multiple source, multiple destination network tomography michael rabbat ieee infocom, hong kong...
TRANSCRIPT
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Multiple Source, Multiple Destination Network Tomography
Michael Rabbat
IEEE Infocom, Hong Kong
Wednesday, March 10, 2004
Co-Authors:
Mark Coates and Robert Nowak
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What is Network Tomography?
Logical Topology
A
1 2 3
Goal: Characterize the internal network using end-to-end measurements
6 754
32
1
Good Bad Ugly
+Link-level Performance Parameters
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Back-to-Back Packet Probes
A
1 2
Similar experience
Independent experiences
(Keshav, ’91) (Carter & Crovella, ’96)
Repeat and average) Take T measurements
Independent behavior onunshared links allows us to separate performance effects(e.g., loss, delay) on the different branches
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Reconstruct The Network (Single Source)
1.5
0.5
1.0 2.5
1.0
2.0
1.0 2.5 1.5
1.5
1.0 3.0 1.0
1.5
• Link-level characteristics (loss, delay) estimation• Network topology identification
Tightly coupled problems
(Duffield, Towsley et al., ’99) (Coates & Nowak, ’00) (Byers et al., ’00)
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Probe From Multiple HostsA
1 2 3
B(Bu et al., ’02)
…
…
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Canonical Subproblem: Two Senders & Two Receivers
two sender, two receiver problem characterizes network tomography problem in general
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Shared and Non-Shared Topologies
Natural dichotomy according to “model order”
5 Links2 Internal Nodes
Shared topology
8 Links4 Internal Nodes
Non-Shared topology
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Mutual Information
Shared Non-Shared
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Mutual Information
Shared Non-Shared
Same branching point Shared component links
Different branching points No shared component links
Combine Measurements!
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Arrival Order and Model Order Selection
1 1 Intuition:• Packets from A,B to 1 mix at joining point• Arrival order fixed at joining point
Assume:• Unique routes between end-hosts• Routes are stationary (5-10min) (Zhang, Paxson, Shenker, ’00)• No reordering (Bellardo & Savage, ’02)
Packets from each sender to receiver 1
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Multiple Source Active Probing
1
1
2
2
random offset
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All Packets to Receiver 1
1
1
2
2
random offset
2
1
2
1
j
repeat many times …1 = percentage different arrival order (should be very small)
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All Packets to Receiver 2
1
1
2
2
random offset
j
2
1
2
1
repeat many times …2 = percentage different arrival order (also very small)
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Send to Both Receivers
1
1
2
2
random offset
22
11 repeat many times …
percentage different arrival order(should it be small?)
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1
1
2
2
random offset
Test: Shared
Shared:
single, sharedjoining point j
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1
1
2
2
random offset
Test: Shared vs. Non-Shared
Shared: vs. Non-Shared:
multiplejoining points
j j
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Arrival Order Based Topology ID
Rice LAN
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Joint Performance & Topology Estimation
1
2
u
Performance Assessment• Link-level parameters 1, 2, …• Packet-pair measurements
1
21
21
2
Topology Characterization• Different arrival order probabilities , 1, 2
• Arrival order measurements
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Decision-Theoretic Framework
HS:
HN:Two branching, joining points unrestricted N 2 unrestricted N 2 [0,1]3
Unique joining point 2536 S 2 1=2= S 2 [0,1]1
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Characterize Topology & Performance
Generalized Likelihood Ratio Test:
Wilks’ Theorem (’38):
Under HS:
(T ! 1)
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Performance Simulation in ns
S S
R
R
R
RR
500k-10MbpsFTP and ExpOO
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Joint Topology/Performance Estimation1000 probes
Loss Only
Arrival Order Only
Arrival Order and Loss
Pro
b. C
orre
ctly
Dec
ide
Non
-Sha
red
Prob. Falsely Decide Non-Shared
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Number of Probes Used
1000
500
200
100
Pro
b. C
orre
ctly
Dec
ide
Non
-Sha
red
Prob. Falsely Decide Non-Shared
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Concluding Remarks
Combining arrival order with joint topology/performance estimation gives us an initial step towards solving this problem
www.cae.wisc.edu/[email protected]