Merging Logical Topologies Using
End-to-end Measurements
Michael Rabbat
Mark Coates
Robert Nowak
Internet Measurement Conference 2003
Tuesday October 28, 2003
Topology Identification via Active Probing
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:
A
1
2
3
– Correlated events on upstream links
– Additive, non-decreasing nature of performance parameters
[Ratnasamy & McCanne], [Duffield et al.], [Bestavros et al.], [Coates et al.]
4
5
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
1
2
B
3
4
5
1
2
3
4
5
No labels on internal nodes  Merging is non-trivial
Merging Strategy
1
2
B
A
A
3
4
B
5
1
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
2
3
4
5
Goal: Identify Shared Joining Nodes
• Two sources, two receivers
• Is there a shared joining node?
• Locate joining node relative to
branching node
A
B
1
2
A
• All other cases have more than one
non-shared joining node
1
• Make measurements and form a
binary hypothesis test:
H0 : One joining node
H1 : More than one joining node
A
B
1
2
B
2
1
2
Packet Arrival Order Measurements
Assumptions:
1. Sources synchronized (for now)
2. Arrival order determined at
first shared queue
t(n) + t
t
t
t(n)
A
v(n)
B
Procedure:
1. At t(n), send packets to Rcv1
2. After t, send packets to Rcv2
 t > O(1/bmin)
3. Compare arrival orders
Rcv1
Rcv2
y(n)
A
A
0
B
B
0
A
B
1
B
A
1
4. Repeat, varying send time at B
v(n) ~ Unif orm(-D, D)
|D| ¼ O(RTTmax) À t
1
2
Analysis: Packet Arrival Order and Timing
A
B
1
Conditions for a Different Arrival Order
Contours of p(d1, d2)
d2
A
B
d1
1
2
Prob. different arrival order | v(n)
For Non-Shared Topologies
A
Contours of p(d1, d2)
d2
B
d1
1
2
Prob. different arrival order | v(n)
• 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)
Measure the Noise
Send all packets to one receiver
 Force one joining node
2
2
t
t
t(n)
1
A
1
v(n)
B
Similar procedure:
1. At t(n), send packets to Rcv1
2. After t, send to Rcv1 again
 t ¼ O(1/bmin)
3. Compare arrival orders
Rcv1
Rcv2
y1(n)
A
A
0
B
B
0
A
B
1
B
A
1
4. Repeat, varying send time at B
v(n) ~ Unif orm(-D, D)
|D| ¼ O(RTTmax)
1
1
1
2
2
2
Must be noise
A
B
A
B
1
2
1
2
Making A Decision
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 Networking
http://spin.rice.edu
[email protected]
Probing from Multiple Sources
A
1
A
2
Exploit correlation on
upstream link, non-decreasing
additive property of metrics
B
1
Not as easy to exploit correlation
on downstream link…