Measurement

2.2 F AST algorithm and its stability

3.1.1 Burstiness in the paket loss proess

3.1.1.1 Measurement

Generalburstinessinthepaketlossproessesisalsowell-doumented[31,41,42℄.

However, in our assumption, we further laim that the loss proess is bursty in sub-

RTT timesale. We support this assumption with evidene from our measurements

in NS-2simulation,Dummynet emulation,and PlanetLab.

Based on these two assumptions, we model the loss synhronization rate as the

detetion probabilityusing one on-oproess (TCP data pakets) tosampleanother

on-oproess (paketloss proess).

Our model predits that the ombination of bursty TCP ows and a drop-tail

router(bursty lossproess)yieldsverylowanduniform synhronizationratesamong

TCP ows with dierent ongestion window sizes and leads topoor fairness onver-

gene. Our model also suggests that the use of paing at the TCP soures and/or

the use of random dropping algorithms in the link (e.g. RED [31℄) an inrease

synhronization rate.

lost pakets, alled the lossinterval, and analyzed the loss proesses by plotting the

umulative distribution funtion (CDF) and the probability density funtion (PDF)

of thelossintervals. Weompared thePDF ofthe paketlossproessestothe orre-

sponding Poisson proesses with the same average event arrival rates. We observed

that the paketloss proesses are muh burstierthan the Poisson proesses.

The measurements from NS-2, Dummynet, and the Internet all suggest that the

sub-RTT paket lossproess isvery bursty.

Results in NS-2 Simulation Figure 3.1 shows the CDF of the loss interval in

NS-2 simulations. The RTTs of the ows insimulation are random between 2ms to

200ms. From the gure, we observed that 80% of the paket losses luster within

short time periods smallerthan 1% of the RTT.

We alsoplotted the PDF of the loss intervaland ompared it with the PDF of a

Poisson proess with the same arrival rate, asshown in Figure3.1 (B) .

Figure 3.1 (C) zooms in to a small time sale of 0 to 2 RTT and uses log-sale

in the Y-axle so that the Poisson proess has a straight line in its PDF. Compared

to the Poisson proess, the loss proess is muh burstier more than 10 times the

paket losses ourred inthe very smalltime interval.

Results in Emulation Network Figure 3.2 is the CDF of the loss interval in

Dummynet emulations. The RTTs of the ows are xed to 4 lasses: 2ms, 10ms,

50ms,and 200ms. The lossintervalCDF shows asimilarpatterntotheNS-2results,

exept that the CDF starts from 0.1% of RTT due to the limited time resolution of

our measurements inthe Dummynet router.

Figure3.2 (B) and (C)showthe PDF ofthe lossinterval. Again, the lossproess

is muhburstier than the orresponding Poisson proess.

Results in the Internet Figure 3.3is the CDF with the Internet measurement.

TheInternetmeasurementshowslessburstinessinlossproessesthanweobserved

10 ⁻⁶ 10 ⁻⁴ 10 ⁻² 10 ⁰ 10 ² 10 ⁴ 0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Loss Interval (RTT)

CDF

Measured

(A)CDF

0 2 4 6 8 10

10 ⁻⁶ 10 ⁻⁵ 10 ⁻⁴ 10 ⁻³ 10 ⁻² 10 ⁻¹ 10 ⁰

Loss Interval (RTT)

PDF

Measured Poisson

(B) PDF (Binsize 0.1RTT)

0 0.5 1 1.5 2

10 ⁻⁶ 10 ⁻⁵ 10 ⁻⁴ 10 ⁻³ 10 ⁻² 10 ⁻¹ 10 ⁰

Loss Interval (RTT)

PDF

Measured Poisson

(C) PDFEnlarged (Binsize 0.02 RTT)

Figure3.1: Loss intervalsin NS-2measurements.

Note that all the CDF gures in this hapter have X-axles in log-sale, and all the

PDF guresin this thesis haveY-axles inlog-sale.

10 ⁻⁶ 10 ⁻⁴ 10 ⁻² 10 ⁰ 10 ² 10 ⁴ 0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Loss Interval (RTT)

CDF

Measured

(A)CDF

0 2 4 6 8 10

10 ⁻⁶ 10 ⁻⁵ 10 ⁻⁴ 10 ⁻³ 10 ⁻² 10 ⁻¹ 10 ⁰

Loss Interval (RTT)

PDF

Measured Poisson

(B) PDF (Binsize 0.1RTT)

0 0.5 1 1.5 2

10 ⁻⁶ 10 ⁻⁵ 10 ⁻⁴ 10 ⁻³ 10 ⁻² 10 ⁻¹ 10 ⁰

Loss Interval (RTT)

PDF

Measured Poisson

(C) PDFEnlarged (Binsize 0.02 RTT)

Figure3.2: Loss intervals inDummynet measurements.

10 ⁻⁶ 10 ⁻⁴ 10 ⁻² 10 ⁰ 10 ² 10 ⁴ 0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Loss Interval (RTT)

CDF

Measured

(A)CDF

0 2 4 6 8 10

10 ⁻⁶ 10 ⁻⁵ 10 ⁻⁴ 10 ⁻³ 10 ⁻² 10 ⁻¹ 10 ⁰

Loss Interval (RTT)

PDF

Measured Poisson

(B) PDF (Binsize 0.1RTT)

0 0.5 1 1.5 2

10 ⁻⁶ 10 ⁻⁵ 10 ⁻⁴ 10 ⁻³ 10 ⁻² 10 ⁻¹ 10 ⁰

Loss Interval (RTT)

PDF

Measured Poisson

(C) Loss intervalsin PlanetLabmeasurements (Bin size 0.02 RTT)

Figure 3.3: Loss intervals inPlanetLab measurements.

ofappliationtypes, trapatterns,and queuingdelay. Insuhanextremelyhetero-

geneous environment,we observed that 60% of the paket losses lusterwithin short

timeperiodsof1RTT,and40%ofthepaketlosseslusterwithintimeperiodsof1%

of RTT. This evideneis stillvery strongfor sub-RTT burstiness inlossproesses.

Weplottedthe PDFin Figure3.3(B)(C) andompared the Internet lossproess

againsta Poisson proess with the same arrival rate. We observed similar burstiness

as in NS-2 and Dummynet. In the smallest interval region (left side), the measured

lossproess isfar burstierthan the Poisson proess.

3.1.1.2 Possible Soures of sub-RTT Burstiness

As shown by the results of the NS-2 simulations, Dummynet emulations and the

Internet measurements,paketlossishighlybursty insub-RTTtimesale. There are

several possible souresthat lead to suhburstiness.

DropTailroutersare onsideredthe major soureofpaket lossburstiness [31℄. A

DropTailrouter serves asa FIFOqueue, aepting inomingpakets untilthe buer

isfull. Working withDropTailrouters,loss-based ongestionontrolalgorithmskeep

inreasingthe datarate whenthe router'sbuerisnot full. Whenthe router'sbuer

is full and pakets are dropped, the aggregate data rate is higher than the router's

apaity and paket loss persists until the loss-based ongestion ontrol algorithms

detet the loss of pakets and redue the data rate, usually one half of an RTT

later. In between the rst paket loss and the redution of data rate, there is a

peak of paket losses in the DropTail router. Some researhers propose introduing

randomness in the router. For example, Floyd and Jaobson proposed to randomly

dropthe pakets earlierbeforethe buerisoverowed [31℄. However, theseproposals

suer from diultparameter settings problems.

Slow start of TCP ows is another soure of paket lossburstiness. A TCP ow

starts with averysmallrate inburst (sending two pakets bak-to-bak every round

trip), and doubles its data rate if no loss is observed. This proess an quikly

inrease the queuesize inthe bottlenek buer injustafewround tripsand produe

burst period of Flow i

burst period of loss signal randomly drop from M

incoming packets Legend:

a dropped packet a packet

from flow i

i i

i i i i

i i i i i

S incoming packets during the RTT of loss event

i

a packet (from any flow)

spanning over K incoming packets

Figure3.4: Congestiondetetionwithinone RTT:aowuses itsdatapaketproess

to samplethe lossproess. The loss synhronization rate is the probabilitythat one

of the

w i

^{pakets fromow}

i

(distributed overKpakets) happens tobeone ofthe L dropped pakets (distributed over M pakets).

algorithms, suh as QuikStart [46℄ and RCP [47℄ have been proposed to avoidsuh

aggressivedetetion. Thesealgorithmsrequirehangesindatapaketformats, whih

are expensive for the existing infrastruture.

Hene, thesoures ofsub-RTTburstiness inpaketlossproesseswillexistinthe

foreseeable future.