We first talk about the motivation of this work.Then we introduce concept of virtual probe and virtual queuing delay.Based on these concepts, we define dominant congested links, and describe their properties.We use these properties to test whether a dominant congested link exists along an end-end network path.We then use simulation and internent experiment to validate our method.finally we to conclusion and future work.
3
Motivation
Dominant congested link (informally): link with “most” losses and significant delays on end-end path
Applicationso traffic engineeringo understand dynamics of network
Direct measurement of an individual link difficulto commercial reasonso existence of multiple ISPs along path
WW
due to commercial reasons, ISPs are not willing to disclose information regarding performance of their routers.And also, there are multiple isps along a network path.This leaves us no choice but to use end-end approach to identify whether dominant congested link exists along a network path
4
Virtual Probe, Virtual Queuing DelayVirtual Probe: infinitesimally small
packet: o does not disturb real traffic, never droppedo queuing delay due to queue occupancyo If queue full, mark as lost, experience
maximum queuing delay, go to next linkVirtual Queuing Delay: W
o End-end queuing delay of virtual probes with loss marks
Two important questions about Wo “Most” loss marks at one link?o “Major” part of W due to experiencing
maximum queuing delay?
WW
In order to do so, we introduce the following two concepts.When a virtual probe reaches a queue, it obtain queuing delay from the queuing occupancy, if it sees a full queue, it make a loss mark and obtain maximum queuing delay, and go on to the next link.
WW
Therefore we can regard the virtual queueing delay as would-be end-end queuing delay of lost packets.
WW
whether most losses coccur at one link?Whether major part of W are due to maximum queuing delay from where it get loss mark?
WW
We need to add motivation why we want to define these two concepts to connect from the previous slide to this slide.
5
Virtual Probe, Virtual Queuing Delay –cont.
+ +
+ +
6
Strongly Dominant Congested Link (SDCL)
Link k is a strongly dominant congested link in [t1,t2) iff for any virtual probe sent at any time t in [t1,t2) satisfies,o all losses occur only at link ko If experience max queuing delay on link k,
this max queuing delay is at least sum of queuing delays it experiences on other links
.1)|(
,1)|(
kki
it
kt
k
FtDDP
LtLtP
WW
the following two conditions.
WW
when this virtual probe experience maximum queueing delay on this link,
WW
If it experience maximum queuing delay on link k, this maximum queing delay is greater or equal to sum of its queuing delay on the other links.
WW
Based on the concept of virual probe, we now define strongly dominant congested link.
7
Weakly Dominant Congested Link (WDCL)
Link k is a weakly dominant congested link with parameter θ and in [t1, t2], iff a virtual probe sent at t satisfies
.1)|(
,1)|(
kki
it
kt
k
FtDDP
LtLtP
where 0 θ <0.5, 0 1,
WW
We generalize SDCL by introducing two parameters. Theta and phi.We relax the two conditions by using probabilites less than one.When theta = 0 and phi=0, WDCL is SDCL.
8
SDCL IllustrationQk
≥ +Qk
Qk Qk
Qk≤ ≤W
Qk: maximum queuing delayW: virtual queuing delay
WW
remember to mention loss can only occur on link k besides the delay requirement.
9
Property of SDCL
Hypothesis H0: A SDCL exists.Find D= min{w|FW(w) > 0},Check FW(2D). If FW(2D) < 1, reject. Otherwise, accept.
Example:
WW
From the previous slide, we know the virtual delay w are bounded between Qk and 2Qk as shown in this graph.We do not know qk, but we can observe D.
10
Property of WDCL
Hypothesis H0: A WDCL exists.Find D= min{w|FW(w) > θ},Check FW(2D). If FW(2D) < (1- θ)(1-φ), reject. Otherwise, accept.
Example:
11
An Example – Test of SDCL
H0 rejected
+ +=
>
+ +=D=
WW
We now see how the hypothesis tests work. We give an example of testing SDCL.
12
Inferring Virtual Queuing Delay Distribution FW(w)
Use virtual queuing delay distribution to test if DCL exist
Infer FW(w)o Linear Interpolationo Hidden Markov modelo Markov model with a hidden
dimension
WW
so far, we have already known how to test whether a DCL exists using virtual queuing delay distribution. The problem remains is how do get the virtual queuing delay distribution. The idea is to think observed dealys are governed by certain model and regard losses as unobserved delay and try to infer the delay distribution of the lost packets.It turns out the first two method is not accurate as the third one. Therefore, we will only discuss the third method - Markov model with a hidden dimension.
13
Markov Model with a Hidden Dimension
Model componentso State: (Xt, Yt), Yt: delay, Xt: hidden stateo N: # of hidden states o M: # of delay binso π(i,j): initial distributiono P(i,j)(k,l): transition matrixo s(j): P(loss|delay =j)
When N=1, a Markov model
WW
We use Markov model with a hidden dimension to model the end-end queuing delay of the network path of interest and regard losses as unobserved delay and use the model to infer the virtual delay distribution from end-end packet probes.We think (x,y) follows a markov model. That is delay with hidden states follows a two dimensional Markov model.The parameter that we are most interested in is s(j).
14
Packet Probes and Model Inference
One-way End-end Periodic probeso Delay Yt, t=1, 2, …, T.o Yt= * if probe t is lost
After algorithm convergeso s(j)=P(loss|delay=j), j=1,2, …, M.
15
Obtain Virtual Queuing Delay Distribution FW(w) from s(w)
Obtain virtual queuing delay distribution from model and trace
)(
)()(
)(
)()|(
)|(
lossP
wdelayPws
lossP
wdelayPwdelaylossP
losswdelayP
)(wfW
16
Evaluation
Ns simulationo Controlled environmento Global knowledgeo Validation of methodology
Internet experimento Applying methodology in “real world”o Probe duration needed to obtain
correct identification
WW
We use both ns simulation and internet experiments to validate our method.
WW
we check if the virual queuing distribution obtained from the end-end measurment agrees with the virtual queuing delay distribution obtained from monitoring every single router.
17
Simulation Setup
p1 p2 p3
WW
probe packets are sent from the left to the right.the loss rate of the three links in the middle are p1, p2 and p3 respectively.
18
Validation via Simulation
(p1,p2,p3)= (0, .002, .038)
D=4 FW(8) =1 > (1-.07)(1-.1)YES
WDCL(.07, .1)?
WW
In the first setting, we observe the loss prob. of the three links as (, , ).In the first setting, the loss prob. of the three links are We can see that the third link has loss prob. about 20 times larger than the second link. We want to see if our method can detect this.cdf of virtual queuing distribution.The black line is the virtual queuing distribution obtained by monitoring queue occupancy of each router.The red and blue lines are the virtual queuing delay distribution obtained from the end-end measurement. We use hidden state as 1 and 2, as we can see, all the three distributions are very close.From the graph, we can see that D=4.
19
Internet ExperimentsResidence House – USCLoss prob. = 0.04WDCL(.1,.1)?
D=1, FW(2D)<(1-.1)(1-.1)No
WW
We also conduct internet experiments, we use tcpdump to record the delay and loss sequence, also remove the clock skew caused by different clocks on both sides.
20
Conclusions and Future WorkExistence of DCLIntroduce virtual queuing delayModel-based approach from one-way
end-end measurementOnly minutes of probes neededFuture work
o Controlled test-bed experiments and more/richer Internet experiments
