towards unbiased end-to-end network diagnosis
DESCRIPTION
Towards Unbiased End-to-End Network Diagnosis. Yao Zhao 1 , Yan Chen 1 , David Bindel 2. Lab for Internet & Security Tech, Northwestern Univ Courant Institute of Mathematical Science , New York University. Outline. Background and Motivation MILS in Undirected Graphs MILS in Directed Graphs - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Towards Unbiased End-to-End Network Diagnosis](https://reader035.vdocuments.net/reader035/viewer/2022062410/5681602d550346895dcf4258/html5/thumbnails/1.jpg)
Yao Zhao1, Yan Chen1, David Bindel2
Towards Unbiased End-to-End Network Diagnosis
1. Lab for Internet & Security Tech, Northwestern Univ
2. Courant Institute of Mathematical Science , New York University
![Page 2: Towards Unbiased End-to-End Network Diagnosis](https://reader035.vdocuments.net/reader035/viewer/2022062410/5681602d550346895dcf4258/html5/thumbnails/2.jpg)
2
Outline
• Background and Motivation• MILS in Undirected Graphs• MILS in Directed Graphs• Evaluation• Conclusions
![Page 3: Towards Unbiased End-to-End Network Diagnosis](https://reader035.vdocuments.net/reader035/viewer/2022062410/5681602d550346895dcf4258/html5/thumbnails/3.jpg)
3
End-to-End Network Diagnosis
93 hours
?
![Page 4: Towards Unbiased End-to-End Network Diagnosis](https://reader035.vdocuments.net/reader035/viewer/2022062410/5681602d550346895dcf4258/html5/thumbnails/4.jpg)
4
Linear Algebraic Model
Path loss rate pi, link loss rate lj:)1)(1(1 211 llp
1
3
2
1
011 bxxx
A
D
C
B
1
2
3p1
p2
)1log()1log()1log( 211 llp
)1log()1log()1log(
0113
2
1
lll
2
1
3
2
1
111011
bb
xxx
Usually an underconstrained syste
m G
![Page 5: Towards Unbiased End-to-End Network Diagnosis](https://reader035.vdocuments.net/reader035/viewer/2022062410/5681602d550346895dcf4258/html5/thumbnails/5.jpg)
5
Unidentifiable Links
• Vectors That Are Linear Combinations of Row Vectors of G Are Identifiable– The property of a link (or link sequence) can
be computed from the linear system if and only if the corresponding vector is identifiable
• Otherwise, Unidentifiable
111011
G(1) 121 bxx
(2) 2321 bxxx (1)-(2) 123 bbx
A
D
C
B
1
2
3p1
p2 [ 0 0 1 ]
[ 1 0 0 ] ? ?1 x
![Page 6: Towards Unbiased End-to-End Network Diagnosis](https://reader035.vdocuments.net/reader035/viewer/2022062410/5681602d550346895dcf4258/html5/thumbnails/6.jpg)
6
Virtual Link
Motivation
• Biased statistic assumptions were introduced to infer unidentifiable virtual links, but can be inaccurate.
0.1
0.1
0
Loss rate = 0.1 if linear optimization
Loss = 0 if unicast tomography & RED
Loss rate?
![Page 7: Towards Unbiased End-to-End Network Diagnosis](https://reader035.vdocuments.net/reader035/viewer/2022062410/5681602d550346895dcf4258/html5/thumbnails/7.jpg)
7
Least-biased End-to-end Network Diagnosis (LEND)
• Basic Assumptions– End-to-end measurement can infer the end-to-
end properties accurately– Link level properties are independent
• Problem Formulation– Given end-to-end measurements, what is the
finest granularity of link properties can we achieve under basic assumptions?
Basic assumptions
More and stronger statistic assumptions
Virtual linkDiagnosis granularity?
Better accuracy
![Page 8: Towards Unbiased End-to-End Network Diagnosis](https://reader035.vdocuments.net/reader035/viewer/2022062410/5681602d550346895dcf4258/html5/thumbnails/8.jpg)
8
Least-biased End-to-end Network Diagnosis (LEND)
• Contributions– Define the minimal identifiable unit under basic
assumptions (MILS)– Prove that only E2E paths are MILS with a
directed graph topology (e.g., the Internet) – Propose good path algorithm (incorporating
measurement path properties) for finer MILS
Basic assumptions
More and stronger statistic assumptions
Virtual linkDiagnosis granularity?
Better accuracy
![Page 9: Towards Unbiased End-to-End Network Diagnosis](https://reader035.vdocuments.net/reader035/viewer/2022062410/5681602d550346895dcf4258/html5/thumbnails/9.jpg)
9
Outline
• Background and Motivation• MILS in Undirected Graphs• MILS in Directed Graphs• Evaluation• Conclusions
![Page 10: Towards Unbiased End-to-End Network Diagnosis](https://reader035.vdocuments.net/reader035/viewer/2022062410/5681602d550346895dcf4258/html5/thumbnails/10.jpg)
10
Minimal Identifiable Link Sequence
• Definition of MILS– The smallest path segments with loss rates t
hat can be uniquely identified through end-to-end path measurements
– Related to the sparse basis problem• NP-hard Problem
• Properties of MILS– The MILS is a consecutive sequence of links– A MILS cannot be split into MILSes (minimal)– MILSes may be linearly dependent, or some
MILSes may contain other MILSes
![Page 11: Towards Unbiased End-to-End Network Diagnosis](https://reader035.vdocuments.net/reader035/viewer/2022062410/5681602d550346895dcf4258/html5/thumbnails/11.jpg)
11
Examples of MILSes in Undirected Graph
Real links (solid) and all of the overlay paths (dotted) traversing them
1
231’
2’
3’4’
4
5
4
3
2
1
11000011011011000011
vvvv
G
MILSes
a
b
c
de
3’+2’-1’-4’ → link 3
4132 vvvv
001002
![Page 12: Towards Unbiased End-to-End Network Diagnosis](https://reader035.vdocuments.net/reader035/viewer/2022062410/5681602d550346895dcf4258/html5/thumbnails/12.jpg)
12
Identify MILSes in Undirected Graphs
• Preparation– Active or passive end-to-end path measure
ment– Optimization
• Measure O(nlogn) paths and infer the n(n-1) end-to-end paths [SIGCOMM04]
![Page 13: Towards Unbiased End-to-End Network Diagnosis](https://reader035.vdocuments.net/reader035/viewer/2022062410/5681602d550346895dcf4258/html5/thumbnails/13.jpg)
13
• Preparation• Identify MILSes
– Enumerate each link sequence to see if it is identifiable
– Computational complexity: O(r×k×l2)• r: the number of paths (O(n2))• k: the rank of G (O(nlogn))• l: the length of the paths
– Only takes 4.2 seconds for the network with 135 Planetlab hosts and 18,090 Internet paths
Identify MILSes in Undirected Graphs
![Page 14: Towards Unbiased End-to-End Network Diagnosis](https://reader035.vdocuments.net/reader035/viewer/2022062410/5681602d550346895dcf4258/html5/thumbnails/14.jpg)
14
Outline
• Background and Motivation• MILS in Undirected Graphs• MILS in Directed Graphs• Evaluation• Conclusions
![Page 15: Towards Unbiased End-to-End Network Diagnosis](https://reader035.vdocuments.net/reader035/viewer/2022062410/5681602d550346895dcf4258/html5/thumbnails/15.jpg)
15
What about Directed Graphs?• Intuition
– Directed graphs is similar to undirected graph, although more complicate
Theorem: In a directed graph, no end-to-end path contains an identifiable subpath if only considering topology information
A
B C
N
A
B C
N
IncomingLinks
OutgoingLinks
1
23
4
6 5
010100001100100010001010100001010001654321
G
[1 0 0 0 0 0] ?
Sum=1 Sum=1Sum=1 Sum=1
Sum=1 Sum=0
![Page 16: Towards Unbiased End-to-End Network Diagnosis](https://reader035.vdocuments.net/reader035/viewer/2022062410/5681602d550346895dcf4258/html5/thumbnails/16.jpg)
16
Good Path Algorithm
• Consider Only Topology– Works for undirected graph
• Incorporate Measurement Path Property– Most paths have no loss
• PlanetLab experiments show 50% of paths in the Internet have no loss
– All the links in a path of no loss are good links (Good Path Algorithm)
![Page 17: Towards Unbiased End-to-End Network Diagnosis](https://reader035.vdocuments.net/reader035/viewer/2022062410/5681602d550346895dcf4258/html5/thumbnails/17.jpg)
17
Good Path Algorithm
A
B C
N
A
B C
N
IncomingLinks
OutgoingLinks
1
23
4
6 5
010100001100100010001010100001010001654321
G
• Symmetric property is broken when using good path algorithm.
![Page 18: Towards Unbiased End-to-End Network Diagnosis](https://reader035.vdocuments.net/reader035/viewer/2022062410/5681602d550346895dcf4258/html5/thumbnails/18.jpg)
18
Other Features of LEND
• Dynamic Update for Topology and Link Property Changes– End hosts join or leave, routing changes or pa
th property changes– Incremental update algorithms very efficient
• Combine with Statistical Diagnosis– Inference with MILSes is equivalent to inferen
ce with the whole end-to-end paths– Reduce computational complexity because MI
LSes are shorter than paths• Example: applying statistical tomography methods i
n [Infocom03] on MILSes is 5x faster than on paths
![Page 19: Towards Unbiased End-to-End Network Diagnosis](https://reader035.vdocuments.net/reader035/viewer/2022062410/5681602d550346895dcf4258/html5/thumbnails/19.jpg)
19
Outline
• Motivation• MILS in Undirected Graphs• MILS in Directed Graphs• Evaluation• Conclusions
![Page 20: Towards Unbiased End-to-End Network Diagnosis](https://reader035.vdocuments.net/reader035/viewer/2022062410/5681602d550346895dcf4258/html5/thumbnails/20.jpg)
20
Evaluation Metrics• Diagnosis Granularity
– Average length of all the lossy MILSes in lossy path
• Accuracy– Simulations
• Absolute error and relative error
– Internet experiments• Cross validation • IP spoof based consistency check
• Speed– Running time for finding all MILSes and loss rat
e inference
![Page 21: Towards Unbiased End-to-End Network Diagnosis](https://reader035.vdocuments.net/reader035/viewer/2022062410/5681602d550346895dcf4258/html5/thumbnails/21.jpg)
21
Methodology• Planetlab Testbed
– 135 end hosts, each from different institute – 18,090 end-to-end paths
• Topology Measured by Traceroute– Avg path length is 15.2
• Path Loss Rate by Active UDP Probing with Small Overhead
Areas and Domains # of hosts
US (77)
.edu 50.org 14.net 2.com 10.us 1
Inter- national (58)
Europe 25Asia 25
Canada 3South America 3
Australia 2
![Page 22: Towards Unbiased End-to-End Network Diagnosis](https://reader035.vdocuments.net/reader035/viewer/2022062410/5681602d550346895dcf4258/html5/thumbnails/22.jpg)
22
Diagnosis Granularity
# of End-to-end Paths 18,090
Avg Path Length 15.2
# of MILSes 1009
Avg length of MILSes 2.3 virtual links (3.9 physical links)
Avg diagnosis granularity 2.3 virtual links (3.8 physical links)
Loss rate
[0, 0.05)
lossy path [0.05, 1.0] (15.8%)[0.05,
0.1) [0.1, 0.3) [0.3,
0.5) [0.5,
1.0) 1.0
% 84.2 17.2 15.6 24.9 15.8 26.5
![Page 23: Towards Unbiased End-to-End Network Diagnosis](https://reader035.vdocuments.net/reader035/viewer/2022062410/5681602d550346895dcf4258/html5/thumbnails/23.jpg)
23
Distribution of Length of MILSes
• Most MILSes are pretty short• Some MILSes are longer than 10 hops
– Some paths do not overlap with any other paths
Most MILSes are short
A few MILSes are very long
![Page 24: Towards Unbiased End-to-End Network Diagnosis](https://reader035.vdocuments.net/reader035/viewer/2022062410/5681602d550346895dcf4258/html5/thumbnails/24.jpg)
24
Other Results• MILS to AS Mapping
– 33.6% lossy MILSes comprise only one physical link
• 81.8% of them connect two ASes
• Accuracy– Cross validation (99.0%)– IP spoof based consistency check (93.5%)
• Speed– 4.2 seconds for MILS computations– 109.3 seconds for setup of scalable active
monitoring [SIGCOMM04]
![Page 25: Towards Unbiased End-to-End Network Diagnosis](https://reader035.vdocuments.net/reader035/viewer/2022062410/5681602d550346895dcf4258/html5/thumbnails/25.jpg)
25
Conclusion• Link-level property inference in directed
graphs is completely different from that in undirected graphs
• With the least biased assumptions, LEND uses good path algorithm to infer link level loss rates, achieving– Good inference accuracy– Acceptable diagnosis granularity in practice– Online monitoring and diagnosis
• Continuous monitoring and diagnosis services on PlanetLab under construction
![Page 26: Towards Unbiased End-to-End Network Diagnosis](https://reader035.vdocuments.net/reader035/viewer/2022062410/5681602d550346895dcf4258/html5/thumbnails/26.jpg)
26
Thank You!
For more info:http://list.cs.northwestern.edu/lend/
Questions?
![Page 27: Towards Unbiased End-to-End Network Diagnosis](https://reader035.vdocuments.net/reader035/viewer/2022062410/5681602d550346895dcf4258/html5/thumbnails/27.jpg)
27
![Page 28: Towards Unbiased End-to-End Network Diagnosis](https://reader035.vdocuments.net/reader035/viewer/2022062410/5681602d550346895dcf4258/html5/thumbnails/28.jpg)
28
Motivation
• End-to-End Network Diagnosis• Under-constrained Linear System
– Unidentifiable Links exist
To simplify presentation, assume
undirected graph model
A R B
![Page 29: Towards Unbiased End-to-End Network Diagnosis](https://reader035.vdocuments.net/reader035/viewer/2022062410/5681602d550346895dcf4258/html5/thumbnails/29.jpg)
29
Linear Algebraic Model (2)
! system dconstraine-underan Usually )( sGrankk
…=
11 vectorrate losspath vectorrate losslink
matrix path where
,
}1|0{,
rs
sr
bx
GbGx
![Page 30: Towards Unbiased End-to-End Network Diagnosis](https://reader035.vdocuments.net/reader035/viewer/2022062410/5681602d550346895dcf4258/html5/thumbnails/30.jpg)
30
Identifiable and Unidentifiable
• Vectors That Are Linear Combinations of Row Vectors of G Are Identifiable
• Otherwise, Unidentifiable
111011
G(1) 121 bxx (2) 2321 bxxx
(1)-(2) 123 bbx
A
D
C
B
1
2
3p1
p2
(1,1,0)
Row(path) space(identifiable)
x1
x2
(1,1,1)
(0,0,1)
x3
![Page 31: Towards Unbiased End-to-End Network Diagnosis](https://reader035.vdocuments.net/reader035/viewer/2022062410/5681602d550346895dcf4258/html5/thumbnails/31.jpg)
31
Examples of MILSes in Undirected Graph
1 2
1
2 3
1’
Real links (solid) and all of the overlay paths (dotted) traversing them
1’ 2’
1
231’
2’
Rank(G)=1
Rank(G)=3
Rank(G)=4
3’4’
a
4
11G
110
101
011
Ga
b c3’
5
11000011011011000011
G
MILSes
a
b
c
de
3’+2’-1’-4’ → link 3
![Page 32: Towards Unbiased End-to-End Network Diagnosis](https://reader035.vdocuments.net/reader035/viewer/2022062410/5681602d550346895dcf4258/html5/thumbnails/32.jpg)
32
Identify MILSes in Undirected Graphs
• Preparation• Identify MILSes
– Compute Q as the orthonormal basis of R(GT) (saved by preparation step)
– For a vector v in R(GT) , ||v|| = ||QTv||
x1
x2
x3
v1 1~v
||~|||||| 22 vv v2
![Page 33: Towards Unbiased End-to-End Network Diagnosis](https://reader035.vdocuments.net/reader035/viewer/2022062410/5681602d550346895dcf4258/html5/thumbnails/33.jpg)
33
Flowchart of LEND System• Step 1
– Monitors O(n·logn) paths that can fully describe all the O(n2) paths (SIGCOMM04)
– Or passive monitoring
• Step 2 – Apply good path algorithm before identifying MILSes as in
undirected graph
Measure topology to get G
Active or passive monitoring
Iteratively check all possible MILSes
Compute loss rates of MILSes
Good pathalgorithm on G
Stage 2: online update the measurements and diagnosisStage 1: set up scalablemonitoring system for diagnosis
![Page 34: Towards Unbiased End-to-End Network Diagnosis](https://reader035.vdocuments.net/reader035/viewer/2022062410/5681602d550346895dcf4258/html5/thumbnails/34.jpg)
34
Evaluation with Simulation
• Metrics– Diagnosis granularity
• Average length of all the lossy MILSes in lossy path (in the unit of link or virtual link)
– Accuracy• Absolute error |p – p’ |: • Relative error
)',max()('),,max()(where)()(',
)(')(max)',(
pppppp
ppppF
![Page 35: Towards Unbiased End-to-End Network Diagnosis](https://reader035.vdocuments.net/reader035/viewer/2022062410/5681602d550346895dcf4258/html5/thumbnails/35.jpg)
35
Simulation Methodology• Topology type
– Three types of BRITE router-level topologies
– Mecator topology • Topology size
– 1000 ~ 20000 or 284k nodes• Number of end hosts on the overlay net
work– 50 ~ 300
• Link loss rate distribution– LLRD1 and LLRD2 models
• Loss model– Bernoulli and Gilbert
![Page 36: Towards Unbiased End-to-End Network Diagnosis](https://reader035.vdocuments.net/reader035/viewer/2022062410/5681602d550346895dcf4258/html5/thumbnails/36.jpg)
36
Sample of Simulation Results
# of endhost on OL
# ofpaths
AvgPL
# oflinks
# ofLP
# of linksin LP
Avg MILSlength
Avg diagnosisgranularity
50 2450 8.86 3798 1042 903 2.23(3.03) 2.24(3.07)
100 9900 8.80 9802 3551 1993 1.71(2.27) 2.05(2.95)
200 39800 8.80 22352 14706 4335 1.49(1.92) 1.77(2.38)
• Mercator (284k nodes) with Gilbert loss model and LLRD1 loss distribution
![Page 37: Towards Unbiased End-to-End Network Diagnosis](https://reader035.vdocuments.net/reader035/viewer/2022062410/5681602d550346895dcf4258/html5/thumbnails/37.jpg)
37
Related Works
• Pure End-to-End Approaches– Internet Tomography
• Multicast or unicast with loss correlation– Uncorrelated end-to-end schemes
• Router Response Based Approach– Tulip and Cing
0
A
B C
N0.1
A
B C
N
0.19
0
0.1
0.1
0.19 0.19 0.19 0.19
(a) (b)
![Page 38: Towards Unbiased End-to-End Network Diagnosis](https://reader035.vdocuments.net/reader035/viewer/2022062410/5681602d550346895dcf4258/html5/thumbnails/38.jpg)
38
MILS to AS Mapping
• IP-to-AS mapping constructed from BGP routing tables
• Consider the short MILSes with length 1 or 2– Consist of about 44% of all lossy MILSes.– Most lossy links are connecting two dierent
ASes
1 AS 2 ASes 3 ASes >3 ASesLen 1 MILSes (33.6%) 6.1% 27.5% 0 0Len 2 MILSes (9.8%) 2.6% 5.8% 1.3% 0
Len > 2 MILSes (56.6%) 6.8% 17.8% 21.8% 10.2%
![Page 39: Towards Unbiased End-to-End Network Diagnosis](https://reader035.vdocuments.net/reader035/viewer/2022062410/5681602d550346895dcf4258/html5/thumbnails/39.jpg)
39
Accuracy Validation
• Cross Validation (99.0% consistent)• IP Spoof based Consistency Checking.
• UDP: Src: A, Dst: C, TTL=255
A
C
B
• UDP: Src: A, Dst: B, TTL=255• UDP: Src: C, Dst: B, TTL=2• ICMP: Src: R3, Dst: C, TTL=255
R1
R2R3
IP Spoof based Consistency: 93.5%