Merging Logical Topologies UsingMerging Logical Topologies UsingEnd-to-end MeasurementsEnd-to-end Measurements

Michael Rabbat Mark Coates Robert Nowak

Internet Measurement Conference 2003

Tuesday October 28, 2003

Motivation:• BGP data gives the big picture• ICMP-based techniques (i.e. traceroute) don’t work

everywhere

Existing end-to-end techniques:• Single active source, many receivers• Assume tree structured logical topology• Exploit:

– Correlated events on upstream links– Additive, non-decreasing nature of performance parameters

[Ratnasamy & McCanne], [Duffield et al.], [Bestavros et al.], [Coates et al.]

A

3 5421

Topology Identification via Active Probing

Extending to Multiple Sources

• Marginal Utility [Barford et al., ‘01]– Can gain by using a few more sources

• Net. Tomo. on General Topologies [Bu et al., ’02]– Evaluate various algorithms for inferring internal characteristics– Sources make measurements separately– Identifiability conditions given the general topology

A

3 5421 3 5421

B

No labels on internal nodes Merging is non-trivial

Merging Strategy

A

3 54213 5421

BA B

1 2 3 4 5

• Identify joining nodes merge topologies– Placement is logical, relative

• Non-shared joining node– Merging node for routes to a single receiver

• Shared joining node– Routes to multiple receivers merge at one node

Goal: Identify Shared Joining Nodes• Two sources, two receivers• Is there a shared joining node?• Locate joining node relative to

branching node

• All other cases have more than one non-shared joining node

• Make measurements and form a binary hypothesis test:

H0 : One joining node

H1 : More than one joining node

A B

1 2

A B

1 2

A

21

B

21

Packet Arrival Order MeasurementsAssumptions:1. Sources synchronized (for now)2. Arrival order determined at

first shared queue

A B

1 2

t(n)

t(n) + t

tv(n)

t

Procedure:1. At t(n), send packets to Rcv12. After t, send packets to Rcv2

t > O(1/bmin)3. Compare arrival orders

4. Repeat, varying send time at Bv(n) ~ Unif orm(-D, D)|D| ¼ O(RTTmax) À t

Rcv1 Rcv2 y(n)

A A 0

B B 0

A B 1

B A 1

Analysis: Packet Arrival Order and Timing

A B

1

Conditions for a Different Arrival Order

Prob. different arrival order | v(n)

A B

1 2

Contours of p(d1, d2)

d1

d2

For Non-Shared Topologies

• On packet reordering [Bellardo & Savage, ’02]– Pr{In-network reordering} / 1/(time-spacing)

• Sources of measurement noise– Packet reordering for a few values of v(n)– Spacing t distorted by queueing (also, for few values of v)

Prob. different arrival order | v(n)

A B

1 2

Contours of p(d1, d2)

d1

d2

Measure the Noise

Send all packets to one receiver Force one joining node

A B

1 2

t(n)t

v(n)t

Similar procedure:1. At t(n), send packets to Rcv12. After t, send to Rcv1 again

t ¼ O(1/bmin)3. Compare arrival orders

4. Repeat, varying send time at Bv(n) ~ Unif orm(-D, D)|D| ¼ O(RTTmax)

Rcv1 Rcv2 y1(n)

A A 0

B B 0

A B 1

B A 1

Must be noise

1

11

1

22

22

Making A DecisionA B

1 2

A B

1 2

Some Experiments

• Rice ECE LAN– 18 Unix/Linux hosts

– Spread across two buildings, two VLANs

– Mostly layer-2, two routers

– Validated with help from IT

• Internet “Test bed”– 11 academic hosts

– Mostly N. American, few in Europe

– Validated using traceroute

• Extremely successful

Summary

• Merge logical topologies by identifying joining nodes– Shared joining nodes located relative to branching node

• Novel multiple source active probing scheme– Uniform random offset– Look for packet arrival order differences

• A few concluding remarks– Unicast or multicast– O(NS2 R2) measurements, reduce to O(NS2 R) using “stripes”– Infrastructure independent (layer-3 or layer-2)

Signal Processing In Networkinghttp://spin.rice.edu

rabbat@cae.wisc.edu