As per Relevance of the word efficiency, we have this rfc below:
Network Working Group C.
Request for Comments: 1715
Category: Informational November 1994
The H Ratio for Address Assignment
Status of this
This memo provides information for the Internet community. This
does not specify an Internet standard of any kind. Distribution
this memo is unlimited
This document was submitted to the IETF IPng area in response to
1550. Publication of this document does not imply acceptance by
IPng area of any ideas expressed within. Comments should
submitted to the author and/or the sipp@sunroof.eng.sun.com
list
Table of
1. Efficiency of address assignment . . . . . . . . . . . . . . 1
2. Estimating reasonable values for the ratio H . . . . . . . . 2
3. Evaluating proposed address plans. . . . . . . . . . . . . . 3
4. Security Considerations . . . . . . . . . . . . . . . . . . 4
5. Author's Address . . . . . . . . . . . . . . . . . . . . . . 4
1. Efficiency of address
A substantial part of the "IPng" debate was devoted to the choice
an address size. A recurring concept was that of "
efficiency", which most people involved in the discussion
as a the ratio of the effective number of systems in the network
the theoretical maximum. For example, the 32 bits IP addressing
could in theory number over 7 billions of systems; as of today,
have about 3.5 millions of addresses reported in the DNS, which
translate in an efficiency of 0.05%.
Huitema [Page 1]
RFC 1715 H Ratio November 1994
But this classic evaluation is misleading, as it does not take
account the number of hierarchical elements. IP addresses,
example, have at least three degrees of hierarchy: network,
and host. In order to remove these dependencies, I propose to use
logarithmic scale for the efficiency ratio
log (number of objects
H = -----------------------
available
The ratio H is not too dependent of the number of
levels. Suppose for example that we have the choice between
levels, encoded on 8 bits each, and one single level, encoded in 16
bits. We will obtain the same efficiency if we allocate in
100 elements at each 8 bits level, or simply 10000 elements in
single 16 bits level
Note that I use base 10 logs in what follows, because they are
to compute mentally. When it comes to large numbers, people tend
use "powers of 10", as in "IPng should be capable of numbering 1 E+15
systems". It follows from this choice of units that H varies
0 and a theoretical maximum of 0.30103 (log base 10 of 2).
2. Estimating reasonable values for the ratio H
Indeed, we don't expect to achieve a ratio of 0.3 in practice,
the interesting question is to assert the values which can
reasonably expected. We can try to evaluate them from
numbering plans. What is especially interesting is to consider
moment where the plans broke, i.e. when people were forced to
digits to phone number, or to add bits to computer addresses. I
a number of such figures handy, e.g.:
* 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. The log value is 7, the number of bits was about 27 (1
digit is about 3.3 bits). The ratio is thus 0.26
* Expending the number of areas in the US telephone system, making
effectively 10 digits long, for about 1.0 E+8 subscribers. The
value is 8, the number of bits is 33, the ratio is about 0.24
* Expending the size of the Internet addresses, from 32 bits
something else. There are currently about 3 million hosts on
net, for 32 bits. The log of 3.E6 is about 6.5; this gives a
of 0.20. Indeed, we believe that 32 bits will still be enough
some years, e.g. to multiply the number of hosts by 10, in
case the ratio would climb to 0.23
Huitema [Page 2]
RFC 1715 H Ratio November 1994
* Expending the size of the SITA 7 characters address. According
their documentation, they have about 64000 addressed points
their network, scattered in 1200 cities, 180 countries. An
case character provides about 5 bits of addressing, which
in an efficiency of 0.14. This is an extreme case, as SITA
fixed length tokens in its hierarchy
* The globally-connected physics/space science DECnet (Phase IV
stopped growing at about 15K nodes (i.e. new nodes were hidden
which in a 16 bit space gives a ratio of 0.26
* There are about 200 million IEEE 802 nodes in a 46 bit space,
gives a ratio of 0.18. That number space, however, is
saturated
From these examples, we can assert that the efficiency ratio
lies between 0.14 and 0.26.
3. Evaluating proposed address
Using a reverse computation, we get the following population
in the network
Pessimistic (0.14) Optimistic (0.26)
32 bits 3 E+4 (!) 2 E+8
64 bits 9 E+8 4 E+16
80 bits 1.6 E+11 2.6 E+27
128 bits 8 E+17 2 E+33
I guess that the figure explains well why some feel that 64 bits
"not enough" while other feel it is "sufficient by a large margin":
depending of the assignment efficiency, we are either well below
target or well above. But there is no question, in my view, that 128
bits is "more than enough". Even if we presume the lowest efficiency
we are still way above the hyperbolic estimate of 1.E+15
hosts
It is also interesting to note that if we devote 80 bits to
"network" and use 48 bits for "server less autoconfiguration", we
number more that E.11 networks in the pessimistic case - it
only take an efficiency of 0.15 to reach the E+12 networks hyperbole
I guess this explains well why I feel that 128 bits is entirely
for the next 30 year. The level of constraints that we will have
incorporate in the address assignment appears very much in line
what we know how to do, today
Huitema [Page 3]
RFC 1715 H Ratio November 1994
4. Security
Security issues are not discussed in this memo
5. Author's
Christian
INRIA, Sophia-
2004 Route des
BP 109
F-06561 Valbonne
Phone: +33 93 65 77 15
EMail: Christian.Huitema@MIRSA.INRIA.
Huitema [Page 4]
if you see any problems within the linking, don't worry be happy,
this is version 0.1 of the Relevance System and you gotta expect some crappy subroutines sometimes,
just be content we did not write this in Java, which would have made this "bigger and better" HAHAHHA.
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