80%  2,466,810,934    0% 178
   /8  1,099,511,627,776   879,609,302,221  80%  4,294,967,296    0% 205
   /7  2,199,023,255,552 1,759,218,604,442  80%  7,477,972,398    0% 235
   /6  4,398,046,511,104 3,518,437,208,884  80% 13,019,906,166    0% 270
   /5  8,796,093,022,208 7,036,874,417,767  80% 22,668,973,294    0% 310


   Table 1: Comparison of Fixed Efficiency threshold vs HD-Ratio
   Threshold

                                Figure 7

   One possible assumption behind the HD ratio is that the
   inefficiencies that are a consequence of large scale deployments are
   an outcome of increased number of levels of hierarchical structure
   within the network.  The following table calculates the depth of the
   hierarchy in order to achieve a 0.8 HD ratio, assuming a 0.8
   utilization efficiency at each level in the hierarchy.




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   Prefix          Size              0.8 Structure
                                HD Ratio    Levels
   /48                 1               1         1
   /47                 2               2         1
   /46                 4               3         2
   /45                 8               5         2
   /44                16               9         3
   /43                32              16         4
   /42                64              28         4
   /41               128              49         5
   /40               256              84         5
   /39               512             147         6
   /38             1,024             256         7
   /37             2,048             446         7
   /36             4,096             776         8
   /35             8,192           1,351         9
   /34            16,384           2,353         9
   /33            32,768           4,096        10
   /32            65,536           7,132        10
   /31           131,072          12,417        11
   /30           262,144          21,619        12
   /29           524,288          37,641        12
   /28         1,048,576          65,536        13
   /27         2,097,152         114,105        14
   /26         4,194,304         198,668        14
   /25         8,388,608         345,901        15
   /24        16,777,216         602,249        15
   /23        33,554,432       1,048,576        16
   /22        67,108,864       1,825,677        17
   /21       134,217,728       3,178,688        17
   /20       268,435,456       5,534,417        18
   /19       536,870,912       9,635,980        19
   /18     1,073,741,824      16,777,216        19
   /17     2,147,483,648      29,210,830        20
   /16     4,294,967,296      50,859,008        20
   /15     8,589,934,592      88,550,677        21
   /14    17,179,869,184     154,175,683        22
   /13    34,359,738,368     268,435,456        22
   /12    68,719,476,736     467,373,275        23
   /11   137,438,953,472     813,744,135        23
   /10   274,877,906,944   1,416,810,831        24
   /9    549,755,813,888   2,466,810,934        25
   /8  1,099,511,627,776   4,294,967,296        25
   /7  2,199,023,255,552   7,477,972,398        26
   /6  4,398,046,511,104  13,019,906,166        27
   /5  8,796,093,022,208  22,668,973,294        27





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   Table 2: Number of Structure Levels assumed by HD-Ratio

                                Figure 8

   An alternative approach is to use a model of network deployment where
   the number of levels of hierarchy increases at a lower rate than that
   indicated in a 0.8 HD ratio model.  One such model is indicated in
   the following table.  This is compared to using an HD-Ratio value of
   0.94.



   Per-Level Target Efficiency: 0.75

   Prefix           Size Stepped      Stepped Efficiency    HD-Ratio Efficiency Ratio
                         Levels          0.75                   0.94

   /48                 1  1                 1 100%                 1 100%   1.0
   /47                 2  1                 2 100%                 2 100%   1.0
   /46                 4  1                 3  75%                 4 100%   0.8
   /45                 8  1                 6  75%                 7  88%   0.9
   /44                16  1                12  75%                13  81%   0.9
   /43                32  1                24  75%                25  78%   1.0
   /42                64  1                48  75%                48  75%   1.0
   /41               128  1                96  75%                92  72%   1.0
   /40               256  1               192  75%               177  69%   1.1
   /39               512  2               384  75%               338  66%   1.1
   /38             1,024  2               576  56%               649  63%   0.9
   /37             2,048  2             1,152  56%             1,244  61%   0.9
   /36             4,096  2             2,304  56%             2,386  58%   1.0
   /35             8,192  2             4,608  56%             4,577  56%   1.0
   /34            16,384  2             9,216  56%             8,780  54%   1.0
   /33            32,768  2            18,432  56%            16,845  51%   1.1
   /32            65,536  2            36,864  56%            32,317  49%   1.1
   /31           131,072  3            73,728  56%            62,001  47%   1.2
   /30           262,144  3           110,592  42%           118,951  45%   0.9
   /29           524,288  3           221,184  42%           228,210  44%   1.0
   /28         1,048,576  3           442,368  42%           437,827  42%   1.0
   /27         2,097,152  3           884,736  42%           839,983  40%   1.1
   /26         4,194,304  3         1,769,472  42%         1,611,531  38%   1.1
   /25         8,388,608  3         3,538,944  42%         3,091,767  37%   1.1
   /24        16,777,216  3         7,077,888  42%         5,931,642  35%   1.2
   /23        33,554,432  4        14,155,776  42%        11,380,022  34%   1.2
   /22        67,108,864  4        21,233,664  32%        21,832,894  33%   1.0
   /21       134,217,728  4        42,467,328  32%        41,887,023  31%   1.0
   /20       268,435,456  4        84,934,656  32%        80,361,436  30%   1.1
   /19       536,870,912  4       169,869,312  32%       154,175,684  29%   1.1
   /18     1,073,741,824  4       339,738,624  32%       295,790,403  28%   1.1



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   /17     2,147,483,648  4       679,477,248  32%       567,482,240  26%   1.2
   /16     4,294,967,296  4     1,358,954,496  32%     1,088,730,702  25%   1.2
   /15     8,589,934,592  5     2,717,908,992  32%     2,088,760,595  24%   1.3
   /14    17,179,869,184  5     4,076,863,488  24%     4,007,346,185  23%   1.0
   /13    34,359,738,368  5     8,153,726,976  24%     7,688,206,818  22%   1.1
   /12    68,719,476,736  5    16,307,453,952  24%    14,750,041,884  21%   1.1
   /11   137,438,953,472  5    32,614,907,904  24%    28,298,371,876  21%   1.2
   /10   274,877,906,944  5    65,229,815,808  24%    54,291,225,552  20%   1.2
   /9    549,755,813,888  5   130,459,631,616  24%   104,159,249,331  19%   1.3
   /8  1,099,511,627,776  5   260,919,263,232  24%   199,832,461,158  18%   1.3
   /7  2,199,023,255,552  6   521,838,526,464  24%   383,384,219,730  17%   1.4
   /6  4,398,046,511,104  6   782,757,789,696  18%   735,533,451,805  17%   1.1
   /5  8,796,093,022,208  6 1,565,515,579,392  18% 1,411,141,697,760  16%   1.1



   Table 3: Limited Levels of Structure

                                Figure 9


Appendix B.  Draft Notes

   [This section not for RFC publication]

   This memo has been reviewed by an ad hoc advisory committee to advise
   the IAB on a number of matters relating to IPv6.  It is proposed that
   the note be published as an informational RFC, as it does not propose
   any specific alteration to the IPv6 specification.

   With respect to the recommendation made in this document that further
   study of address efficiency metrics and the relationship between
   network structure and address efficiency models considered, it is
   noted that this study could be undertaken in the context of the Open
   Policy Forums hosted by the Regional Address Registries in addition
   to any IETF activity.  Given the intersection of interests in this
   work between the IETF and the RIR-hosted policy forums, some level of
   collaboration in any such study would appear to be strongly
   advisable.












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