H. Ohsaki ITCom 20011

A control theoretical analysis of a window-based flow control

mechanism for TCP connections

with different propagation delaysHiroyuki OhsakiCybermedia CenterOsaka University, Japanoosaki@cmc.osaka-u.ac.jp

H. OhsakiITCom 20012

Contents Introduction Analytic model

– A window-based flow control based on TCP Vegas– TCP connections with different propagation

delays Stability and transient behavior analysis Numerical examples Conclusion

H. OhsakiITCom 20013

TCP (Transmission Control Protocol) Packet retransmission mechanism

– Retransmit lost packets in the network Congestion avoidance mechanism

– A window-based flow control mechanism Several versions of TCP

– TCP Tahoe– TCP Reno– TCP Vegas

H. OhsakiITCom 20014

TCP Reno Implemented in BSD UNIX Widely used in the current Internet Use packet loss as feedback information

1. Source host continuously increases window size2. Packet loss occurs at the bottleneck router3. Source host detects packet loss by duplicate

ACK4. Source host reduces its window size to 1/2

Packet loss is inevitable

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TCP Vegas Advantages over TCP Reno

– A new retransmission mechanism– An improved congestion avoidance mechanism– A modified slow-start mechanism

Uses measured RTT as feedback information1. Source host measures the RTT for a specific packet2. Source host estimates severity of congestion3. Source host changes window size

Packet loss can be prevented

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Objectives

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

Vegas– Connections have different propagation delays– Stability and transient behavior using a control

theoretic approach Show numerical examples

– Parameter tuning of TCP Vegas

H. OhsakiITCom 20017

Congestion avoidance mechanism of TCP Vegas

Source host maintains the minimum RTT:

Source host measures the actual RTT: r(k)

Window size is changed based on d(k)

)()()()(

krkwkwkd nn

otherwise )()( if1)(

)( if1)()1(

kwkdkw

kdkwkw

n

n

n

n

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Analytic Model (M = 2)

Group 1

Group 2

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Assumptions

A single bottleneck router in the network TCP connections in a group are

synchronized All TCP connections are greedy

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Derivation of state transition equations Window size: wm,n(k)

m,n: control parameter (i.e., feedback gain) ｍ： Frequency of window size change

Queue length: q(k)

System state

0)),(()(max)( ,,,,, kdkwkw nmnmnmnmmnm

)()()()( 21 kqkwkwkw M

LkwN

BkwkwNkqM

mM

mmm

mmmm ,0,

)()()(maxmin)1(

11

H. OhsakiITCom 200111

Stability and transient behavior analysis Obtain a linearized model

– x(k) : state vector (current state – equilibrium state)

Eigenvalues of A determine stability and transient behavior– s: the maximum eigenvalues of A

– s < 1: stable– s > 1: unstable– smaller s: better transient performance

*

*

*11

)()(

)(

)(

qkqwkw

wkw

kMM

x

)()( kk LCM xAx

)(max iiss

H. OhsakiITCom 200112

Numerical examples Network parameters

– M = 2: 2 groups of TCP connections (short and large delay)

– N １ =10 ： # of TCP connections in group 1– N2=10 ： # of TCP connections in group 2– B=150Mbps: processing speed of the bottleneck router

Control parameters– １ = ２ =3 ： control parameter adjusting # of in-

flight packets– 1, 2: control parameter adjusting a feedback gain

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Queuing delay ratio: Fm

Ratio of queuing delay to propagation delay– Nm m: # of packets in the router's buffer

– Large Fm: the queuing delay is not negligible– Small Fm: the queuing delay is negligible

If Fm is identical, stability and transient behavior are not changed

BNF mm

m

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0.0150.15

1.5

15

150

1 2 3 4 5 6 7

1

2

3

4

5

6

7

1

2

1

2

1.515

150

0.150.015

1 2 3 4 5 6 7

1

2

3

4

5

6

7

124

12=2:3

Stability region in 1-2 plane

Fm

Fm

H. OhsakiITCom 200115

1

2

1.0

0.60.4

0.30.2

0.8

0.5 1 1.5 2 2.5 3

0.5

1

1.5

2

2.5

3

1

2

1.0

0.992

0.994

0.9960.998

0.5 1 1.5 2 2.5 3

0.5

1

1.5

2

2.5

3

Fm=4.5, 1=1ms, 2=2msnon-negligible queuing

delayFm=0.0045, 1=1ms, 2=2ms

negligible queuing delay

Maximum eigenvalue s in 1-2 plane

H. OhsakiITCom 200116

Conclusion– A window-based flow control based on TCP Vegas– TCP connections have different propagation delays– Stability and transient behavior analysis– if Fm is small (i.e., propagation delay > queuing delay)...

Parameter should be proportional to TCP's propagation delay

Transient behavior cannot be improved– if Fm is large (i.e., propagation delay < queuing delay)...

Parameter should be between 0 and 2 Transient behavior can be greatly improved