GENWiki

Premier IT Outsourcing and Support Services within the UK

User Tools

Site Tools


rfc:rfc4692

Network Working Group G. Huston Request for Comments: 4692 APNIC Category: Informational October 2006

           Considerations on the IPv6 Host Density Metric

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 (2006).

Abstract

 This memo provides an analysis of the Host Density metric as it is
 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.  Note that for large allocations there are very
 significant variations in the target efficiency metric between the
 two approaches.

Table of Contents

 1. Introduction ....................................................2
 2. IPv6 Address Structure ..........................................2
 3. The Host Density Ratio ..........................................3
 4. The Role of an Address Efficiency Metric ........................4
 5. Network Structure and Address Efficiency Metric .................6
 6. Varying the HD-Ratio ............................................7
    6.1. Simulation Results .........................................8
 7. Considerations .................................................10
 8. Security Considerations ........................................11
 9. Acknowledgements ...............................................11
 10. References ....................................................12
    10.1. Normative References .....................................12
    10.2. Informative References ...................................12
 Appendix A.  Comparison Tables ....................................13

Huston Informational [Page 1] RFC 4692 IPv6 Host Density Metric October 2006

1. Introduction

 Metrics of address assignment efficiency are used in the context of
 the Regional Internet Registries' (RIRs') address allocation
 function.  Through the use of a common address assignment efficiency
 metric, individual networks can be compared to a threshold value 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 or exceeded the threshold
 address efficiency value, and it forms part of the supportive
 material relating to the justification of the allocation of a further
 address block.
 Public and private IP networks have significant differences in
 purpose, structure, size, and technology.  Attempting to impose a
 single efficiency metric across this very diverse environment is a
 challenging task.  Any address assignment efficiency threshold value
 has to represent a balance between stating an achievable outcome for
 any competently designed and operated service platform while without
 setting a level of consumption of address resources that imperils the
 protocol's longer term viability through consequent address scarcity.
 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 metric and threshold
 value as currently adopted in the allocation of IPv4 network
 addresses and the framework used by the address allocation process
 for the IPv6 protocol.

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
 [RFC4291] as follows (Figure 1).
  |         64 - m bits    |   m bits  |       64 bits              |
  +------------------------+-----------+----------------------------+
  | global routing prefix  | subnet ID |       interface ID         |
  +------------------------+-----------+----------------------------+
                        IPv6 Address Structure
                               Figure 1

Huston Informational [Page 2] RFC 4692 IPv6 Host Density Metric October 2006

 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, referring to the subnet ID, is commonly a 16-bit field.
 Therefore, the end-site 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 [RFC3177].
 In relating this address structure to the address allocation
 function, the efficiency metric is not intended to refer to the use
 of individual 128-bit IPv6 addresses nor that of the use of the 64-
 bit subnet prefix.  Instead, it is limited to a measure of efficiency
 of use of the end-site global routing prefix.  This allocation model
 assumes that each customer is allocated a minimum of a single /48
 address block.  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 that the address assignment efficiency in this context is the
 efficiency of assignment of /48 address allocation units.  However,
 the analysis presented here refers more generally to end-site address
 allocation practices rather than /48 address prefixes in particular,
 and is applicable in the context of any size of end-site global
 routing prefix.

3. The Host Density Ratio

 The "Host Density Ratio" was first described in [RFC1715] and
 subsequently updated in [RFC3194].
 The "H Ratio", as defined in RFC 1715, is:
                          log (number of objects)
                      H = -----------------------
                                available bits
                               Figure 2
 The argument presented in [RFC1715] draws on a number of examples to
 support the assertion that this metric reflects a useful generic
 measure of address assignment efficiency in a range of end-site
 addressed networks, and furthermore that the optimal point for such a
 utilization efficiency metric lies in an H Ratio value between 0.14
 and 0.26.  Lower H Ratio values represent inefficient address use,
 and higher H Ratio values tend to be associated with various forms of
 additional network overhead related to forced re-addressing
 operations.

Huston Informational [Page 3] RFC 4692 IPv6 Host Density Metric October 2006

 This particular metric has a maximal value of log base 10 of 2, or
 0.30103.
 The metric was 'normalized' in RFC 3194, and a new metric, the "HD-
 Ratio" was introduced, with the following definition:
                      log(number of allocated objects)
            HD = ------------------------------------------
                 log(maximum number of allocatable objects)
                               Figure 3
 HD-Ratio values are proportional to the H ratio, and the values of
 the HD-Ratio range from 0 to 1.  The analysis described in [RFC3194]
 applied this HD-Ratio metric to the examples given in [RFC1715] and,
 on the basis of these examples, postulated that HD-Ratio values of
 0.85 or higher force the network into some form of renumbering.  HD-
 Ratio values of 0.80 or lower were considered an acceptable network
 efficiency metric.
 The HD-Ratio is referenced within the IPv6 address allocation
 policies used by the Regional Internet Registries, and their IPv6
 address allocation 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 that 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 level that indicates at
 what point a network's address resource may be considered "fully
 utilized".
 The objective here is to allow the network service provider to deploy
 addresses across both network infrastructure and the network's
 customers in a manner that does not entail periodic renumbering, and

Huston Informational [Page 4] RFC 4692 IPv6 Host Density Metric October 2006

 in a manner that allows both the internal routing system and inter-
 domain routing system to operate without excessive fragmentation of
 the address space and consequent expansion of the number of route
 objects carried within the routing systems.  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 network
 address plan, the network's 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 when 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 [RFC1715].  Note that the examples used in the HD-
 Ratio are drawn from, among other sources, the Public Switched
 Telephone Network (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, a 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

Huston Informational [Page 5] RFC 4692 IPv6 Host Density Metric October 2006

 of routing hierarchy may be obtained using various forms of routing
 confederations, but this is not an extremely 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.
 Also, note that large-scale IP deployments typically use a relatively
 flat routing structure, as compared to a deeply hierarchical
 structure.  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 and aggregated at the point
 where the routes are announced in eBGP sessions.  This implies that
 per-POP or per-region address aggregations according to some fixed
 address hierarchy is not a necessary feature of large IP networks, so
 strict hierarchical address structure within all parts of the network
 is not a necessity in such routing environments.

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 e^n.  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.
 The most common form of interior routing structure used in IP
 networks is a two-level routing structure.  It is consistent with
 this constrained routing architecture that network address plans
 appear to be commonly devised using up to a three-level hierarchical
 structure, while for larger networks a four-level structure may
 generally be used.

Huston Informational [Page 6] RFC 4692 IPv6 Host Density Metric October 2006

 Table 3 of Attachment A (Figure 9) shows an example of address
 efficiency outcomes using a per-level efficiency metric of 0.75 (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.
 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
 for their end site, then the following table Figure 4 indicates 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 Level      /23               4
       0.94 HD-Ratio                /23               4
                                  Figure 4
 Note 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.

Huston Informational [Page 7] RFC 4692 IPv6 Host Density Metric October 2006

        Prefix Length (bits)
        |
        |
        | Limited    HD-Ratio
        |  Levels    0.98    0.94    0.90    0.86    0.82    0.80
        |       |       |       |       |       |       |       |
        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
                               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
 IPv6 address allocation, using the HD-Ratio to map from a customer
 count to the size of an address allocation.

Huston Informational [Page 8] RFC 4692 IPv6 Host Density Metric October 2006

 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 of that consumed when using an HD-Ratio of 0.94.
               HD-Ratio       Total 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 imply that an IPv6 address registry
 will probably see sufficient distribution of allocation request sizes
 such that the choice of a threshold HD-Ratio will impact the 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 address consumption over an extended period of time.  The
 simulation also indicates that the overall majority of allocations
 fall within a /32 minimum allocation size (between 74% to 95% of all
 address allocations), and that the selection of a particular HD-Ratio
 value has a significant impact in terms of allocation sizes for a

Huston Informational [Page 9] RFC 4692 IPv6 Host Density Metric October 2006

 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 'impacted' 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 heavy-tail 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 in the IPv4 address allocation
 policy, uses the assumption that as the allocation block becomes
 larger, the network structure remains at a fixed level of levels; if
 the number of levels is increased, then efficiency achieved at each
 level increases significantly.  There is little evidence to suggest
 that increasing a 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
 utilization at each level in the network hierarchy, leading to either
 customer renumbering or deployment of technologies such as Network
 Address Translation (NAT) to meet the target efficiency value in a

Huston Informational [Page 10] RFC 4692 IPv6 Host Density Metric October 2006

 hierarchically structured 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 extremely inefficient use of address
 resources.  If the objective of IPv6 is to encompass a number of
 decades of deployment, and to span a public network that ultimately
 encompasses many billions of end customers and a very high range and
 number of end use devices and components, 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, in that the total
 address consumption targets may be achieved too early.
 This study concludes that 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 in the context of IPv6
 network deployment.

8. Security Considerations

 Considerations of various forms of host density metrics create 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, Brian Haberman, and Marcelo
 Bagnulo.

Huston Informational [Page 11] RFC 4692 IPv6 Host Density Metric October 2006

10. References

10.1. Normative References

 [RFC1715]   Huitema, C., "The H Ratio for Address Assignment
             Efficiency", RFC 1715, November 1994.
 [RFC3177]   IAB and IESG, "IAB/IESG Recommendations on IPv6 Address
             Allocations to Sites", RFC 3177, September 2001.
 [RFC3194]   Durand, A. and C. Huitema, "The H-Density Ratio for
             Address Assignment Efficiency An Update on the H ratio",
             RFC 3194, November 2001.
 [RFC4291]   Hinden, R. and S. Deering, "IP Version 6 Addressing
             Architecture", RFC 4291, February 2006.

10.2. Informative References

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

Huston Informational [Page 12] RFC 4692 IPv6 Host Density Metric October 2006

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
                                     0.8                     0.8
 /48                 1                 1 100%              1  100%
 /47                 2                 2 100%              2   87%
 /46                 4                 4 100%              3   76%
 /45                 8                 7  88%              5   66%
 /44                16                13  81%              9   57%
 /43                32                26  81%             16   50%
 /42                64                52  81%             28   44%
 /41               128               103  80%             49   38%
 /40               256               205  80%             84   33%
 /39               512               410  80%            147   29%
 /38             1,024               820  80%            256   25%
 /37             2,048             1,639  80%            446   22%
 /36             4,096             3,277  80%            776   19%
 /35             8,192             6,554  80%          1,351   16%
 /34            16,384            13,108  80%          2,353   14%
 /33            32,768            26,215  80%          4,096   13%
 /32            65,536            52,429  80%          7,132   11%
 /31           131,072           104,858  80%         12,417    9%
 /30           262,144           209,716  80%         21,619    8%
 /29           524,288           419,431  80%         37,641    7%
 /28         1,048,576           838,861  80%         65,536    6%
 /27         2,097,152         1,677,722  80%        114,105    5%
 /26         4,194,304         3,355,444  80%        198,668    5%
 /25         8,388,608         6,710,887  80%        345,901    4%
 /24        16,777,216        13,421,773  80%        602,249    4%
 /23        33,554,432        26,843,546  80%      1,048,576    3%
 /22        67,108,864        53,687,092  80%      1,825,677    3%
 /21       134,217,728       107,374,180  80%      3,178,688    2%
 /20       268,435,456       214,748,365  80%      5,534,417    2%
 /19       536,870,912       429,496,730  80%      9,635,980    2%
 /18     1,073,741,824       858,993,460  80%     16,777,216    2%
 /17     2,147,483,648     1,717,986,919  80%     29,210,830    1%

Huston Informational [Page 13] RFC 4692 IPv6 Host Density Metric October 2006

 /16     4,294,967,296     3,435,973,837  80%     50,859,008    1%
 /15     8,589,934,592     6,871,947,674  80%     88,550,677    1%
 /14    17,179,869,184    13,743,895,348  80%    154,175,683    1%
 /13    34,359,738,368    27,487,790,695  80%    268,435,456    1%
 /12    68,719,476,736    54,975,581,389  80%    467,373,275    1%
 /11   137,438,953,472   109,951,162,778  80%    813,744,135    1%
 /10   274,877,906,944   219,902,325,556  80%  1,416,810,831    1%
 /9    549,755,813,888   439,804,651,111  80%  2,466,810,934    0%
 /8  1,099,511,627,776   879,609,302,221  80%  4,294,967,296    0%
 /7  2,199,023,255,552 1,759,218,604,442  80%  7,477,972,398    0%
 /6  4,398,046,511,104 3,518,437,208,884  80% 13,019,906,166    0%
 /5  8,796,093,022,208 7,036,874,417,767  80% 22,668,973,294    0%
         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 an 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.
 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

Huston Informational [Page 14] RFC 4692 IPv6 Host Density Metric October 2006

 /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
        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
                       Levels          0.75                   0.94
 /48                 1  1                1 100%                 1 100%
 /47                 2  1                2 100%                 2 100%
 /46                 4  1                3  75%                 4 100%
 /45                 8  1                6  75%                 7  88%
 /44                16  1               12  75%                13  81%
 /43                32  1               24  75%                25  78%
 /42                64  1               48  75%                48  75%
 /41               128  1               96  75%                92  72%
 /40               256  1              192  75%               177  69%
 /39               512  2              384  75%               338  66%
 /38             1,024  2              576  56%               649  63%
 /37             2,048  2            1,152  56%             1,244  61%

Huston Informational [Page 15] RFC 4692 IPv6 Host Density Metric October 2006

 /36             4,096  2            2,304  56%             2,386  58%
 /35             8,192  2            4,608  56%             4,577  56%
 /34            16,384  2            9,216  56%             8,780  54%
 /33            32,768  2           18,432  56%            16,845  51%
 /32            65,536  2           36,864  56%            32,317  49%
 /31           131,072  3           73,728  56%            62,001  47%
 /30           262,144  3          110,592  42%           118,951  45%
 /29           524,288  3          221,184  42%           228,210  44%
 /28         1,048,576  3          442,368  42%           437,827  42%
 /27         2,097,152  3          884,736  42%           839,983  40%
 /26         4,194,304  3        1,769,472  42%         1,611,531  38%
 /25         8,388,608  3        3,538,944  42%         3,091,767  37%
 /24        16,777,216  3        7,077,888  42%         5,931,642  35%
 /23        33,554,432  4       14,155,776  42%        11,380,022  34%
 /22        67,108,864  4       21,233,664  32%        21,832,894  33%
 /21       134,217,728  4       42,467,328  32%        41,887,023  31%
 /20       268,435,456  4       84,934,656  32%        80,361,436  30%
 /19       536,870,912  4      169,869,312  32%       154,175,684  29%
 /18     1,073,741,824  4      339,738,624  32%       295,790,403  28%
 /17     2,147,483,648  4      679,477,248  32%       567,482,240  26%
 /16     4,294,967,296  4    1,358,954,496  32%     1,088,730,702  25%
 /15     8,589,934,592  5    2,717,908,992  32%     2,088,760,595  24%
 /14    17,179,869,184  5    4,076,863,488  24%     4,007,346,185  23%
 /13    34,359,738,368  5    8,153,726,976  24%     7,688,206,818  22%
 /12    68,719,476,736  5   16,307,453,952  24%    14,750,041,884  21%
 /11   137,438,953,472  5   32,614,907,904  24%    28,298,371,876  21%
 /10   274,877,906,944  5   65,229,815,808  24%    54,291,225,552  20%
 /9    549,755,813,888  5  130,459,631,616  24%   104,159,249,331  19%
 /8  1,099,511,627,776  5  260,919,263,232  24%   199,832,461,158  18%
                 Table 3: Limited Levels of Structure
                               Figure 9

Author's Address

 Geoff Huston
 APNIC
 EMail: gih@apnic.net

Huston Informational [Page 16] RFC 4692 IPv6 Host Density Metric October 2006

Full Copyright Statement

 Copyright (C) The Internet Society (2006).
 This document is subject to the rights, licenses and restrictions
 contained in BCP 78, and except as set forth therein, the authors
 retain all their rights.
 This document and the information contained herein are provided on an
 "AS IS" basis and THE CONTRIBUTOR, THE ORGANIZATION HE/SHE REPRESENTS
 OR IS SPONSORED BY (IF ANY), THE INTERNET SOCIETY AND THE INTERNET
 ENGINEERING TASK FORCE DISCLAIM ALL WARRANTIES, EXPRESS OR IMPLIED,
 INCLUDING BUT NOT LIMITED TO ANY WARRANTY THAT THE USE OF THE
 INFORMATION HEREIN WILL NOT INFRINGE ANY RIGHTS OR ANY IMPLIED
 WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE.

Intellectual Property

 The IETF takes no position regarding the validity or scope of any
 Intellectual Property Rights or other rights that might be claimed to
 pertain to the implementation or use of the technology described in
 this document or the extent to which any license under such rights
 might or might not be available; nor does it represent that it has
 made any independent effort to identify any such rights.  Information
 on the procedures with respect to rights in RFC documents can be
 found in BCP 78 and BCP 79.
 Copies of IPR disclosures made to the IETF Secretariat and any
 assurances of licenses to be made available, or the result of an
 attempt made to obtain a general license or permission for the use of
 such proprietary rights by implementers or users of this
 specification can be obtained from the IETF on-line IPR repository at
 http://www.ietf.org/ipr.
 The IETF invites any interested party to bring to its attention any
 copyrights, patents or patent applications, or other proprietary
 rights that may cover technology that may be required to implement
 this standard.  Please address the information to the IETF at
 ietf-ipr@ietf.org.

Acknowledgement

 Funding for the RFC Editor function is provided by the IETF
 Administrative Support Activity (IASA).

Huston Informational [Page 17]

/data/webs/external/dokuwiki/data/pages/rfc/rfc4692.txt · Last modified: 2006/10/02 23:07 by 127.0.0.1

Donate Powered by PHP Valid HTML5 Valid CSS Driven by DokuWiki