APNIC
October 2006
Considerations on the IPv6 Host Density Metric
Status of This Memo
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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
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Copyright © The Internet Society (2006).
Abstract
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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
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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
1. Introduction
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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
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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
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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, 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
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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
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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.
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
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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
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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 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 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
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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.
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 4Note 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
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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.
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
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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
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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.
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
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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 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
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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
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Considerations of various forms of host density metrics create no new threats to the security of the Internet.
9. Acknowledgements
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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
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[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
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[RIR-Data] RIRs, "RIR Delegation Records", February 2005, <ftp://ftp.apnic.net/pub/stats/>.
Appendix A. Comparison Tables
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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
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Number of /48 allocations to fill the
address block to the threshold level
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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%-
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Table 1. Comparison of Fixed Efficiency Threshold vs
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HD-Ratio Threshold
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Figure 7
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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
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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
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Geoff Huston
APNICEMail:
gih@apnic.net
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