These are bidirectionalresults.
Levente
On 08/02/2013 09:59 AM, Gábor Sándor Enyedi wrote:
Are these the single or the bidirectional coverage results?
Gabor
*From:*[email protected] [mailto:[email protected]] *On
Behalf Of *Levente Csikor
*Sent:* Friday, August 02, 2013 8:25 AM
*To:* [email protected]
*Cc:* [email protected];
[email protected]; [email protected]
*Subject:* Re: draft-ietf-rtgwg-remote-lfa - ready for WGLC? - some
comments and questions
Dear All,
I'm sending my previous mail again since the font for the ASCII art
network was not fixed and may not appear in a right format at everyone.
If it still messy, let me know.
Sorry,
Levente
Dear All,
since our previous works in remote LFA analysis (papers already sent
to these mailing lists) assumed unit cost networks, therefore as I
promised, I calculated the corresponding LFA and rLFA coverages in
those networks with their original link costs.
These networks were inferred from Rocketfuel dataset (/Mahajan, R.,
Spring, N., Wetherall, D., Anderson, T.:
Inferring link weights using end-to-end measurements. In: ACM IMC, pp.
231–236 (2002)/), SNDLib (http://sndlib.zib.de), and
TopologyZoo(http://www.topology-zoo.org). The found coverages and some
details are found in the table below, where /n/ and /m/ denote the
number of nodes and the number of links, respectively. The other
columns mark the different coverages obrtained by simple LFA and
remote LFA, where LP indicates the link-protecting case, while NP
notes the case of node protection.
Topologies marked with an asterisk(*) did not have inferred real link
costs from the datasets, so their costs were initially set to 1 (unit
costs).
I believe that these results computed on real-world networks could
significantly improve the rlfa draft, especially Sec. 9.3., and the
advantages of remote LFA over simple LFA would be more emphasized.
+==============+====+====+==========+===========+============+============+
| Topology | n | m | LFA_LP | LFA_NP | rLFA_LP | rLFA_NP |
+==============+====+====+==========+===========+============+============+
| AS1221 | 7 | 9 | 0.809 | 0.25 | 0.809 | 0.25 |
+--------------+----+----+----------+-----------+------------+------------+
| AS1239 | 30 | 69 | 0.8735 | 0.7554 | 1 |
0.9795 |
+--------------+----+----+----------+-----------+------------+------------+
| AS1755 | 18 | 33 | 0.8725 | 0.7741 | 0.9967 | 0.9959 |
+--------------+----+----+----------+-----------+------------+------------+
| AS3257 | 27 | 64 | 0.923 | 0.7186 | 0.99 |
0.8472 |
+--------------+----+----+----------+-----------+------------+------------+
| AS3967 | 21 | 36 | 0.7857 | 0.6460 | 1 |
0.9325 |
+--------------+----+----+----------+-----------+------------+------------+
| AS6461 | 17 | 37 | 0.9338 | 0.6933 | 0.9963 | 0.7075 |
+--------------+----+----+----------+-----------+------------+------------+
| Abilene* | 12 | 15 | 0.5606 | 0.6078 | 0.9090 | 0.8725 |
+--------------+----+----+----------+-----------+------------+------------+
| Arnes* | 41 | 57 | 0.6225 | 0.3518 | 0.7487 | 0.4562 |
+--------------+----+----+----------+-----------+------------+------------+
| AT&T | 22 | 38 | 0.8225 | 0.5647 | 1 | 0.8497 |
+--------------+----+----+----------+-----------+------------+------------+
| Deltacom | 113| 161| 0.5771 | 0.4910 | 0.8539 | 0.8148 |
+--------------+----+----+----------+-----------+------------+------------+
| Gambia | 28 | 28 | 0.037 | 0.04 | 0.1851 | 0.12 |
+--------------+----+----+----------+-----------+------------+------------+
| Geant | 37 | 55 | 0.6906 | 0.3977 | 0.8303 | 0.6582 |
+--------------+----+----+----------+-----------+------------+------------+
| Germ_50 | 50 | 88 | 0.9004 | 0.8381 | 1 |
0.9995 |
+--------------+----+----+----------+-----------+------------+------------+
| Germany* | 27 | 32 | 0.6948 | 0.599 | 1 |
0.9549 |
+--------------+----+----+----------+-----------+------------+------------+
| InternetMCI | 19 | 33 | 0.9035 | 0.6798 | 0.9415 | 0.9136 |
+--------------+----+----+----------+-----------+------------+------------+
| Italy* | 33 | 56 | 0.784 | 0.5741 | 1 |
0.9269 |
+--------------+----+----+----------+-----------+------------+------------+
| NSF* | 26 | 43 | 0.86 | 0.6347 | 1 | 1
|
+--------------+----+----+----------+-----------+------------+------------+
Furthermore, after reading the draft again-and-again, I have found
that it should be more emphasized in the draft that calculating or
seeking for a remote LFA staging point should be done IF AND ONLY IF
no simple LFA were found. This is important, since normally people
obviously think and observe that the failure coverage of remote LFA
should be greater than or equal to the coverage obtained by simple
LFA. Moreover, people also think that LFAs produce a subset of remote
LFAs. However, if after a failure only P-spaces and Q-spaces are taken
into account in order to seek a (remote) loop-free alternate, then it
is possible that a simple LFA would not be found resulting unprotected
node-pairs. But, this case could only happen when link costs are not
unit costs. For an easier understanding, consider the network depicted
below:
1 1
F--------S-----------X--------E
\ / \
10 \ / 4 \ 1
\ / 1 \
N ---------------------------C
| |
1 | | 1
| |
| 1 1 |
A--------------B-------------D
Assume that S wishes to send a packet to D, and the shortest path goes
through E, therefore it is S-E-C-D. Suppose that the link (s,e)
fails, or even the node e itself fails. In this case, since LFA (and
its calculation) only consider all other neighbors of s, then node N
would be an easy LFA for this failure, since dist(N,D) <
dist(N,S)+dist(S,D).
However, if we only seek possible remote LFAs, than according to the
(r)SPF calculations, or taking into account our distance-function
conditions will result that D's Q-space will contain node N (besides
some other nodes), but S's P-space won't (it will only contain node F
and what is more, if node F does not exist, then S's P-space would be
empty), therefore no intersection of the two spaces will exist,
leaving this network vulnerable to the failure of link (s,e).
This results that a neighbor should be always reached by the
neighboring link, even if there exists a shorter, but definitely
bigger in hop-count path to it.
According to this case (when seeking simple LFA is missed), the
condition of extended P-space described by our distance functions,
should be modified a bit:
For source /s/, destination /d/, and next-hop /e/, some node /n !=
s,d/ is an extended link-protecting remote LFA for the /s-d/ pair if
and only if
/∃//v //∈//neigh(s) : dist(v, n) < dist(v, s) + dist(s, e) + dist(e,
n) *&& dist(s,v) < dist(s,e) + dist(e,v)*/
/dist(n, d) < dist(n, s) + dist(s, d) . /
One can easily observe that emphasizing more that remote LFA seeking
process is only "executed" after no simple LFA is found could much
more ease the understanding and won't result a headache to the reader
who accidentally wants to calculate rLFA coverage in such network.
Please let me know, if my interpretation is not correct.
Thanks.
Best,
Levente
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