1. 2005/10/211 A Survey on Physical Network Topology Estimation October 21, 2005 Chikayama-Taura Lab. Tatsuya Shirai

2. 2005/10/212 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. 2005/10/213 Allocation Policy Needs to closely allocate hosts frequently communicating with each other With multiple clusters, allocate within clusters In single cluster, allocate to use the same switches

4. 2005/10/214 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 1 2 3 4 100Mbps

5. 2005/10/215 Desired Functions Ideally, Present network information to users Configure allocation automatically Needs to analyze network topology

6. 2005/10/216 Other applications Network trouble shooting Discovery of bottlenecks Research on routing protocol Simplification of local network etc …

7. 2005/10/217 Agenda Background Network Topology End-to-End Measurement Researches Conclusion

8. 2005/10/218 Agenda Background Network Topology End-to-End Measurement Researches Conclusion

9. 2005/10/219 Network Topology A structure of a network node host router switch, hub link

10. 2005/10/2110 IP Layer Topology Structure of network node host router switch, hub Link Difficulty in collecting information of LAN structure

11. 2005/10/2111 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 required protocols. Deterministic estimation

12. 2005/10/2112 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. 2005/10/2113 Classification IP layerProtocol based End-to-End Measurement NodesHosts, routers Hosts, routers, switches Hosts, routers, switches, hubs, … Hardware dependency dependent independent EstimationDeterministic Probabilistic

14. 2005/10/2114 Agenda Background Network Topology End-to-End Measurement Researches Conclusion

15. 2005/10/2115 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. 2005/10/2116 Estimated topology using End-to-End Measurement non-branching unused branching actual topology estimated topology

17. 2005/10/2117 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. 2005/10/2118 Variance of measurements With a small variance, estimation is deterministic With a large variance, estimation is probabilistic Use statistics Search the topology that fits the most with measurement

19. 2005/10/2119 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. 2005/10/2120 Agenda Background Network Topology End-to-End Measurement Researches Conclusion

21. 2005/10/2121 Researches Maximum Likelihood Network Topology Identification from edge-based unicast measurements [Coates et al. ’ 01 SIGMETRICS] Metric : Delay Estimation: Maximum Likelihood Estimation

22. 2005/10/2122 Measurement – Sandwich Probe – 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 1 2 34 d d+ ⊿ d

23. 2005/10/2123 Measurement X 42 X 32 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 X 42 = μ 1 +d X 32 = μ 1 +μ 2 +d μ1μ1 μ2μ2 1 2 34 d

24. 2005/10/2124 Estimation Assume delay of each shared link obeys Gaussian f(x) Search the topology best fitting the measurements ⇒ Maximum Likelihood Estimation (MLE)

25. 2005/10/2125 Likelihood 1234 The value of “ fitting ” Set particular topology and delay as a parameter Likelihood = Π f(X ij ) μ1μ1 μ1μ1 X 32 = μ 1 +μ 2 μ1μ1 X 42 = μ 1

26. 2005/10/2126 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. 2005/10/2127 Similar Topologies – Step – Birth step Insert a node 1 2 34 1 2 34 1 2 34 1 2 34 Death step Delete a node

28. 2005/10/2128 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 likelihood is at local maximum, return to procedure 1 5. Otherwise goto2 Can get a great likelihood topology in feasible time

29. 2005/10/2129 2 Experiment Experimental Setup The root host and ten other hosts Measurement Sent 8600 probes (O(n )) For 8 minutes MLE For 30-120 seconds

30. 2005/10/2130 The estimated topology using traceroute The estimated topology using Coates ’ method

31. 2005/10/2131 Agenda Background Network Topology End-to-End Measurement Researches Conclusion

32. 2005/10/2132 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

33. 2005/10/2133 Information of Network Network Tomography Topology (construction of Network) Bandwidth, Packet loss rate, Shared link … Analysis of the topology is the first step to estimating characteristics of a network

34. 2005/10/2134 Researches Maximum Likelihood Network Topology Identification from edge-based unicast measurements [Coates et al. ’ 01 SIGMETRICS] Metric : Delay Estimation: Maximum Likelihood Estimation Multicast Topology Inference from End-to- End Measurements [Duffield et al. ’ 02 IEEE Trans] Metric : Packet loss Estimation: Maximum Likelihood Estimation

35. 2005/10/2135 Coates ’ Method Policy Measure delay of links shared by each pair of hosts Compute likelihood of many topologies and link delay Pick up the topology with the maximum likelihood

36. 2005/10/2136 まとめ – 測定方法 – プロトコル を利用 End-to-End 測定を利用 手法 SNMP, Unique Packet loss delay ハードウェ ア依存 依存する依存しない 正確さ正確推定による

37. 2005/10/2137 Sandwitch Probing

38. 2005/10/2138 Shared Link 1 2 3 4 1 2 3 4

39. 2005/10/2139 Similar Topologies – Step – 1234 Methods to update topologies Birth step Death step μ-step μaμa μcμc μdμd μeμe

40. 2005/10/2140 Death step Delete a node (reverse of Birth step) 1 2 34 μaμa 1 2 34 μaμa μbμb μcμc μdμd μ b +μ c μ b +μ d

41. 2005/10/2141 μ-step Change a delay value of a link 1234 μaμa μbμb 1234 μbμb μa’μa’

42. 2005/10/2142 Birth step Insert a node 1 2 34 μaμa μbμb 1 2 34 μaμa μdμd μcμc μ c -μ b μ d -μ b

43. 2005/10/2143 Death step Delete a node (reverse of Birth step) 1 2 34 μaμa 1 2 34 μaμa μbμb μcμc μdμd μ b +μ c μ b +μ d

44. 2005/10/2144 μ-step Change a delay value of a link 1234 μaμa μbμb 1234 μbμb μa’μa’

45. 2005/10/2145 1 2 3 4 d d+ ⊿ d

46. 2005/10/2146 1 2 3 L2L2 L3L3 L 23 40ms

47. 2005/10/2147 The actual topology The estimated topology