Multiple Source, Multiple Destination Network Tomography

Michael Rabbat

IEEE Infocom, Hong Kong

Wednesday, March 10, 2004

Co-Authors:

Mark Coates and Robert Nowak

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

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

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)

Probe From Multiple HostsA

1 2 3

B(Bu et al., ’02)

…

…

Canonical Subproblem: Two Senders & Two Receivers

two sender, two receiver problem characterizes network tomography problem in general

Shared and Non-Shared Topologies

Natural dichotomy according to “model order”

5 Links2 Internal Nodes

Shared topology

8 Links4 Internal Nodes

Non-Shared topology

Mutual Information

Shared Non-Shared

Mutual Information

Shared Non-Shared

Same branching point Shared component links

Different branching points No shared component links

Combine Measurements!

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

Multiple Source Active Probing

1

1

2

2

random offset

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)

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)

Send to Both Receivers

1

1

2

2

random offset

22

11 repeat many times …

percentage different arrival order(should it be small?)

1

1

2

2

random offset

Test: Shared

Shared:

single, sharedjoining point j

1

1

2

2

random offset

Test: Shared vs. Non-Shared

Shared: vs. Non-Shared:

multiplejoining points

j j

Arrival Order Based Topology ID

Rice LAN

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

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

Characterize Topology & Performance

Generalized Likelihood Ratio Test:

Wilks’ Theorem (’38):

Under HS:

(T ! 1)

Performance Simulation in ns

S S

R

R

R

RR

500k-10MbpsFTP and ExpOO

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

Number of Probes Used

1000

500

200

100

Pro

b. C

orre

ctly

Dec

ide

Non

-Sha

red

Prob. Falsely Decide Non-Shared

Concluding Remarks

Combining arrival order with joint topology/performance estimation gives us an initial step towards solving this problem

www.cae.wisc.edu/~rabbatrabbat@cae.wisc.edu