The UNIVERSITY UNIVERSITY of of NORTH CAROLINA NORTH CAROLINA at at CHAPEL HILL CHAPEL HILL The Tomography with Available Bandwidth with Available Bandwidth Tomography Alok Shriram Shriram Jasleen Kaur Kaur Alok Jasleen Department of Computer Science Department of Computer Science University of North Carolina at Chapel Hill University of North Carolina at Chapel Hill http://www.cs.unc.edu/~jasleen/research www.cs.unc.edu/~jasleen/research/ / http:// 1 1
Network tomography tomography Network ! Idea: Use end Idea: Use end- -to to- -end probes to estimate state of internal links end probes to estimate state of internal links ! − Send simultaneous probes to destinations that share − Send simultaneous probes to destinations that share portions of their path portions of their path X − Study correlations in end − Study correlations in end- -to to- -end metrics end metrics loss XY = 1 – – (1 (1 - - loss loss XR )(1 - - loss loss RY ) loss XY = 1 XR )(1 RY ) loss XZ = 1 – – (1 (1 - - loss loss XR )(1 - - loss loss RZ ) loss XZ = 1 XR )(1 RZ ) R If loss loss XY = loss loss XZ = L, If XY = XZ = L, then loss RY = loss loss RZ = 0, then loss RY = RZ = 0, and loss XR = L and loss XR = L Y Z ! Past Past tomographic tomographic work done mostly with work done mostly with delay delay and and loss loss ! Focus: Available Bandwidth Focus: Available Bandwidth Focus: Available Bandwidth 2 2
Extending tomography tomography to A.B. to A.B. Extending AB XY AB XY = min(AB = min(AB XR XR , AB , AB RY RY ) ) X AB XZ = min(AB XR , AB RZ ) AB XZ = min(AB XR , AB RZ ) AB XR ≥ max( max(AB AB XY , AB XZ ) AB XY , AB XZ ) ⇒ ⇒ XR ≥ R AB RY AB ≥ AB AB XY RY ≥ XY AB RZ ≥ AB AB XZ AB RZ ≥ XZ Y Z Tomography with several sources and destinations may help with several sources and destinations may help Tomography Tomography with several sources and destinations may help identify multiple multiple bottlenecks on end bottlenecks on end- -to to- -end paths end paths identify identify multiple bottlenecks on end-to-end paths 3 3
Identifying bottleneck links Identifying bottleneck links Y W Bottleneck R Z X Bottleneck identification rules: Bottleneck identification rules: ! Rule 1 ! R Rule 1: For each path, R : For each path, ! ! Links with the least A.B. are potential bottlenecks Links with the least A.B. are potential bottlenecks − − Could lead to false positives Could lead to false positives ! Rule 2 Rule 2: For every pair of 2 paths with : For every pair of 2 paths with equal equal end end- -to to- -end A.B. end A.B. ! Non- -shared links are non shared links are non- -bottlenecks bottlenecks Non − − Could lead to false negatives Could lead to false negatives 4 4
Challenge 1: probing tool inconsistency Challenge 1: probing tool inconsistency Y W Bottleneck R Z X Tool inconsistency limits the ability to Tool inconsistency limits the ability to Tool inconsistency limits the ability to distinguish between bottleneck links distinguish between bottleneck links distinguish between bottleneck links Inconsistency of the probing tool Inconsistency of the probing tool 5 5
Challenge 2: probe scheduling Challenge 2: probe scheduling X R Y Z ! Requirements: Requirements: ! − Paths that share links should − Paths that share links should not not be probed concurrently be probed concurrently − Paths that share links should be probed concurrently − Paths that share links should be probed concurrently ! Solution: Solution: ! − Schedule link − Schedule link- -sharing probes in separate steps sharing probes in separate steps − Minimize the total number of steps used − Minimize the total number of steps used This scheduling problem is NP- This scheduling problem is NP -hard! hard! This scheduling problem is NP-hard! 6 6
Challenge 3: limit on topology Challenge 3: limit on topology Available bandwidth dynamics Available bandwidth dynamics Tool run- -time limits the time limits the Tool run Tool run-time limits the number of participating end- number of participating end -nodes nodes number of participating end-nodes 7 7
Hurdles in identifying bottleneck links Hurdles in identifying bottleneck links ! Tool inaccuracy Tool inaccuracy ! − Limits the accuracy of detecting bottlenecks − Limits the accuracy of detecting bottlenecks ! Tool run Tool run- -time and dynamics of available bandwidth time and dynamics of available bandwidth ! − Limit the number of participating end − Limit the number of participating end- -nodes nodes − Limit the reduction in false positives − Limit the reduction in false positives PlanetLab measurements with measurements with Pathload Pathload: ~ 4 end : ~ 4 end- -nodes nodes PlanetLab PlanetLab measurements with Pathload: ~ 4 end-nodes 8 8
PlanetLab tomography tomography results results PlanetLab Rule 1 & 2 Rule 1 Rule 1 & 2 Rule 1 2500 3500 3000 2000 2500 1500 2000 1500 1000 1000 500 500 0 0 0 1 2 3 4 5 1 2 3 4 5 6 7 Number of bottlenecks per path Distance of bottlenecks from source Number of bottlenecks per path Distance of bottlenecks from source ! Results from 4 sets of 4 Results from 4 sets of 4- -node node PlanetLab PlanetLab topologies used topologies used ! − At least 1 bottleneck discovered on half the paths − At least 1 bottleneck discovered on half the paths − No more than 3 bottlenecks listed for most paths − No more than 3 bottlenecks listed for most paths − Most bottlenecks lie at 2 − Most bottlenecks lie at 2- -3 hops from the source 3 hops from the source 9 9
Wish- -list for a probing tool list for a probing tool Wish ! High accuracy and consistency High accuracy and consistency ! − Within 1 Mbps? − Within 1 Mbps? ! High speed High speed ! − Within 1 sec? − Within 1 sec? ! Non Non- -interference interference ! − With cross − With cross- -traffic traffic − With concurrent probing tools? − With concurrent probing tools? 10 10
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