27th, Nov 2001 GLOBECOM2001 1 /16 Analysis of Dynamic Behaviors of Many TCP Connections Sharing...

27th, Nov 200127th, Nov 2001 GLOBECOM2001GLOBECOM2001 11/16/16

Analysis of Dynamic Analysis of Dynamic Behaviors ofBehaviors ofMany TCP ConnectionsMany TCP ConnectionsSharing Tail-Drop / RED Sharing Tail-Drop / RED RoutersRouters

Go HasegawaGo HasegawaOsaka University, JapanOsaka University, [email protected]@cmc.osaka-u.ac.jp

GLOBECOM2001GLOBECOM2001 22/16/16 27th, Nov 200127th, Nov 2001

BackgroundsBackgrounds

TCP TCP (Transmission Control (Transmission Control Algorithm)Algorithm)Majority in the current Internet, Majority in the current Internet,

also in the futurealso in the future Analytic investigation is Analytic investigation is

necessarynecessary 　　 to understand its to understand its characteristicscharacteristics


Past researches on TCP Past researches on TCP throughput analysisthroughput analysis

Long-term average throughputLong-term average throughputShort-term throughput is important for short fiShort-term throughput is important for short fi

le transferle transfer Assume constant packet loss ratioAssume constant packet loss ratio

Packet loss ratio changes dynamically due to Packet loss ratio changes dynamically due to bursty packet loss bursty packet loss

Assume RED works fine at the routerAssume RED works fine at the routerBad parameter setting degrades RED performBad parameter setting degrades RED perform

ance, causing bursty packet lossance, causing bursty packet loss


ObjectivesObjectives

Analysis of Analysis of window size distributionwindow size distribution of TCP conne of TCP connectionsctions Using simple Using simple Markov modelingMarkov modeling of TCP behavior of TCP behavior Many TCP connections accommodatedMany TCP connections accommodated TD (Tail-Drop) and RED (Random Early Detection)TD (Tail-Drop) and RED (Random Early Detection) Effect of Effect of bursty packet lossbursty packet loss

Evaluation of TD/RED routers in terms of …Evaluation of TD/RED routers in terms of … Short-term fairnessShort-term fairness among TCP connections among TCP connections Effect of Effect of poor parameter set of REDpoor parameter set of RED Effect of TD buffer sizeEffect of TD buffer size


Network modelNetwork model

NN sender hosts transmit packets to sender hosts transmit packets to receiver host by TCP Renoreceiver host by TCP Reno

Two packet dropping disciplines at rTwo packet dropping disciplines at routerouter TD (Tail Drop)TD (Tail Drop) RED (Random Early Detection)RED (Random Early Detection)

Focus on changes of window size, aFocus on changes of window size, and ssthresh value of TCP connectionnd ssthresh value of TCP connection

Sender Host 1Sender Host 1

Sender Host 2Sender Host 2

Sender Host Sender Host NN

Receiver HostReceiver Host

TD/RED Router Buffer Size:TD/RED Router Buffer Size:B packetsB packets


Markov modeling of TCP Markov modeling of TCP behaviorbehavior State is a State is a combination of window size and ssthrecombination of window size and ssthre

shsh values of a TCP connection values of a TCP connection ((wwi i , t, ti i ))

State transition occurs at every RTTState transition occurs at every RTT cwndcwnd increasesincreases when no packet loss occurs when no packet loss occurs cwndcwnd and and ssthssth decreasedecrease when packet loss occurs when packet loss occurs

State transition probabilities are dependent on…State transition probabilities are dependent on… Packet loss probabilityPacket loss probability at the router buffer at the router buffer Slow start, congestion avoidanceSlow start, congestion avoidance algorithms of TCP algorithms of TCP


Increasing window sizeIncreasing window size

When no packet loss occursWhen no packet loss occursProbability: (Probability: (1 – 1 – pp))wwii

State transition fromState transition from ((wwi i , t, tii )) to … to … ((2w2wi i , t, tii))

When When wwii < (1/2)t < (1/2)tii ((Slow Start PhaseSlow Start Phase)) ((tti i , t, tii))

When When (1/2)t(1/2)tii < w < wii < t < tii ((Phase ShiftPhase Shift)) ((wwii+1, t+1, tii))

When When ttii < w < wii ((Congestion Avoidance PhaseCongestion Avoidance Phase))


Decreasing window sizeDecreasing window size

When packet loss occursWhen packet loss occurs Probability: Probability: 1- 1- ((1 - 1 - pp))wwii

State transition fromState transition from ((wwi i , t, tii )) to … to … ((1, w1, wi i /2/2))

When When timeouttimeout occurs occurs ((wwi i /2, w/2, wi i /2/2))

When When fast retransmitfast retransmit occurs occurs

Probability of timeoutProbability of timeout Dependent on Dependent on wwii and number of lost packets in a windand number of lost packets in a wind

owow


Packet loss probability: Packet loss probability: pp

Past researches assume Past researches assume pp is constant is constant Actually dependent on…Actually dependent on…

Router buffer size: Router buffer size: BBWindow size: Window size: wwii

Packet discarding disciplinePacket discarding discipline TD (Tail Drop),TD (Tail Drop), RED (Random Early Detection)RED (Random Early Detection)


Tail-drop routerTail-drop router

Bursty packet lossBursty packet loss occurs when the router occurs when the router buffer overflowsbuffer overflows

To calculate To calculate pp, we have derived …, we have derived …ppoverflowoverflow :: frequency of buffer overflowfrequency of buffer overflowLLoverflow overflow : # of lost packets in each buffer overflo: # of lost packets in each buffer overflo

wwLLi i : # of lost packets for each TCP connection i: # of lost packets for each TCP connection i

n each buffer overflown each buffer overflow pp = min(1, p = min(1, poverflowoverflow ・・ LLi i /w/wi i ))


Tail-drop router Tail-drop router (2)(2)

ppoverflowoverflow :: frequency of buffer overflowfrequency of buffer overflow Considering Considering queue dynamicsqueue dynamics 1/(N(W1/(N(Wf f – Nw’)– Nw’)

LLoverflow overflow : # of lost packets in each buffer overflow: # of lost packets in each buffer overflow Each TCP connection increases its window size by 1 pEach TCP connection increases its window size by 1 p

acket at every RTTacket at every RTT N packets are lost in totalN packets are lost in total

LLii : # of lost packets for each TCP connection in e: # of lost packets for each TCP connection in each buffer overflowach buffer overflow Proportional to window sizeProportional to window size of each TCP connection of each TCP connection


RED routerRED router

Packet discarding probability is Packet discarding probability is determined from determined from average queue average queue lengthlength

For applying to our model, we use For applying to our model, we use instantaneous queue lengthinstantaneous queue length;;

qmaxq

maxqmaxq

maxqminminmax

maxqminq

qp

ththp

thththth

th

th

red

if)(

if

if0

)(


RED router RED router (2)(2)

qq: queue length: queue lengthAssume that other TCP connections are in steAssume that other TCP connections are in ste

ady state, and queue length is affected only by ady state, and queue length is affected only by wwi i

q = ((N-1)/N)w* + wq = ((N-1)/N)w* + w i i – 2– 2

pp = p = pred red (q)(q)


Accuracy of AnalysisAccuracy of Analysis

1e-005

0.0001

0.001

0.01

0.1

1

0 10 20 30

Pro

bab

ilit

y D

en

sit

y F

un

cti

on

Window Size

TD: Simulation

TD: AnalysisRED: Analysis

RED: Simulation

1e-005

0.0001

0.001

0.01

0.1

1

0 10 20 30Window Size

TD: Simulation

TD: Analysis

RED: Analysis

RED: Simulation

B=8000 [packets] B=3000 [packets]

N=1000, BW=1.5 Mbps, N=1000, BW=1.5 Mbps, =2 msec=2 msec


Fairness evaluationFairness evaluation

Fairness of TD is Fairness of TD is much affected by much affected by buffer sizebuffer size

Variation of window Variation of window size of RED is small, size of RED is small, regardless of buffer regardless of buffer sizesize

RED can provide RED can provide better fairness in better fairness in short-term TCP short-term TCP throughputthroughput

0

10

20

30

40

50

60

70

80

200 300 400 500 600 700 800 900

Win

do

w S

ize

[pac

kets

]

Buffer Size / maxth [packets]

TD 99.9999%

TD 99.99%

RED 99.9999%

RED 99.99%


ConclusionConclusion

Analysis of window size Analysis of window size distribution of TCP connectionsdistribution of TCP connectionsTD/RED disciplinesTD/RED disciplinesBurst packet lossBurst packet loss

Fairness evaluation of TD/RED Fairness evaluation of TD/RED routerrouterRED can give short-term fairness RED can give short-term fairness

among connectionsamong connections


RED RED routerrouter

Probability is changed according to Probability is changed according to average queue lengthaverage queue length

Avoid buffer overflow, keep queue Avoid buffer overflow, keep queue length lowlength low

maxmaxththminminthth

１１

maxmaxpp

00

2020

4040

6060

8080

100100 105105 110110 115115 120120

Queue LengthQueue Length

Average Queue LengthAverage Queue Length

maxmaxthth

minminthth

Queue Length [packets]Queue Length [packets]

Time [sec]Time [sec]Average Queue Length [packets]Average Queue Length [packets]

Packet Discarding ProbabilityPacket Discarding Probability

27th, Nov 2001 GLOBECOM2001 1 /16 Analysis of Dynamic Behaviors of Many TCP Connections Sharing...

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