A control theoretical analysis of a
window-based flow control mechanism
for TCP connections
with different propagation delays
Hiroyuki Ohsaki
Cybermedia Center
Osaka University, Japan
[email protected]
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H. Ohsaki
ITCom 2001
Contents


Introduction
Analytic model
–
–



2
A window-based flow control based on TCP Vegas
TCP connections with different propagation delays
Stability and transient behavior analysis
Numerical examples
Conclusion
ITCom 2001
H. Ohsaki
TCP (Transmission Control
Protocol)

Packet retransmission mechanism
–

Congestion avoidance mechanism
–

A window-based flow control mechanism
Several versions of TCP
–
–
–
3
Retransmit lost packets in the network
TCP Tahoe
TCP Reno
TCP Vegas
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H. Ohsaki
TCP Reno



Implemented in BSD UNIX
Widely used in the current Internet
Use packet loss as feedback information
1.
2.
3.
4.

4
Source host continuously increases window size
Packet loss occurs at the bottleneck router
Source host detects packet loss by duplicate ACK
Source host reduces its window size to 1/2
Packet loss is inevitable
ITCom 2001
H. Ohsaki
TCP Vegas

Advantages over TCP Reno
–
–
–

Uses measured RTT as feedback information
1.
2.
3.

5
A new retransmission mechanism
An improved congestion avoidance mechanism
A modified slow-start mechanism
Source host measures the RTT for a specific packet
Source host estimates severity of congestion
Source host changes window size
Packet loss can be prevented
ITCom 2001
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Objectives

Analyze a window-based flow control
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–
–

Show numerical examples
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6
Congestion avoidance mechanism of TCP Vegas
Connections have different propagation delays
Stability and transient behavior using a control
theoretic approach
Parameter tuning of TCP Vegas
ITCom 2001
H. Ohsaki
Congestion avoidance mechanism
of TCP Vegas


Source host maintains the minimum RTT: t
Source host measures the actual RTT: r(k)
d (k ) 

wn(k )
t
wn(k )

r (k )
Window size is changed based on d(k)
wn(k )  1 if d (k )  

wn(k  1)  wn(k )  1 if   d (k )
wn(k )
otherwise

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Analytic Model (M = 2)
Group 1
Group 2
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Assumptions



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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)



dm,n: control parameter (i.e., feedback gain)
Dｍ：Frequency of window size change
wm, n(k  Dm)  max wm, n(k )  dm, n(m, n  dm, n(k )), 0
Queue length: q(k)


M

 
w
m ( k ) BDmt


,0 , L 
q(k  1)  min max  Nm wm(k )  M

  

N
m
w
m
(
k
)
m

1

m1

 

 


System state
w (k )
1
10
w2(k )  wM (k ) q(k )
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Stability and transient behavior
analysis

Obtain a linearized model
–

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x(k) : state vector (current state – equilibrium state)
x(k  D LCM )  A x(k )
Eigenvalues of A determine stability and transient
behavior
– s: the maximum eigenvalues of A
 w1 ( k )  w1* 
s  max ( si )


i



– s < 1: stable
x( k ) 
* 

w
M
(
k
)

w
– s > 1: unstable
M

* 
– smaller s: better transient performance
 q ( k )  q 
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Numerical examples

Network parameters
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
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M = 2: 2 groups of TCP connections (short and large delay)
N１=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
–
d1, d2: control parameter adjusting a feedback gain
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Queuing delay ratio: Fm

Ratio of queuing delay to propagation delay
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
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Nm m: # of packets in the router's buffer
N m m
Fm 
Bt
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
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Stability region in d1-d2 plane
7
7
6
5
d2
Fm
0.015
0.15
6
d2
Fm
150
4
3
15
3
0.15
2
150
2
0.015
1
1
1
2
3
d1
4
5
6
7
t1 :t2 1:4
14
15
5
1.5
4
1.5
1
2
3
d1
4
5
6
7
t1 :t2 =2:3
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Maximum eigenvalue s in d1-d2
plane
3
3
2
1.0
0.8
0.6
1.5
0.4
2.5
d2
1
2.5
0.992
2
d2
1.5
0.3
0.2
0.994
1
0.5
0.996
0.998
0.5
1.0
0.5
1
1.5
2
2.5
d1
Fm=4.5, t1=1ms, t2=2ms
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non-negligible queuing delay
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0.5
1
1.5
d1
2
2.5
3
Fm=0.0045, t1=1ms, t2=2ms
negligible queuing delay
H. Ohsaki
Conclusion
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–
–
–
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)...


–
if Fm is large (i.e., propagation delay < queuing delay)...


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Parameter d should be proportional to TCP's propagation delay
Transient behavior cannot be improved
Parameter d should be between 0 and 2
Transient behavior can be greatly improved
ITCom 2001
H. Ohsaki