1. Merging Logical Topologies Using End-to-end Measurements Michael Rabbat Mark Coates Robert Nowak Internet Measurement Conference 2003 Tuesday October 28, 2003

2. Motivation: BGP data gives the big picture ICMP-based techniques (i.e. traceroute ) dont 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 35421 Topology Identification via Active Probing

3. 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 35421 35421 B No labels on internal nodes Merging is non-trivial

4. Merging Strategy A 35421 35421 B A B 1 2 3 45 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

5. 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: H 0 : One joining node H 1 : More than one joining node A B 1 2 A B 1 2 A 21 B 21

6. Packet Arrival Order Measurements Assumptions: 1.Sources synchronized (for now) 2.Arrival order determined at first shared queue A B 1 2 t(n)t(n) t(n) + t t v(n)v(n) t Procedure: 1.At t(n), send packets to Rcv1 2.After t, send packets to Rcv2 t > O(1/b min ) 3.Compare arrival orders 4.Repeat, varying send time at B v(n) ~ Unif orm(-D, D) |D| ¼ O(RTT max ) À t Rcv1Rcv2y(n)y(n) AA0 BB0 AB1 BA1

7. Analysis: Packet Arrival Order and Timing A B 1

8. Conditions for a Different Arrival Order Prob. different arrival order | v(n) A B 1 2 Contours of p(d 1, d 2 ) d1d1 d2d2

9. 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(d 1, d 2 ) d1d1 d2d2

10. Measure the Noise Send all packets to one receiver Force one joining node A B 1 2 t(n)t(n) t v(n)v(n) t Similar procedure: 1.At t(n), send packets to Rcv1 2.After t, send to Rcv1 again t ¼ O(1/b min ) 3.Compare arrival orders 4.Repeat, varying send time at B v(n) ~ Unif orm(-D, D) |D| ¼ O(RTT max ) Rcv1Rcv2y1(n)y1(n) AA0 BB0 AB1 BA1 Must be noise 1 1 1 1 2 2 2 2

11. Making A Decision A B 1 2 A B 1 2

12. 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

13. 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(NS 2 R 2 ) measurements, reduce to O(NS 2 R) using stripes –Infrastructure independent (layer-3 or layer-2) Signal Processing In Networking http://spin.rice.edu rabbat@cae.wisc.edu