network planning of the catv communication networks arthur, k. w. peng, oplab...
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Network Planning of the CATV communication networks
Arthur, K. W. Peng, [email protected]
Advisor: Frank Yeong-Sung LinApril 22, 2005
AgendaIntroduction Problem Description and FormulationFormulation Analysis and ReformulationNumerical ExperimentsConclusionQ&A
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
Network Planning --- Traditional Approaches
製圖幹線系統設計餽線系統設計反向系統設計
幹線系統設計
頭端幹線系統
餽線系統設計Figure 2-10
餽線系統設計
相對信號位準與損失的系統點
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
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.
CATV Network Planning Tools•Stand-alone version •Web-based version
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
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
Performance Requirements (cont’d)
Performance requirements in upstream
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)
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
Problem Decomposition and Reformulation
Part I: Steiner Tree Problemsll
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min
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Vvy
l
lLl v
in
10)14(
1)13(
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1)16(
Problem Decomposition and Reformulation (cont’d)
regular verticesSteiner vertices
Head End
User1
User2
User3
Problem Decomposition and Reformulation (cont’d)
Heuristic approximation algorithms Minimum Cost Paths Heuristic (MPH)
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Problem Decomposition and Reformulation (cont’d)
Problem Decomposition and Reformulation (cont’d)
Part II
topologycandidate given thein nodes ofset the:
topologycandidate given thein links ofset the:
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s.t.
Problem Decomposition and Reformulation (cont’d)
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Problem Decomposition and Reformulation (cont’d)
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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
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s
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VariablesDecision
PV
pV
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Problem Decomposition and Reformulation (cont’d)
WwGsMzsyspc
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pitpi
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5.0*105.0
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amplifier upstream of modulation cross :
:
tM
VariableDecision*
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
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 ,)(][
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
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
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
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
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
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
Future Research Directions
Network Planning and Management CATV network planning and optimization
Layering QoS Fault tolerance/Reliability
CATV network performance Capacity management Admission Control
Q & A