Movatterモバイル変換

Network Working Group                                          A. DurandRequest for Comments: 3194                              SUN MicrosystemsUpdates:1715                                                 C. HuitemaCategory: Informational                                        Microsoft                                                           November 2001The Host-Density Ratio for Address Assignment Efficiency:An update on the H ratioStatus 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 (2001).  All Rights Reserved.Abstract   This document provides an update on the "H ratio" defined inRFC1715.  It defines a new ratio which the authors claim is easier to   understand.1. Evaluating the efficiency of address allocation   A naive observer might assume that the number of addressable objects   in an addressing plan is a linear function of the size of the   address.  If this were true, a telephone numbering plan based on 10   digits would be able to number 10 billion telephones, and the IPv4 32   bit addresses would be adequate for numbering 4 billion computers   (using the American English definition of a billion, i.e. one   thousand millions.) We all know that this is not correct: the 10   digit plan is stressed today, and it handles only a few hundred   million telephones in North America; the Internet registries have   started to implement increasingly restrictive allocation policies   when there were only a few tens of million computers on the Internet.   Addressing plans are typically organized as a hierarchy: in   telephony, the first digits will designate a region, the next digits   will designate an exchange, and the last digits will designate a   subscriber within this exchange; in computer networks, the most   significant bits will designate an address range allocated to a   network provider, the next bits will designate the network of an   organization served by that provider, and then the subnet to which   the individual computers are connected.  At each level of theDurand & Huitema             Informational                      [Page 1]

RFC 3194                An update on the H ratio           November 2001   hierarchy, one has to provide some margins:  one has to allocate more   digits to the region code than the current number of regions would   necessitate, and more bits in a subnet than strictly required by the   number of computers.  The number of elements in any given level of   the   hierarchy will change over time, due to growth and mobility.   If the current allocation is exceeded, one has to engage in   renumbering, which is painful and expensive.  In short, trying to   squeeze too many objects into a hierarchical address space increases   the level of pain endured by operators and subscribers.   Back in 1993, when we were debating the revision of the Internet   Protocol, we wondered what the acceptable ratio of utilization was of   a given addressing plan.  Coming out with such a ratio was useful to   assess how many computers could be connected to the Internet with the   current 32-bit addresses, as well as to decide the size of the next   generation addresses.  The second point is now decided, with 128-bits   addresses for IPv6, but the first question is still relevant:   knowing the capacity of the current address plan will help us predict   the date at which this capacity will be exceeded.   Participants in the IPNG debates initially measured the efficiency of   address allocation by simply dividing the number of allocated   addresses by the size of the address space.  This is a simple   measure, but it is largely dependent on the size of the address   space.  Loss of efficiency at each level of a hierarchical plan has a   multiplicative effect; for example, 50% efficiency at each stage of a   three level hierarchy results in a overall efficiency of 12.5%.  If   we want a "pain level indicator", we have to use a ratio that takes   into account these multiplicative effects.   The "H-Ratio" defined inRFC 1715 proposed to measure the efficiency   of address allocation as the ratio of the base 10 logarithm of the   number of allocated addresses to the size of the address in bits.   This provides an address size independent ratio, but the definition   of the H ratio results in values in the range of 0.0 to 0.30103, with   typical values ranging from 0.20 to 0.28.  Experience has shown that   these numbers are difficult to explain to others; it would be easier   to say that "your address bits are used to 83% of their H-Density",   and then explain what the H-Density is, than to say "you are hitting   a H ratio of 0.25" and then explain what exactly the range is.   This memo introduces the Host Density ratio or "HD-Ratio", a proposed   replacement for the H-Ratio defined inRFC 1715.  The HD values range   from 0 to 1, and are generally expressed as percentage points; the   authors believe that this new formulation is easier to understand and   more expressive than the H-Ratio.Durand & Huitema             Informational                      [Page 2]

RFC 3194                An update on the H ratio           November 20012. Definition of the HD-ratio   When considering an addressing plan to allocate objects, the host   density ratio HD is defined as follow:              log(number of allocated objects)   HD = ------------------------------------------         log(maximum number of allocatable objects)   This ratio is defined for any number of allocatable objects greater   than 1 and any number of allocated objects greater or equal than 1   and less than or equal the maximum number of allocatable objects.   The ratio is usually presented as a percentage, e.g. 70%.  It varies   between 0 (0%), when there is just one allocation, and 1 (100%), when   there is one object allocated to each available address.  Note that   for the calculation of the HD-ratio, one can use any base for the   logarithm as long as it is the same for both the numerator and the   denominator.   The HD-ratio can, in most cases, be derived from the H ratio by the   formula:           H   HD = --------        log10(2)3. Using the HD-ratio as an indicator of the pain level   In order to assess whether the H-Ratio was a good predictor of the   "pain level" caused by a specific efficiency,RFC1715 used several   examples of networks that had reached their capacity limit.  These   could be for example telephone networks at the point when they   decided to add digits to their numbering plans, or computer networks   at the point when their addressing capabilities were perceived as   stretched beyond practical limits.  The idea behind these examples is   that network managers would delay renumbering or changing the network   protocol until it became just too painful; the ratio just before the   change is thus a good predictor of what can be achieved in practice.   The examples were the following:   * Adding one digit to all French telephone numbers, moving from 8   digits to 9, when the number of phones reached a threshold of 1.0   E+7.Durand & Huitema             Informational                      [Page 3]

RFC 3194                An update on the H ratio           November 2001                                  log(1.0E+7)      HD(FrenchTelephone8digit) = ----------- = 0.8750 = 87.5%                                  log(1.0E+8)                                  log(1.0E+7)      HD(FrenchTelephone9digit) = ----------- = 0.7778 = 77.8%                                  log(1.0E+9)   * Expanding the number of areas in the US telephone system, making   the phone number effectively 10 digits long instead of "9.2" (the   second digit of area codes used to be limited to 0 or 1) for about   1.0 E+8 subscribers.                                log(1.0E+8)      HD(USTelephone9.2digit) = ------------ = 0.8696 = 87.0 %                                log(9.5E+9)                                log(1.0E+8)      HD(USTelephone10digit)  = ------------ = 0.8000 = 80.0 %                                log(1E+10)   * The globally-connected physics/space science DECnet (Phase IV)   stopped growing at about 15K nodes (i.e. new nodes were hidden) in a   16 bit address space.                      log(15000)      HD(DecNET IV) = ---------- = 0.8670 = 86.7 %                      log(2^16)   From those examples, we can note that these addressing systems   reached their limits for very close values of the HD-ratio.  We can   use the same examples to confirm that the definition of the HD-ratio   as a quotient of logarithms results in better prediction than the   direct quotient of allocated objects over size of the address space.   In our three examples, the direct quotients were 10%, 3.2% and 22.8%,   three very different numbers that don't lead to any obvious   generalization.  The examples suggest an HD-ratio value on the order   of 85% and above correspond to a high pain level, at which operators   are ready to make drastic decisions.   We can also examine our examples and hypothesize that the operators   who renumbered their networks tried to reach, after the renumbering,   a pain level that was easily supported.  The HD-ratio of the French   or US network immediately after renumbering was 78% and 80%,   respectively.  This suggests that values of 80% or less corresponds   to comfortable trade-offs between pain and efficiency.Durand & Huitema             Informational                      [Page 4]

RFC 3194                An update on the H ratio           November 20014. Using the HD-ratio to evaluate the capacity of addressing plans   Directly using the HD-ratio makes it easy to evaluate the density of   allocated objects.  Evaluating how well an addressing plan will scale   requires the reverse calculation.  We have seen insection 3.1 that   an HD-ratio lower than 80% is manageable, and that HD-ratios higher   than 87% are hard to sustain.  This should enable us to compute the   acceptable and "practical maximum" number of objects that can be   allocated given a specific address size, using the formula:   number allocatable of objects               = exp( HD x log(maximum number allocatable of objects))               = (maximum number allocatable of objects)^HD   The following table provides example values for a 9-digit telephone   plan, a 10-digit telephone plan, and the 32-bit IPv4 Internet:                                             Very  Practical                     Reasonable  Painful  Painful    Maximum                         HD=80%   HD=85%   HD=86%     HD=87%   ---------------------------------------------------------   9-digits plan           16 M     45 M     55 M       68 M   10-digits plan         100 M    316 M    400 M      500 M   32-bits addresses       51 M    154 M    192 M      240 M   Note: 1M = 1,000,000   Indeed, the practical maximum depends on the level of pain that the   users and providers are willing to accept.  We may very well end up   with more than 154M allocated IPv4 addresses in the next years, if we   are willing to accept the pain.5. Security considerations   This document has no security implications.6. IANA Considerations   This memo does not request any IANA action.Durand & Huitema             Informational                      [Page 5]

RFC 3194                An update on the H ratio           November 20017. Author addresses   Alain Durand   SUN Microsystems, Inc   901 San Antonio Road MPK17-202   Palo Alto, CA 94303-4900   USA   EMail: Alain.Durand@sun.com   Christian Huitema   Microsoft Corporation   One Microsoft Way Redmond, WA 98052-6399   USA   EMail: huitema@microsoft.com8. Acknowledgment   The authors would like to thank Jean Daniau for his kind support   during the elaboration of the HD formula.9. References   [RFC1715] Huitema, C., "The H Ratio for Address Assignment             Efficiency",RFC 1715, November 1994.   [IANAV4]  INTERNET PROTOCOL V4 ADDRESS SPACE, maintained by the IANA,http://www.iana.org/assignments/ipv4-address-space   [DMNSRV]  Internet Domain Survey, Internet Software Consortium,http://www.isc.org/ds/   [NETSZR]  Netsizer, Telcordia Technologies,http://www.netsizer.com/Durand & Huitema             Informational                      [Page 6]

RFC 3194                An update on the H ratio           November 200110. Full Copyright Statement   Copyright (C) The Internet Society (2001).  All Rights Reserved.   This document and translations of it may be copied and furnished to   others, and derivative works that comment on or otherwise explain it   or assist in its implementation may be prepared, copied, published   and distributed, in whole or in part, without restriction of any   kind, provided that the above copyright notice and this paragraph are   included on all such copies and derivative works.  However, this   document itself may not be modified in any way, such as by removing   the copyright notice or references to the Internet Society or other   Internet organizations, except as needed for the purpose of   developing Internet standards in which case the procedures for   copyrights defined in the Internet Standards process must be   followed, or as required to translate it into languages other than   English.   The limited permissions granted above are perpetual and will not be   revoked by the Internet Society or its successors or assigns.   This document and the information contained herein is provided on an   "AS IS" basis and THE INTERNET SOCIETY AND THE INTERNET ENGINEERING   TASK FORCE DISCLAIMS 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.Acknowledgement   Funding for the RFC Editor function is currently provided by the   Internet Society.Durand & Huitema             Informational                      [Page 7]