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
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.
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/>.
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%
/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
/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%
/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
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