1

Analysis of a window-based flow Analysis of a window-based flow control mechanism based on TCP control mechanism based on TCP

Vegas Vegas in heterogeneous network in heterogeneous network

environmentenvironment

Hiroyuki OhsakiHiroyuki OhsakiCybermedia Center, Osaka University, JapanCybermedia Center, Osaka University, Japan

oosaki@cmc.osaka-u.ac.jpoosaki@cmc.osaka-u.ac.jp

2

ContentsContents

IntroductionIntroduction Analytic modelAnalytic model

Window-based flow control based on TCP VegasWindow-based flow control based on TCP Vegas Heterogeneous networkHeterogeneous network

Analysis of throughput and fairnessAnalysis of throughput and fairness Analysis of stability and transient behaviorAnalysis of stability and transient behavior Numerical examplesNumerical examples

Two bottleneck links with 30 TCP connectionsTwo bottleneck links with 30 TCP connections ConclusionConclusion

3

TCP (Transmission Control Protocol)TCP (Transmission Control Protocol)

Packet retransmission mechanismPacket retransmission mechanism Retransmit lost packets in the network Retransmit lost packets in the network

Congestion avoidance mechanismCongestion avoidance mechanism A window-based flow control mechanismA window-based flow control mechanism

Several versions of TCPSeveral versions of TCP TCP TahoeTCP Tahoe TCP RenoTCP Reno TCP VegasTCP Vegas

4

TCP VegasTCP Vegas

Advantages over TCP RenoAdvantages over TCP Reno A new retransmission mechanismA new retransmission mechanism An improved An improved congestion avoidance mechanismcongestion avoidance mechanism A modified slow-start mechanismA modified slow-start mechanism

Uses Uses measured RTTmeasured RTT as feedback information as feedback information1. Measures RTT for a specific packet1. Measures RTT for a specific packet2. Estimates 2. Estimates severity of congestionseverity of congestion3. Changes window size3. Changes window size

Packet loss can be Packet loss can be preventedprevented

5

ObjectivesObjectives

Analyze a window-based flow controlAnalyze a window-based flow control Congestion avoidance mechanism of Congestion avoidance mechanism of TCP TCP

VegasVegas Connections with Connections with different propagation different propagation

delaysdelays Several Several bottleneck linksbottleneck links Using a control theoretic approachUsing a control theoretic approach

Show numerical examplesShow numerical examples ThroughputThroughput and and fairnessfairness StabilityStability and transient behavior and transient behavior

6

Source host maintains the Source host maintains the minimum minimum RTTRTT: :

Source host measures the Source host measures the actual RTTactual RTT: : r(k)r(k)

Window size is changed based on Window size is changed based on d(k)d(k)

Congestion avoidance of TCP VegasCongestion avoidance of TCP Vegas

7

AssumptionsAssumptions

Network topology is Network topology is arbitraryarbitrary All routers employ All routers employ static routingstatic routing All routers have a FIFO buffer for each All routers have a FIFO buffer for each

portport All TCP connections are All TCP connections are symmetrysymmetry Backward path is never congestedBackward path is never congested

8

Window sizeWindow size of connection of connection c c : : wwcc

cc: : control parametercontrol parameter that determines the amount of inc that determines the amount of increase/decrease in window sizerease/decrease in window size

State transition equation: window State transition equation: window sizesize

9

State transition equation: queue State transition equation: queue lengthlength

Queue lengthQueue length of the buffer for link of the buffer for link ll : : qqll b(c,l) b(c,l) : the previous link of link : the previous link of link ll for connection for connection cc llcc : the access link of connection : the access link of connection cc

10

Throughput and fairnessThroughput and fairness

Focus on equilibrium values (denoted by *)Focus on equilibrium values (denoted by *) cc* * : : throughputthroughput of connection of connection cc cc* * : sum of : sum of all queuing delaysall queuing delays of connection of connection cc

Can be regarded as a Can be regarded as a Little's lawLittle's law

Fairness between TCP connections Fairness between TCP connections cc and and c'c'

11

Stability and transient behaviorStability and transient behavior

Obtain a Obtain a linearizedlinearized model model x(t)x(t) : state vector (current state – equilibrium state) : state vector (current state – equilibrium state) LCMLCM : Lowest Common Multiple of all : Lowest Common Multiple of all cc//'s's

EigenvaluesEigenvalues of of AA determine determinestability and transient behaviorstability and transient behavior

12

Numerical example: network modelNumerical example: network model

Two bottleneck links and 30 TCP Two bottleneck links and 30 TCP connectionsconnections

C1

C2

N2

C3Source Host

Destination Host

Router

N1 N3

L1 L2

13

Numerical example: throughputNumerical example: throughput

Effect of difference in link capacities (Effect of difference in link capacities (l1l1 = 20)= 20)

0

1

2

3

4

5

6

7

8

9

10

0 20 40 60 80 100

Th

rou

gh

pu

t (p

ack

et/

ms)

Link capacity of l2 (packet/ms)

c1*c2*c3*

14

Numerical example: stabilityNumerical example: stability

Effect of link capacity (Effect of link capacity (ll = = l1 = l2l1 = l2))

0

1

2

3

4

5

6

7

0 1 2 3 4 5 6 7

l = 0.2

l = 2

l = 20

l = 200

l = 2000

Control parameter c of connection C1

Contr

ol para

mete

r c

of

connect

ion

C2,

C3

15

ConclusionConclusion

Analytic modelAnalytic model Window-based flow control based on Window-based flow control based on TCP VegasTCP Vegas Homogeneous networkHomogeneous network

Throughput and fairnessThroughput and fairness Can be explained by Can be explained by Little's lawLittle's law Has a bias against Has a bias against link capacity link capacity and and

# of bottleneck links# of bottleneck links Window size in steady stateWindow size in steady state

(bandwidth) x (propagation delay) + (control parameter (bandwidth) x (propagation delay) + (control parameter cc))

16

Conclusion (cont.)Conclusion (cont.)

Stability and transient behaviorStability and transient behavior Determined by Determined by eigenvalueseigenvalues of state transition matrix of state transition matrix

AA Link capacity significantly affects stabilityLink capacity significantly affects stability Investigation using Investigation using trajectories of eigenvaluestrajectories of eigenvalues

Future workFuture work More simulation studiesMore simulation studies Extension to TCP Tahoe or TCP RenoExtension to TCP Tahoe or TCP Reno