04/19/23 INFOCOM'04

TCP Networks Stabilized by Buffer-Based AQMs

Huaizhong Han, C. V. Hollot, Yossi Chait (University of Massachusetts at Amherst), Vishal Misra (Columbia

University)

Thanks to NSF Grant #ANI-0125979

Presented by H. Han

ECE at UMass-Amherst

04/19/23 INFOCOM'04

Internet

TCP

TCP

router

Buffer-based AQM

Background (I)

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AQM

tcpsources

x

q

p

bwddelay

aqmrouter

fwddelay

x

p

AQM

q

u

Background (II)

lpflpf

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Network Congestion

TCP

TCP

congested

links

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Linearized Model of Network Congestion

lpf

x

R(s)

RT(-s)pu

aqmrouters

tcpsources

ijsijR e

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R(s)

RT(-s)

AQMrouters

F(s) bufferbased

1( )( )D s sI

G(s)ratebased

0 1( ) ( ) ( ) ( ) ( )( )TL s R s F s R s D s sI

Linear Stability

TCP

04/19/23 INFOCOM'04

Generalized Nyquist Theorem

[ ( )]iλ L jω

-1+j0

Re

not encircling -1+j0

linear closed-loop stability

: [ ( )]ii λ L jω

Im

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Main Result (I)

2{ ,1} { ( ) ( )}[ ( )] : ( )

{ ( )}R k

i

Co Co d j f jL j S

Co g j

2

1minRx

Rx

xroutinggain

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[ ( )]L j

( )S

Illustration(two-source, two links)

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Main Result (II)

linear closed-loop stability

-1+j0

[ ( )]i L j

( )SRe

Im

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Impact of Routing Matrix R (I)

big large stability margins

stability margins

R

R

σ

σ small small

2{ ,1} { ( ) ( )}[ ( )]

{ ( )}R k

i

Co Co d j f jL j

Co g j

04/19/23 INFOCOM'04

Impact of Routing Matrix R (II)

2

1 1 0 0 0 0

(0) 0 0 1 1 0 0 ; 2

0 0 0 0 1 1RR

2

0 1 0 1 1 1

(0) 0 1 1 1 1 1 ; 0.37

1 0 1 1 1 1RR

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0 50 100 150 200 250 300 3500

100

200

300

400

500R

bigR

small

Network Simulation

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Uncertainty in Routing Gain

maxint[ / ]

min

RA

RA

m n m

m = # of tcp sourcesn = # of congested liksA = binary full rank matrices

measure of

routing gain

uncertainty

robustness decreases with # of tcp sources and congested links

04/19/23 INFOCOM'04

Contribution of Work

• Stability condition for buffer-based AQMs– RED, REM, PI …

• Connection between routing and stability

• “Gain of Routing” as robustness measure -expressed in terms of numbers of sources and links.

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Future Research

• In practice how many congested links do sourcesencounter?

• Do present routing algorithms result in specific pattern of routing matrices R(0)? For example: how does shortest-path routing impact congestion control?