Rafael C. Nunez - Gonzalo R. Arce

Department of Electrical and Computer EngineeringUniversity of Delaware

May 19th, 2005

Diffusion Marking Mechanisms for Active

Queue Management

2

TCP Congestion Control

TCP controls congestion at end points (AIMD)

3

Dropping Packets in the Router’s Queue Tail Dropping Problems:

Penalizes bursty traffic Discriminates against

large propagation delay connections.

Global synchronization. Solution: Active Queue

Management (AQM).0 2 4 6 8 10 12 14 16 18 20

0

10

20

30

40

50

60

70

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100Instantaneous Queue Size - Drop Tail

Time (seconds)

Que

ue (

Pac

kets

)

4

Active Queue Management

Router becomes active in congestion control.

Random Early Detection (Floyd and Jacobson, 1993).

0 2 4 6 8 10 12 14 16 18 200

10

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40

50

60

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80

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100Queue Behavior in RED

Time (seconds)

Que

ue (

Pac

kets

)

Instantaneous QueueAverage Queue

0 2 4 6 8 10 12 14 16 18 200

10

20

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40

50

60

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100Queue Behavior in Drop Tail

Time (seconds)

Que

ue (

Pac

kets

)

REDDrop Tail(Not AQM)

5

Random Early Detection (RED)

Drop probability based on average queue:

q n6@

= 1- wq

_ i$q n - 1

6 @+wq$q n

6@

Four parameters: qmin , qmax, Pmax, wq Overparameterized

ECN marking

6

Queue Behavior in RED 20 new flows every 20 seconds qmin = 20, qmax = 40

Wq = 0.01 Wq = 0.001

0 10 20 30 40 50 60 70 80 90 1000

10

20

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40

50

60

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80Queue Behavior in RED

Time (seconds)

Que

ue (

Pac

kets

)

Instantaneous QueueAverage Queue

0 10 20 30 40 50 60 70 80 90 1000

10

20

30

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50

60

70

80

90

100Queue Behavior in RED

Time (seconds)

Que

ue (

Pac

kets

)

Instantaneous QueueAverage Queue

7

Extensive Research in AQM

Adaptive RED, REM, GREEN, BLUE,… Problems:

Over-parameterization Not easy to implement in routers Not much better performance than drop

tail We introduce a statistical approach

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Diffusion Marking Mechanisms Three components in AQM algorithms:

Drop Probability Function Packet Dropping Scheme (Quantizer) Packet Selection Algorithm (Not exploited

yet)

Diffusion Marking

DropProbabilityFunction

PacketDroppingScheme

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Defining a New Packet Dropping Scheme with Error Diffusion Packet marking is analogous to

quantization: convert a continuous gray-scale image into black or white dots.

Error diffusion: The error between input (continuous) and output (quantized) is diffused in subsequent outputs.

Diffusion Marking

DropProbabilityFunction

PacketDroppingScheme

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Packet Marking in DM D(n) is a quantized representation of P(n)

Acumulated Error Feedback model Condition for stability

Diffusion Marking

DropProbabilityFunction

PacketDroppingScheme

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Error Diffusion vs. Random Drops

80 85 90 95 1000

123

Time (Seconds)

Error Diffusion0

123

Random drops

Dro

ps

80 85 90 95 1000

100

200

Time (Seconds)

Error Diffusion0

100

200Random Drops

Que

ue O

ccup

ancy

rate = 0.0001rate = 0.0003

rate = 0.001rate = 0.003

rate = 0.01

100

101

10210

-1

100

101

102

103

104

105

106

number of flows

vari

ance

que

ue o

ccup

ancy

Probabilistic = dashed Error diffusion = solid

Diffusion Marking

DropProbabilityFunction

PacketDroppingScheme

12

Probability of Marking a Packet

Gentle RED function closely follows:

P [n] / P (qn) = Sqncma

(A)

Diffusion Marking

DropProbabilityFunction

PacketDroppingScheme

13

Evolution of the Congestion Window

TCP in steady state:

PacketsBetweenDrops= 83W2

p1 = 8

3W2

(B)

Diffusion Marking

DropProbabilityFunction

PacketDroppingScheme

14

Traffic in the Network

Congestion Window = Packets In The Pipe + Packets In The Queue

Or:

43W $N = MSS

B $RTT +qd(C)

From (A), (B), (C), and knowing that: RTT =D +q$ BMSS

P (q) = Sqcma

$N2

a =Log S

qd; E

Log 23: D

- 2 $Log MSSB $D +2 $qd

; D

where

Diffusion Marking

DropProbabilityFunction

PacketDroppingScheme

15

Probability Function

P (q) = Sqcma

$N2, if q>S$ N2̂h1/a

1 , otherwise

*

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1P(Q/S, N)

Q/S

P(Q

/S,

N)

N = 1N = 5N = 10

Diffusion Marking

DropProbabilityFunction

PacketDroppingScheme

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Algorithm Summary

D[n] =1, if (P [n] - Pe[n]) H 0.50, otherwise

)

P (q) = Sqcma

$N2, if q>S$ N2̂h1/a

1 , otherwise

*

a =Ln S

qd; E

Ln 23: D

- 2 $Ln MSSB $D +2 $qd

; D

• Diffusion Marking decides whether to mark a packet or not as:

Where:

Pe[n]= bi$De[n - i]

i = 1

M

!

De[n] =(P [n] +Pe[n]) - D[n]

M=2, b1=2/3, b2=1/3

Remember:

17

Optimizing the Control Mechanism

Adaptive Threshold Control Dynamic Detection of Active

Flows

18

Adaptive Threshold Control

Dynamic changes to the threshold improve the quality of the output.

D[n] =1, if (P [n] - Pe[n]) H 0.50, otherwise

)

D[n] =1, if (P [n] - Pe[n]) H k$P [n]0, otherwise

)

f(P [n]) =k$P [n]

19

Dynamic Detection of Active Flows DEM requires the number of active

flows

Effect of not-timed out flows and flows in timeout during less than RTT:

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Dynamic Detection of Active Flows (cont’d) The number of packets:

The number of active flows:

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Active Flows Estimate

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20

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35Diffusion Early Marking - Flows Estimate

Time (seconds)

Num

ber of F

low

s

MeasuredDEM EstimatorSRED Estimator

40 60 80 100 120 140 160

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18Diffusion Early Marking - Flows Estimate

Time (seconds)

Num

ber of F

low

s

MeasuredDEM EstimatorSRED Estimator

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Results - Window Size

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100RED: Congestion Window Size vs. Time (2 Flows)

Time (seconds)

Con

gest

ion

win

dow

siz

e (p

acke

ts)

Congestion Window 1Congestion Window 2Average Congestion Window 1Average Congestion Window 2

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100Diffusion Early Marking: Congestion Window Size vs. Time (2 Flows)

Time (seconds)C

onge

stio

n w

indo

w s

ize

(pac

kets

)

Congestion Window 1Congestion Window 2Average Congestion Window 1Average Congestion Window 2

RED Diffusion Based

Larger congestion window more data!

23

Stability of the Queue

100 long lived connections (TCP/Reno, FTP) Desired queue size = 30 packets

0 2 4 6 8 10 12 14 16 18 200

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100Queue Behavior in RED

Time (seconds)

Que

ue (

Pac

kets

)

Instantaneous QueueAverage Queue

0 2 4 6 8 10 12 14 16 18 200

10

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50

60

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80

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100Diffusion Early Marking Queue

Time (seconds)

Que

ue (

Pac

kets

)

Instantaneous QueueAverage Queue

RED Diffusion Based

24

Changing the Number of Flows

20 new flows every 20 seconds

0 10 20 30 40 50 60 70 80 90 1000

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100Queue Behavior in RED

Time (seconds)

Que

ue (

Pac

kets

)

Instantaneous QueueAverage Queue

0 10 20 30 40 50 60 70 80 90 1000

10

20

30

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50

60

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80

90

100Diffusion Early Marking Queue

Time (seconds)

Que

ue (

Pac

kets

)

Instantaneous QueueAverage Queue

RED Diffusion Based

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Long Lived Flows

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Long Lived Flows (cont’d)

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HTTP Flows

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HTTP Flows (cont’d)

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Evolution of DM DM has evolved to avoid the estimation of

network parameters (RTT, N). The new approach uses a maximum likelihood

ratio for congestion detection.

Queue Size Dropping Rate

30

Conclusions

Error Diffusion dithering can be used in AQM.

Advantages: Increased stability Simpler (only one parameter) Increased throughput

Current Work: Parameter optimization Additional traffic control applications Extension to wireless environments