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1 Model-based Identification of Dominant Congested Links Wei Wei, Bing Wang, Don Towsley, Jim Kurose {weiwei, bing, towsley,

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2 Outline Motivation Virtual probe, virtual queuing delay Dominant congested links Identifying dominant congested links Validation Conclusions, future work

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3 Motivation Dominant congested link (informally): link with most losses and significant delays on end-end path Applications otraffic engineering ounderstand dynamics of network Direct measurement of an individual link difficult ocommercial reasons oexistence of multiple ISPs along path

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4 Virtual Probe, Virtual Queuing Delay Virtual Probe: infinitesimally small packet: odoes not disturb real traffic, never dropped oqueuing delay due to queue occupancy oIf queue full, mark as lost, experience maximum queuing delay, go to next link Virtual Queuing Delay: W oEnd-end queuing delay of virtual probes with loss marks Two important questions about W oMost loss marks at one link? oMajor part of W due to experiencing maximum queuing delay?

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5 Virtual Probe, Virtual Queuing Delay –cont

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6 Strongly Dominant Congested Link (SDCL) Link k is a strongly dominant congested link in [t 1,t 2 ) iff for any virtual probe sent at any time t in [t 1,t 2 ) satisfies, oall losses occur only at link k oIf experience max queuing delay on link k, this max queuing delay is at least sum of queuing delays it experiences on other links

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7 Weakly Dominant Congested Link (WDCL) Link k is a weakly dominant congested link with parameter θ and in [t 1, t 2 ], iff a virtual probe sent at t satisfies where 0 θ <0.5, 0 1,

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8 SDCL Illustration QkQk + QkQk QkQk QkQk QkQk W Q k : maximum queuing delay W: virtual queuing delay

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9 Property of SDCL Hypothesis H 0 : A SDCL exists. Find D= min{w|F W (w) > 0},Check F W (2D). If F W (2D) < 1, reject. Otherwise, accept. Example:

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10 Property of WDCL Hypothesis H 0 : A WDCL exists. Find D= min{w|F W (w) > θ},Check F W (2D). If F W (2D) < (1- θ)(1-φ), reject. Otherwise, accept. Example:

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11 An Example – Test of SDCL H 0 rejected ++ = > + + = D=

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12 Inferring Virtual Queuing Delay Distribution F W (w) Use virtual queuing delay distribution to test if DCL exist Infer F W (w) oLinear Interpolation oHidden Markov model oMarkov model with a hidden dimension

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13 Markov Model with a Hidden Dimension Model components oState: (X t, Y t ), Y t : delay, X t : hidden state oN: # of hidden states oM: # of delay bins oπ(i,j): initial distribution oP (i,j)(k,l) : transition matrix os(j): P(loss|delay =j) When N=1, a Markov model

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14 Packet Probes and Model Inference One-way End-end Periodic probes oDelay Y t, t=1, 2, …, T. oY t = * if probe t is lost Parameter inference algorithm oForward-backward inference oIterative approach After algorithm converges os(j)=P(loss|delay=j), j=1,2, …, M.

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15 Obtain Virtual Queuing Delay Distribution F W (w) from s(w) Obtain virtual queuing delay distribution from model and trace

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16 Evaluation Ns simulation oControlled environment oGlobal knowledge oValidation of methodology Internet experiment oApplying methodology in real world oProbe duration needed to obtain correct identification

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17 Simulation Setup p1p1 p2p2 p3p3

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18 Validation via Simulation (p1,p2,p3)= (0,.002,.038) D=4 F W (8) =1 > (1-.07)(1-.1) YES WDCL(.07,.1)?

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19 Internet Experiments Residence House – USC Loss prob. = 0.04 WDCL(.1,.1)? D=1, F W (2D)<(1-.1)(1-.1) No

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20 Conclusions and Future Work Existence of DCL Introduce virtual queuing delay Model-based approach from one-way end-end measurement Only minutes of probes needed Future work oControlled test-bed experiments and more/richer Internet experiments oScenarios where wireless network is present

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21 Thank you!

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