Router Level Flow Control in Data Networks Stephan Bohacek University of Southern California

Router Level Flow Control in Data Networks

Stephan Bohacek

University of Southern California

• introduction• 1-hop controllers

– system description

– stability

– blocking

• 2-hop controllers– system description

– classical design methods (intuition)• hop over

• back pressure

• forward pressure

• time constant

– modern design methods• LQ

• L1

• distributed parameter

– stability• future work and conclusions

Outline

Objective: To avoid transmission of packets that will be dropped (best to drop packets at the entry point of the network).

For very high speed networks it might be better to use hop-by-hop flow control instead of end-to-end flow control.

Method: Control the router sending rates to ease and regulate network congestion.

Problem: Sending a packet that will be dropped is inefficient.

jijiji

ik

ikikj

jijii

qFqFrr

urrq

21,,

,,,,

otherwise

router to connects router if

0

1,

jiji

Queue dynamics

Link rate dynamics

one hop controller

pressure back applies

queue empties Parameters Control

2

1

F

F

Output - Inputiu

ijji ,, Let iqi router in size queue -

jir ji to router from rate ontransmissi - ,

CAACAC

BAABAB

AACABCABAA

qFqFrr

qFqFrr

urrrrq

21

21

Router B

one hop controller

CAr

ACr

ABr

Cq

Aq

BqAq

Au

BAr

Router C

Router A

sqFsqFs

sr

susrsrsq

jiji

kikik

jjijii

21,

,,,,

1

susqNFFs

ssq

12

1

ji

jiN

kki

ji

ji for

for

,

,

,

zero to sum columnsand rows

stable is from Mapping yu

stability of one hop controller

Blocking

Slow linkCongested router

A

B

C

D

E

• The data leaving A is destined for C.• The data leaving B is destined for D.• Link E-D is slow, so the queue in E fills.• Back pressure slows down both links A-E and B-E.• However, the link from E-C is high speed, hence the link A-E is slowed needlessly.

j. to travels then that i to h router from

travels that data the of part the is jih ,,

1,, j

jih Hence

two hop controller

BA

C

D

BAr ,

BACBA r ,,,

BADBA r ,,,

(queues in B are empty)

hihihjih

kkjkjkji

jijiji

hihjihjiji

tqFtqFt

tqFtqFt

tqFtqFtr

trttrtq

,6,5,,

,4,3,,

,2,1,

,,,,,

Queue Dynamics

Rate Controller

parameters Control - 654321 ,,,,, FFFFFF

two hop controller

How to set control parameters?

intuition vs. optimizationclassical vs. modern

CongestedRouter

Forward Pressure

Data

Control

Back Pressure 43 ,FF 65 ,FF

large - 1F As queue fills, out going data rates rapidly increase

small - 1F As queue fills, out going datarates slowly increase

jiji qr F ,1,

h

ihjihjiji rrq ,,,,,

1F of effect The

.1 F routers typical In

That is, the router sends data at the maximum rate whenever the queue is not empty.

0 200 400 600 800 1000 12000

0.1

0.2

queu

e si

ze

0 200 400 600 800 1000 12000

1

2

3

rate

s

time

A B C

Small 1F

0 200 400 600 800 1000 12000

0.05

0.1

queu

e si

ze

0 200 400 600 800 1000 12000

2

4

rate

s

time

A B C

Large 1F

k

kjkjkjiji tqFtqFttr ,4,3,,,

Back Pressure

A B C D

large 43 ,FF

• If queue C-D fills• Rate B-C slows• Queue B-C fills• Rate A-C slows• Queue A-C fills

constant input

Back Pressure

constant input

input

input

Back Pressure

0 1000 2000 3000 4000 5000 60000

0.2

0.4

queu

e si

ze

0 1000 2000 3000 4000 5000 60000

1

2

rate

s

time

Without Back Pressure

0 1000 2000 3000 4000 5000 60000

0.2

0.4

queu

e si

ze

0 1000 2000 3000 4000 5000 60000

1

2

rate

s

time

With Back Pressure

hihihjih

kkjkjkji

jijiji

qFqF

qFqF

qFqFr

,6,5,,

,4,3,,

,2,1,

Forward Pressure

Forward Pressure

1. inputdata

2. queuefills

3. dataflows

4. queuefills

5. data flows rapidly- queue B-C is filling- queue A-C is filling

A B C

Forward Pressure

h

ihihjihji qFqFr ,6,5,,,

0 200 400 600 8000

0.05

0.1

0.15

0.2

queu

e si

ze

0 200 400 600 8000

1

2

3

rate

s

time

Without forward pressure

0 200 400 600 8000

0.05

0.1

0.15

0.2

queu

e si

ze

0 200 400 600 8000

1

2

3

rate

s

time

With forward pressure

00

Input

Input

Input

Input

Input

Output

Output

Output

Output

Output

1 2 3 4 5

6 7 8 9 10

11 12 13 14 15

16 17 18 19 20

21 22 23 24 25

Blocking

0

0

Input

Input

Input

Input

Input

Output

Output

Output

Output

Output

1 2 3 4 5

6 7 8 9 10

11 12 13 14 15

16 17 18 19 20

2122 23 24 25

Blocking

0

0

Input

Input

Input

Input

Input

Output

Output

Output

Output

Output

1 2 3 4 5

6 7 8 9 10

11 12 1314 15

1617

18 19 20

2122 23 24 25

Blocking

0

0

Input

Input

Input

Input

Input

Output

Output

Output

Output

Output

1 2 3 4 5

6 7 8 9 10

11 12 1314 15

1617

18 19 20

2122 23 24 25

Blocking

modern control methods(with truncation)

• optimal control with quadratic cost

• minimize peak queue/rate size

• distributed parameter

linear quadratic

0

22min tutqu

Quadratic Cost

uIr

qA

r

q

0

01 IXXBBXAXA TT

Let

022 XRX NLNL , with

control minimizing

r

qXItu 0

1

NLNLRA 22

sizes queue of vector - NLRq

rates data of vector - NLRr

input control - NLRu

Show plot of gains

Note: gains decay, hence truncationLQ doesn’t make much use of back pressurelack of back pressure can be seen by the smallgains from 26-27, 26-19 and 26-33

0 1 2 3 4 5 6 7 80

1

2

3

4

5

6

7

8 gains for hop 25 to 26

1 2 3 4 5 6 7

8 9 10 11 12 13 14

15 16 17 18 19 20 21

22 23 24 25 26 27 28

29 30 31 32 33 34 35

36 37 38 39 40 41 42

43 44 45 46 47 48 49

queu

e ga

ins

0 1 2 3 4 5 6 7 80

1

2

3

4

5

6

7

8

1 2 3 4 5 6 7

8 9 10 11 12 13 14

15 16 17 18 19 20 21

22 23 24 25 26 27 28

29 30 31 32 33 34 35

36 37 38 39 40 41 42

43 44 45 46 47 48 49

rate

gai

ns 25,2425,2426,2526,2525,2425,2426,2526,2526,25 rrqqr

L1 Control methods

tv

tq

t

t

u max

maxmin

BvuIr

qA

r

q

0

data entering v

Objective: Minimize peakqueue size

0

00

IB

BZIVZAVI

AZ

T

TT

0

ZVZ

V

ZI

T

VZ ,

min

subject to

L1 Control methods

00

gains for hop 2 to 5

1 2 3

4 5 6

7 8 9

queu

e ga

ins

00

1 2 3

4 5 6

7 8 9

rate

gai

ns 3,23,22,12,13,23,22,12,15,2 rrqqr

00

gains for hop 5 to 2

1 2 3

4 5 6

7 8 9

queu

e ga

ins

00

1 2 3

4 5 6

7 8 9

rate

gai

ns

3,23,22,12,13,23,22,12,12,5 rrqqr

Note on previous slide, good back pressure, some forwardpressure. But no back pressure from 8-5. Why? These optimization procedures don’t always give intuitive answers.Is it that the optimization procedure is better, or doing somethingstupid.

Distributed Parameter Methods

1,1,

1,1,

,,,

,1,,,

65

43

21

itqKitqK

itqKitqK

itqKitqKitr

ituitritritq

Simple 1-D spatially invariant system

1,

1,

itr

itq itr

itq

,

, 1,

1,

itr

itq

I/OData Flow

ControlInformation

1, itv 1, itv

ituitritritq oo ,,,,

itqKitqK

itqKitqK

itqKitqKitr ooo

,,

,,

,,,

65

43

21

itritr

itqitq

o

o

,1,

,1,

itritr

itqitq

o

o

,1,

,1,

Temporal Dynamics

(only depends on local variables)

Spatial dynamics


0

0

0

0

,

,

0

0

0

0

,

,

,

,

,

,

,

,

,

,

,

,

,

,

22

1

itvK

itv

ituK

itu

itr

itq

itr

itq

itr

itq

itr

itq

itr

itq

itr

itq

Iz

zI

sIo

o

o

o

A

shift spatialbackward -

shift spatialforward -

derivative time -

1z

z

s


- Compact description of large system- Controllers will depend on local variables only

Requires systems be homogeneous. Extending it to nonhomogeneous systems may lead to computational difficulties.

advantages

disadvantages -


kji ,, varying of face the in Stability

r

qA

r

q

0Re Aseigenvalue

stability

kji

kji

totravled also will which to router

fromtravled that data of portion the is ,,

1,, k

kji k, some to goes eventually

j to i from travels that data all Since


Note that there still are some slow eigenvalues.These are from alphas that result in data taking along time to get out of the network. That is, nonsensical alphas. It seems that making reasonable alphas is difficult

The previous network is 3 x 3, with K4 and K6 = 0

1

2 3

4

1,1,1 1,4,24,2,12,1,1 in

Has a pole at zero, integrator

sense. make not do Some P

1in

2in

4in

3in


1

2 3

4

1

2 3

4

kjia ,,

Take the “sum” of possible input-output pairs.

These sums lead to sensible kjia ,,

kji ,, sensible for sEigenvalue

r

qA

r

q


IXAXA T

NLNLRX 22 0X

?

stability

Future Directions

• characterization of alphas• simulation with TCP and CBR data• rigorous controller synthesis • rigorous stability and performance analysis

• investigation of differences between TCP and CBR traffic in such a network

Documents

Router Level Flow Control in Data Networks Stephan Bohacek University of Southern California