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 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

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

Reconstruct The Network (Single Source) 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 Hosts A 123 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 Links 2 Internal Nodes Shared topology 8 Links 4 Internal Nodes Non-Shared topology

Mutual Information SharedNon-Shared

Mutual Information SharedNon-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 random offset  

All Packets to Receiver random offset   j repeat many times …  1 = percentage different arrival order (should be very small)

All Packets to Receiver random offset   j repeat many times …  2 = percentage different arrival order (also very small)

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

random offset Test: Shared Shared:   single, shared joining point j

random offset Test: Shared vs. Non-Shared Shared: vs. Non-Shared:   multiple joining 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 Topology Characterization Different arrival order probabilities ,  1,  2 Arrival order measurements

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

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

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

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

Number of Probes Used Prob. Correctly Decide Non-Shared Prob. Falsely Decide Non-Shared

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