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

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

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

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?

5 Virtual Probe, Virtual Queuing Delay –cont

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

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,

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

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:

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:

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

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

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

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.

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

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

17 Simulation Setup p1p1 p2p2 p3p3

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

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

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

21 Thank you!