1. Multiple Source, Multiple Destination Network Tomography Michael Rabbat IEEE Infocom, Hong Kong Wednesday, March 10, 2004 Co-Authors: Mark Coates and Robert Nowak

2. What is Network Tomography? Logical Topology A 123 Goal: Characterize the internal network using end-to-end measurements 66 77 55 44 33 22 11 GoodBad Ugly + Link-level Performance Parameters

3. Back-to-Back Packet Probes A 12 Similar experience Independent experiences (Keshav, ’91) (Carter & Crovella, ’96) Repeat and average ) Take T measurements Independent behavior on unshared links allows us to separate performance effects (e.g., loss, delay) on the different branches

4. Reconstruct The Network (Single Source) 1.5 0.5 1.02.5 1.0 2.0 1.02.51.5 1.03.01.0 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)

5. Probe From Multiple Hosts A 123 B (Bu et al., ’02) … …

6. Canonical Subproblem: Two Senders & Two Receivers two sender, two receiver problem characterizes network tomography problem in general

7. Shared and Non-Shared Topologies Natural dichotomy according to “model order” 5 Links 2 Internal Nodes Shared topology 8 Links 4 Internal Nodes Non-Shared topology

8. Mutual Information SharedNon-Shared

9. Mutual Information SharedNon-Shared Same branching point  Shared component links Different branching points  No shared component links Combine Measurements!

10. 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

11. Multiple Source Active Probing 1 1 2 2 random offset  

12. 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)

13. 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)

14. Send to Both Receivers 1 1 2 2 random offset   2 2 1 1 repeat many times …  percentage different arrival order (should it be small?)

15. 1 1 2 2 random offset Test: Shared Shared:   single, shared joining point j

16. 1 1 2 2 random offset Test: Shared vs. Non-Shared Shared: vs. Non-Shared:   multiple joining points j j

17. Arrival Order Based Topology ID Rice LAN

18. Joint Performance & Topology Estimation 1 2  u  Performance Assessment Link-level parameters  1,  2, … Packet-pair measurements 1 2 1 2 1 2 Topology Characterization Different arrival order probabilities ,  1,  2 Arrival order measurements

19. Decision-Theoretic Framework HS:HS: HN:HN: Two branching, joining points  unrestricted   N 2  unrestricted   N 2 [0,1] 3 Unique joining point  2  5  3  6   S 2  1 =  2 =    S 2 [0,1] 1

20. Characterize Topology & Performance Generalized Likelihood Ratio Test: Wilks’ Theorem (’38): Under H S : (T ! 1)(T ! 1)

21. Performance Simulation in ns S S R R R R R 500k-10Mbps FTP and ExpOO

22. Joint Topology/Performance Estimation 1000 probes Loss Only Arrival Order Only Arrival Order and Loss Prob. Correctly Decide Non-Shared Prob. Falsely Decide Non-Shared

23. Number of Probes Used 1000 500 200 100 Prob. Correctly Decide Non-Shared Prob. Falsely Decide Non-Shared

24. Concluding Remarks Combining arrival order with joint topology/performance estimation gives us an initial step towards solving this problem www.cae.wisc.edu/~rabbat rabbat@cae.wisc.edu