A Survey on Physical Network Topology Estimation

1. A Survey on Physical Network Topology Estimation October 21, 2005 Chikayama-Taura Lab. Tatsuya Shirai

2. Background • Progress of parallel processing technologies • Costs of parallel processing • Cost of computation • Cost of communication • Clusters, Grid Environments • Cost of communication becomes bigger with larger scale

3. Allocation Policy • Needs toclosely allocate hosts frequently communicating with each other • With multiple clusters, allocate within clusters • In single cluster, allocate to use the same switches

4. 1 3 2 4 Difficulty of estimate the cost of communication • Shared link • Each hosts can solely communicate at 100Mbps • But all hosts can communicate at less than 50Mbps at a time • All hosts need to work together to know this relation 100Mbps

5. Desired Functions • Ideally, • Present network information to users • Configure allocation automatically • Needs to analyze networktopology

6. Other applications • Network trouble shooting • Discovery of bottlenecks • Research on routing protocol • Simplification of local network • etc…

7. Agenda • Background • Network Topology • End-to-End Measurement • Researches • Conclusion

8. Agenda • Background • Network Topology • End-to-End Measurement • Researches • Conclusion

9. Network Topology • A structure of a network • node • host • router • switch, hub • link

10. IP Layer Topology • Structure of network • node • host • router • switch, hub • Link • Difficulty in collecting information of LAN structure

11. Protocol-Based Algorithms • Protocol • SNMP [Yuri et al, ’01], Customized Protocol [Richard et al, ‘04] , etc. • Hardware-dependent • Some hubs or switches doesn’t support requiredprotocols. • Deterministic estimation

12. End-to-End Measurement • Metric • Packet loss rates [Bestavros et al, ‘02] Delays [Coates et al, ‘01] • Hardware independent • Always possible to measure topologies of hosts who can communicate with root • Probabilistic

13. Classification

14. Agenda • Background • Network Topology • End-to-End Measurement • Researches • Conclusion

15. End-to-End Measurement • Assume topologies are Tree-structured • Only one route exists between two hosts. • Does not be changed while measuring • Estimate branches of routes connecting hosts

16. unused non-branching branching Estimated topology using End-to-End Measurement actual topology estimated topology

17. End-to-End Measurement • Assume topologies are Tree-structured • Only one route exists between two hosts. • Does not be changed while measuring • Estimate branches of routes connecting hosts • Variance in the measurements

18. Variance of measurements • With a small variance, estimation is deterministic • With a large variance, estimation is probabilistic • Use statistics • Search thetopology that fits the most with measurement

19. End-to-End Measurement • Assume topologies are Tree-structured • Only one route exists between two hosts. • Does not be changed while measuring • Estimate branches of routes connecting hosts • Variance in the measurements • Procedures consist of 2 steps 1. Measurement 2. Estimation

20. Agenda • Background • Network Topology • End-to-End Measurement • Researches • Conclusion

21. Researches • Maximum Likelihood Network Topology Identification from edge-based unicast measurements [Coates et al. ’01 SIGMETRICS] • Metric : Delay • Estimation: Maximum Likelihood Estimation

22. Measurement –Sandwich Probe – 1 • Measure delay of a link shared 2 hosts (e.g. 2 and 4) 1. Send a small packet to 4 2. After constant time, send a large packet to 2 3. Without break, send a small packet to 4 again d 3 4 2 d+⊿d

23. X32 Measurement 1 • The arrival of the second packet is delayed because the large packet is slower • Assume that all branched nodes are not store & forward • Can measure delay (or bandwidth) of shared link X42 = μ1+d X32= μ1+μ2+d d μ1 μ2 3 4 2 X42

24. Estimation • Assume delay of each shared link obeys Gaussian f(x) • Search thetopology best fitting the measurements ⇒Maximum Likelihood Estimation (MLE)

25. 1 2 3 4 Likelihood • The value of “fitting” • Set particular topology and delay as a parameter • Likelihood = Π f(Xij) μ1 X42= μ1 X32= μ1+μ2 μ1 μ1

26. Search Space of MLE • Give many possible topologies to search for MLE • Too wide to compute all topologies • Premise • Similar topologies have similar likelihoods ⇒ Markov Chain Monte Carlo (MCMC) (e.g. Hill Climbing)

27. Similar Topologies –Step– • Birth step • Insert a node • Death step • Delete a node 1 1 1 1 3 4 2 3 4 2 3 4 2 3 4 2

28. Procedure of MLE 1. Give a topology at random 2. Make a small modification 3. If the new topology has greater likelihood, adopt new topology 4. If a likelihoodis at local maximum, return to procedure 1 5. Otherwise goto2 • Can get a great likelihood topology in feasible time

29. Experiment • Experimental Setup • The root host and ten other hosts • Measurement • Sent 8600 probes (O(n )) • For 8 minutes • MLE • For 30-120 seconds 2

30. The estimated topology using traceroute The estimated topology using Coates’ method

31. Agenda • Background • Network Topology • End-to-End Measurement • Researches • Conclusion

32. Conclusion • Conclusion • I Indicated importance of topology estimation and introduced one methods with End-to-End measurement • Future Works • Topology Estimation within LAN of many nodes