Individual Submission G. Huston
Internet-Draft APNIC
Expires: August 12, 2005 February 11, 2005
Considerations on the IPv6 Host density Metric
draft-huston-ipv6-hd-metric-00.txt
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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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