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Network Planning of the CATV communication networks Arthur, K. W. Peng, OPLAB d[email protected] Advisor: Frank Yeong-Sung Lin April 22, 2005
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Network Planning of the CATV communication networks Arthur, K. W. Peng, OPLAB [email protected]@im.ntu.edu.tw Advisor: Frank Yeong-Sung Lin.

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Page 1: Network Planning of the CATV communication networks Arthur, K. W. Peng, OPLAB d6725005@im.ntu.edu.tw6725005@im.ntu.edu.tw Advisor: Frank Yeong-Sung Lin.

Network Planning of the CATV communication networks

Arthur, K. W. Peng, [email protected]

Advisor: Frank Yeong-Sung LinApril 22, 2005

Page 2: Network Planning of the CATV communication networks Arthur, K. W. Peng, OPLAB d6725005@im.ntu.edu.tw6725005@im.ntu.edu.tw Advisor: Frank Yeong-Sung Lin.

AgendaIntroduction Problem Description and FormulationFormulation Analysis and ReformulationNumerical ExperimentsConclusionQ&A

Page 3: Network Planning of the CATV communication networks Arthur, K. W. Peng, OPLAB d6725005@im.ntu.edu.tw6725005@im.ntu.edu.tw Advisor: Frank Yeong-Sung Lin.

CATV Communication Network Technology

Head End

Satellite dish

Radio tower

Television

TRUNKNETWORK

DistributionNetwork

TrunkAmplifier

BridgerAmplifier

SplitterDirectionCouplers

Line Extender

Tap

The Network Structure of CATV Networks

Page 4: Network Planning of the CATV communication networks Arthur, K. W. Peng, OPLAB d6725005@im.ntu.edu.tw6725005@im.ntu.edu.tw Advisor: Frank Yeong-Sung Lin.

Network Planning --- Traditional Approaches

製圖幹線系統設計餽線系統設計反向系統設計

Page 5: Network Planning of the CATV communication networks Arthur, K. W. Peng, OPLAB d6725005@im.ntu.edu.tw6725005@im.ntu.edu.tw Advisor: Frank Yeong-Sung Lin.

幹線系統設計

頭端幹線系統

Page 6: Network Planning of the CATV communication networks Arthur, K. W. Peng, OPLAB d6725005@im.ntu.edu.tw6725005@im.ntu.edu.tw Advisor: Frank Yeong-Sung Lin.

餽線系統設計Figure 2-10

Page 7: Network Planning of the CATV communication networks Arthur, K. W. Peng, OPLAB d6725005@im.ntu.edu.tw6725005@im.ntu.edu.tw Advisor: Frank Yeong-Sung Lin.

餽線系統設計

相對信號位準與損失的系統點

Page 8: Network Planning of the CATV communication networks Arthur, K. W. Peng, OPLAB d6725005@im.ntu.edu.tw6725005@im.ntu.edu.tw Advisor: Frank Yeong-Sung Lin.

反向系統設計Similar to the design of downlink.Noise Funneling Limit the number of branch and amplifier. Addressable Bridger Leg Switch

前向 --- 反向放大器

Page 9: Network Planning of the CATV communication networks Arthur, K. W. Peng, OPLAB d6725005@im.ntu.edu.tw6725005@im.ntu.edu.tw Advisor: Frank Yeong-Sung Lin.

CAD ToolsThe traditional way is calculation-intensive and repetitive.Comparison of the CAD tools[Yermolov,2000]

CATV CAD: Gen Enterprise Ltd. Symplex Suite of software: SpanPro Inc. Program System : Lode Data Corporation CADIX International Inc. Cable Tools: Goldcom Inc.

Feature Auto-tracking the signal quality. Helping the design to calculate the network requirement, co

st, etc. The design is still depend on the experience of the network

designer.

Page 10: Network Planning of the CATV communication networks Arthur, K. W. Peng, OPLAB d6725005@im.ntu.edu.tw6725005@im.ntu.edu.tw Advisor: Frank Yeong-Sung Lin.

CATV Network Planning Tools•Stand-alone version •Web-based version

Page 11: Network Planning of the CATV communication networks Arthur, K. W. Peng, OPLAB d6725005@im.ntu.edu.tw6725005@im.ntu.edu.tw Advisor: Frank Yeong-Sung Lin.

Mathematical Formulation and Network Optimization

Basic ideas: formulate the network and using network optimization technique to find the optimal solution.

Head End

User

)( )(

equipmentlink

A

M

F

G

F

B

O

MF

GA

v

v

v

v

v

v

vl

vl

vl

*

*

*

CNR

X-MOD

CNRX-MOD

CSOCTB

Page 12: Network Planning of the CATV communication networks Arthur, K. W. Peng, OPLAB d6725005@im.ntu.edu.tw6725005@im.ntu.edu.tw Advisor: Frank Yeong-Sung Lin.

Performance Requirements

Performance requirements in downstream CNR (Carrier to Noise Ratio) ≧43dB X-MOD (Cross Modulation ) ≦-46dB CSO (Composite Second Order) ≦-

53dB CTB (Composite Triple Beat) ≦-53dB

Page 13: Network Planning of the CATV communication networks Arthur, K. W. Peng, OPLAB d6725005@im.ntu.edu.tw6725005@im.ntu.edu.tw Advisor: Frank Yeong-Sung Lin.

Performance Requirements (cont’d)

Performance requirements in upstream

Page 14: Network Planning of the CATV communication networks Arthur, K. W. Peng, OPLAB d6725005@im.ntu.edu.tw6725005@im.ntu.edu.tw Advisor: Frank Yeong-Sung Lin.

Problem Formulation

Problem description Given :

downstream performance objectives upstream performance objectives specifications of network components cost structure of network components number and position of endusers terrain which networks will pass through and the associated

cost Determine:

routing allocation of network components operational parameters (e.g., gain of each amplifier)

Page 15: Network Planning of the CATV communication networks Arthur, K. W. Peng, OPLAB d6725005@im.ntu.edu.tw6725005@im.ntu.edu.tw Advisor: Frank Yeong-Sung Lin.

Problem FormulationFeatures Nonlinear problems Hard to solve directly by standard methods Some techniques needed

Problem Decomposition Steiner Tree Problem Network Optimization

Geometric Programming Posynomial form

Gradient-based Optimization

Page 16: Network Planning of the CATV communication networks Arthur, K. W. Peng, OPLAB d6725005@im.ntu.edu.tw6725005@im.ntu.edu.tw Advisor: Frank Yeong-Sung Lin.

Problem Decomposition and Reformulation

Part I: Steiner Tree Problemsll

LlCy

min

Llory

Vvy

l

lLl v

in

10)14(

1)13(

LlWyx lpplPpWw w

||)15(

WwPporx

Wwx

wp

pPp w

, 10)17(

1)16(

Page 17: Network Planning of the CATV communication networks Arthur, K. W. Peng, OPLAB d6725005@im.ntu.edu.tw6725005@im.ntu.edu.tw Advisor: Frank Yeong-Sung Lin.

Problem Decomposition and Reformulation (cont’d)

regular verticesSteiner vertices

Head End

User1

User2

User3

Page 18: Network Planning of the CATV communication networks Arthur, K. W. Peng, OPLAB d6725005@im.ntu.edu.tw6725005@im.ntu.edu.tw Advisor: Frank Yeong-Sung Lin.

Problem Decomposition and Reformulation (cont’d)

Heuristic approximation algorithms Minimum Cost Paths Heuristic (MPH)

11

111

1

11

321

to add

})(min{

that such in a vertex find

do 32eachfor :2

}{:1

ofcost the:)),((

in a vertex to

component connecteda from pathshortest :),(

,...,,, ),,(

i-ii-i

i-jji-ii-

i-i

k

V),vPATH(VV

S-V | v),vPATH(V)),vPATH(V

S-Vv

,...,k, istep

vVstep

Path(W,s)sWPATH

Gs

WsWPATH

}vvv{vSVSdEVG

Page 19: Network Planning of the CATV communication networks Arthur, K. W. Peng, OPLAB d6725005@im.ntu.edu.tw6725005@im.ntu.edu.tw Advisor: Frank Yeong-Sung Lin.

Problem Decomposition and Reformulation (cont’d)

Page 20: Network Planning of the CATV communication networks Arthur, K. W. Peng, OPLAB d6725005@im.ntu.edu.tw6725005@im.ntu.edu.tw Advisor: Frank Yeong-Sung Lin.

Problem Decomposition and Reformulation (cont’d)

Part II

topologycandidate given thein nodes ofset the:

topologycandidate given thein links ofset the:

V

L

]})([

])()()([])()(

)()()([{])([min

110

19

18

17

16

15

14

13

12

11

vv

vvvvvv

vvvvVv

lLl

Adz

MdGdFdzOdBd

MdGdFdzAd

*

* ***

s.t.

Page 21: Network Planning of the CATV communication networks Arthur, K. W. Peng, OPLAB d6725005@im.ntu.edu.tw6725005@im.ntu.edu.tw Advisor: Frank Yeong-Sung Lin.

Problem Decomposition and Reformulation (cont’d)

5.0*10

1

11

5.0

110)()3(

syspcM

pjpj

n

jpipi

n

ipipi

H

iAAGMz

10)()4(5.0*

101

11

5.0

1

syspcB

pjpj

n

jpipi

n

ipipi

H

iAAGBz

101

11

1

110)()5(

syspcO

pjpj

n

jpipi

n

ipipi

H

iAAGOz

Ww

Ww

AAGS

Fz syspcC

pjpj

n

jpipi

n

i

pnpnH

n

10)

10*

( (2) 10

10

591

1

1

1

1

WwAAGS pjpj

H

jpipi

H

ii

pcpc

10)1(11

Page 22: Network Planning of the CATV communication networks Arthur, K. W. Peng, OPLAB d6725005@im.ntu.edu.tw6725005@im.ntu.edu.tw Advisor: Frank Yeong-Sung Lin.

Problem Decomposition and Reformulation (cont’d)

1)6(

pj

H

Hjpipi

H

HiAAG

pc

pv

pc

pv

*pVvWw

WwzzFssys

Pp

C

vVv

vVv

t

10)(10 )7( 105.019.5

*

****

amplifier upstream of figure noise :

amplifier upstream tostrength signalinput :

amplifier upstream of gain:

:

set path ofset node the:

path ofset node the:

t

v

P

p

F

s

G

VariablesDecision

PV

pV

**

*

Page 23: Network Planning of the CATV communication networks Arthur, K. W. Peng, OPLAB d6725005@im.ntu.edu.tw6725005@im.ntu.edu.tw Advisor: Frank Yeong-Sung Lin.

Problem Decomposition and Reformulation (cont’d)

WwGsMzsyspc

M

pitpi

H

i

10)()8(

5.0*105.0

1

*

* ***

amplifier upstream of modulation cross :

:

tM

VariableDecision*

Page 24: Network Planning of the CATV communication networks Arthur, K. W. Peng, OPLAB d6725005@im.ntu.edu.tw6725005@im.ntu.edu.tw Advisor: Frank Yeong-Sung Lin.

Solution ApproachesPosynomial problem

aij : arbitrary real numbers ci : positive gk(t) : posynomials

)(min 0 tg ( I P )

0,...,0,0:.. 21 mtttts ( 1 )

1)(,...,1)(,1)( 21 tgtgtg p( 2 )

,...,,1,0,...)( 21

22][

pktttctg imii am

aai

kJik

Page 25: Network Planning of the CATV communication networks Arthur, K. W. Peng, OPLAB d6725005@im.ntu.edu.tw6725005@im.ntu.edu.tw Advisor: Frank Yeong-Sung Lin.

Solution Approaches (cont’d)

Dual problem)(

1i

i

1)(])

c([)(max i

k

k

p

k

n

iv

( I P )

0...,0,0:.. 21 nts P o s i t i v i t y c o n d i t i o n

1]0[

iJj

N o r m a l i t y c o n d i t i o n

pja iij

n

i,...,2,1 0

1

O r t h o g o n a l i t y c o n d i t i o n

pkikJi

k ,...,2,1 ,)(][

Page 26: Network Planning of the CATV communication networks Arthur, K. W. Peng, OPLAB d6725005@im.ntu.edu.tw6725005@im.ntu.edu.tw Advisor: Frank Yeong-Sung Lin.

Solution Approaches (cont’d)

Penalty method

Steepest descent methodRounding procedure

numbers. positive large are and where

,...,2,1 )()1()(lnmin

21

2

12

2

]0[1

JJ

mjaJJv iij

n

ii

Ji

Page 27: Network Planning of the CATV communication networks Arthur, K. W. Peng, OPLAB d6725005@im.ntu.edu.tw6725005@im.ntu.edu.tw Advisor: Frank Yeong-Sung Lin.

Computational ExperimentsSolution modules

Module 1Determining the Interconnection and

Routing of CATV Networks

Module 2Determining Locations to Place

Amplifiers

Module 3Determining Configurations and

Parameters of CATV Components

Module 4Determining Configurations and

Parameters of CATV Reverse Modules

Page 28: Network Planning of the CATV communication networks Arthur, K. W. Peng, OPLAB d6725005@im.ntu.edu.tw6725005@im.ntu.edu.tw Advisor: Frank Yeong-Sung Lin.

Computational Experiments

1

11

21

31

41

51

61

71

81

91

2 3 4 5 6 7 8 9 10

20

30

40

50

60

70

80

90

100

Page 29: Network Planning of the CATV communication networks Arthur, K. W. Peng, OPLAB d6725005@im.ntu.edu.tw6725005@im.ntu.edu.tw Advisor: Frank Yeong-Sung Lin.

Computational ExperimentsThe constructed steiner tree

1

11

21

31

41

51

61

71

81

91

2 3 4 5 6 7 8 9 10

20

30

40

50

60

70

80

90

100

Page 30: Network Planning of the CATV communication networks Arthur, K. W. Peng, OPLAB d6725005@im.ntu.edu.tw6725005@im.ntu.edu.tw Advisor: Frank Yeong-Sung Lin.

Computational ExperimentsDeciding the locations and parameters of amplifiers

1

11

21

31

41

51

61

71

81

91

2 3 4 5 6 7 8 9 10

20

30

40

50

60

70

80

90

100

zg=0.117608

zg=0.064212

zg=0.053235

zg=0.064211

Page 31: Network Planning of the CATV communication networks Arthur, K. W. Peng, OPLAB d6725005@im.ntu.edu.tw6725005@im.ntu.edu.tw Advisor: Frank Yeong-Sung Lin.

ConclusionIt is feasible to use mathematical programming methods in CATV network planningThe solution provided by this approach can be used to evaluate the QoS in many situation.As a core module, we can add more features: New network components New Services

Page 32: Network Planning of the CATV communication networks Arthur, K. W. Peng, OPLAB d6725005@im.ntu.edu.tw6725005@im.ntu.edu.tw Advisor: Frank Yeong-Sung Lin.

Future Research Directions

Network Planning and Management CATV network planning and optimization

Layering QoS Fault tolerance/Reliability

CATV network performance Capacity management Admission Control

Page 33: Network Planning of the CATV communication networks Arthur, K. W. Peng, OPLAB d6725005@im.ntu.edu.tw6725005@im.ntu.edu.tw Advisor: Frank Yeong-Sung Lin.

Q & A