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Network Planning Algorithms in CATV Networks. 博士論文計劃. Kuo-Wei Peng PhD. Student Department of Information Management National Taiwan University 6/20/2006. Outline. Introduction Problem Formulation Single-Layered Solution Procedure and Computational Experiments

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network planning algorithms in catv networks

Network Planning Algorithmsin CATV Networks

博士論文計劃

Kuo-Wei Peng

PhD. Student

Department of Information Management

National Taiwan University

6/20/2006

outline
Outline
  • Introduction
  • Problem Formulation
  • Single-Layered Solution Procedure and Computational Experiments
  • Multi-Layered Solution Procedure and Computational Experiments
  • Conclusion and Future Work
outline1
Outline
  • Introduction
  • Problem Formulation
  • Single-Layered Solution Procedure and Computational Experiments
  • Multi-Layered Solution Procedure and Computational Experiments
  • Conclusion and Future Work
introduction
Overview

Research Scope

Research Background

Introduction

Introduction of CATV Communication Networks

overview
Overview
  • 有線電視網路已經廣泛使用在各個地區。
  • 在有線電視網路上,提供雙向數位服務是可行的。
  • 有線電視網路的優點:
    • 高頻寬
    • 高覆蓋率
    • 易於擴充
  • 有線電視網路適於作為資訊基礎建設中的一部份。
overview1
Overview
  • 建構一個服務品質符合要求的有線電視網路是不容易的。
  • 政府法規再加上各類新式服務的興起,這個工作變得更複雜而不易預測。
    • 雙向服務的通訊品質如何滿足。
  • 再加上網路成本的考量,這個問題變成了一個網路最佳化問題。
overview2
Overview
  • 傳統的網路規劃方法,建構的網路品質有賴於網路規劃者的經驗
    • 必須滿足所有通訊品質的限制
    • 如何降低所需的成本
  • 本論文的目標,在以最低的成本,建構符合服務品質要求的有線電視網路。
research scope
Research Scope
  • 有線電視網路規劃問題的數學模型的建立
    • 數學模型的建立
    • 數學方程式的調整
    • 對偶問題的轉換
  • 單層網路解題程序
    • 解題程序
    • 相關參數的影響
    • 解題過程中參數的設定與調整
  • 多層網路解題程序
    • 分群演算法
    • 次層網路的頭端(下節點, drop points)的選擇演算法
research background
Research Background
  • CATV Communication Network Technology
    • Network Architecture
    • Noise-funneling effect
    • Traditional Network Planning Methods
  • Research Methods
    • Mathematical Programming
    • Geometric Programming
catv communication network technology
CATV Communication Network Technology

Figure 1-1. The Network Structure of CATV Networks

noise funneling effect
Noise Funneling Effect

Figure1-7. Noise-funnelling effect

catv network planning traditional approaches
CATV Network Planning --- Traditional Approaches
  • 製圖
  • 幹線系統設計
  • 餽線系統設計
  • 反向系統設計
slide13
幹線系統設計

Figure 1-8. 頭端幹線系統

concluding remark
Concluding Remark
  • It is difficult to design an CATV network systems
    • Intensive computational work.
    • Number of possible solutions is very large.
  • CAD tools for CATV network design
    • To help designer to reduce the overhead of computational work.
    • To track the signal quality and to make sure the end-to-end signal quality is feasible.
    • Unable to suggest or create a good design of CATV system
    • The quality of design is still relied on the experience and expertise of the designers.
research methods
Research Methods
  • Mathematical Programming
  • Geometric Programming Method
  • Steepest Descent Method
  • Enhanced Steepest Descent Method
  • Surrogate Functions
  • Projection Method
  • Integer Programming
  • Linear Relaxation
geometric programming method
Geometric Programming Method
  • Formulation of the Primal Problem
geometric programming method1
Geometric Programming Method
  • Formulation of the Dual Problem
outline2
Outline
  • Introduction
  • Problem Formulation
  • Single-Layered Solution Procedure and Computational Experiments
  • Multi-Layered Solution Procedure and Computational Experiments
  • Conclusion and Future Work
problem formulation
Problem Formulation
  • Mathematical Formulation of the CATV Network Planning Problem
  • Reformulation of the original problem
  • The Dual Problem
mathematical formulation and network optimization
Mathematical Formulation and Network Optimization
  • Basic ideas: formulate the network and try to optimize it.
performance requirements
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
problem formulation1
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 formulation2
Problem Formulation
  • Features
    • Nonlinear problems
    • Hard to solve directly by standard methods
    • Some technique needed
      • Problem Decomposition
        • Stiner Tree Problem
        • Network Optimization
      • Geometric Programming
        • Posynomial form
      • Gradient-based Optimization
reformulation of the catv network design problem
Reformulation of the CATV Network Design Problem
  • Surrogate Function
    • Surrogate function of the objective function
    • Surrogate functions of the constraints
surrogate function of the objective function
Surrogate function of the objective function
  • Original objective function
  • Surrogate function of the objective function
surrogate functions of the constraints
Surrogate functions of the constraints
  • Original Constraints for X-Mod
  • Surrogate function for X-Mod
surrogate functions of the constraints1
Surrogate functions of the constraints
  • Figure 2-2. SURROGATE FUNCTIONS OF X-MOD, CTB, AND CSO
  • Figure 2-3. Comparison of functions for X-MOD
outline3
Outline
  • Introduction
  • Problem Formulation
  • Single-Layered Solution Procedure and Computational Experiments
  • Multi-Layered Solution Procedure and Computational Experiments
  • Conclusion and Future Work
single layered solution procedure and computational experiments
Single-Layered Solution Procedure and Computational Experiments
  • Solution Procedure
  • Analysis of Starting Points
  • Analysis of Initial Step Size
  • Analysis of Computing Time
comparison of gradient methods
Comparison of Gradient Methods
  • Figure 3-2. Comparison of Solution Quality
analysis of starting points
Analysis of Starting Points
  • Figure 3-7. Comparison of starting point: network example 3.
analysis of starting points1
Analysis of Starting Points
  • Figure3-8. Comparison of starting point: data for network example 3
analysis of initial step size
Analysis of Initial Step Size
  • Figure 3-7. Comparison of starting point: network example 3.
analysis of initial step size1
Analysis of Initial Step Size
  • Figure 3-11. Comparison of initial step size: data for network example3
analysis of initial step size2
Analysis of Initial Step Size
  • Initial Step Size vs. Number of Nodes on Steiner Tree Constructed
analysis of initial step size3
Analysis of Initial Step Size
  • Initial Step Size vs. Penalty Parameter J
adjustment procedure for initial step size and penalty parameter j

Set initial step size ss=10^-k:

If #(tree)<2, k=2

Else If #(tree) < 7, k=3

Else if #(tree) < 25, k=4

Else k=6;

Set J=1;

Set J=10*J,

k=k+1,

Compute the optimal

X^2 == 0

End

Adjustment Procedure for Initial Step Size and Penalty parameter J
  • Initial Step Size vs. Number of Nodes on Steiner Tree Constructed
analysis of computing time
Analysis of Computing Time
  • Figure 3-12. Number of Network Users versus Computing Time
analysis of computing time1
Analysis of Computing Time
  • Figure 3-13. Network Size versus Computing Time
outline4
Outline
  • Introduction
  • Problem Formulation
  • Single-Layered Solution Procedure and Computational Experiments
  • Multi-Layered Solution Procedure and Computational Experiments
  • Conclusion and Future Work
multi layered solution procedure and computational experiments
Multi-Layered Solution Procedure and Computational Experiments
  • Multi-layered Solution Procedure
  • Adaptive Placement Algorithms for Drop Points
  • Conclusion
multi layered solution procedure concept
Multi-layered Solution Procedure: Concept
  • Figure 4-1. 階層式規劃:第一層
multi layered solution procedure concept cont
Multi-layered Solution Procedure: Concept (Cont.)
  • Figure 4-2. 階層式規劃:第二層
modified agglomerative hierarchical
Modified Agglomerative Hierarchical分群演算法
  • 給定:網路使用者座標,最大容忍半徑R
  • 求解:將網路使用者分群,每個使用群的半徑皆不得大於R
  • 將所有網路使用者各自為一群,此時所有使用群的半徑為0。
  • 建立一距離矩陣,記錄所有使用群間的距離。
  • 找到距離矩陣中,距離最近的二個使用群i與j。
  • 計算i與j合併後的使用群半徑為R’,比較半徑R’與R。若R’>R,則程式結束。
  • 若R’<R,則合併使用群i與j為使用群i’,並更新距離矩陣。
  • 回到步驟3.
network example for clustering
Network Example for Clustering
  • Figure 4-4. Network Example for Clustering
network example after clustering
Network Example after Clustering
  • Figure 4-5. Network Example after Clustering
adaptive placement algorithms for drop points
Adaptive Placement Algorithms for Drop Points
  • Figure 4-7. Different placement for drop points
comparison of network cost
Comparison of Network cost
  • Centroid Placement vs. Near-HE
  • No one is good for all clusters
  • Adaptive placement algorithm for drop points
    • Globally adaptive placement algorithm
    • Partially adaptive placement algorithm
global adaptive placement algorithm for drop points
Global Adaptive placement algorithm for drop points
  • 步驟一:採用分群演算法,將所有節點分成多個使用群。
  • 步驟二:以重心為下一層的下節點,計算網路的總體成本。
  • 步驟三:考慮各個使用群,以不同選取策略計算網路總體成本,選擇最低成本的選取策略為該使用群的下節點。
  • 步驟四:重複步驟三,直到所有使用群都被考慮過為止。
layer 1 network topology
Layer 1 network topology
  • Figure 4-11. Layer 1 network topology for different placement of drop points
partially adaptive placement algorithm
Partially Adaptive Placement algorithm

Partially Adaptive placement algorithm for drop points

步驟一:採用分群演算法,將所有節點分成多個使用群。

步驟二:以重心為下一層的下節點,計算網路的總體成本。

步驟三:選擇任一終端節點所代表的使用群,以不同選取策略計算網路總體成本,選擇最低成本的選取策略為該使用群的下節點。

步驟四:重複步驟三,直到所有第一層網路的終端節點都被考慮過為止。

comparison
Comparison
  • Adaptive placement is better than both Centroid-based and NearHE-based placement.
  • Global Adaptive algorithm is better than Partial Adaptive algorithm.
    • However, it spends more time.
conclusion
Conclusion
  • Multi-layered solution procedure
    • Clustering
      • To separate the large network into several small networks that can be solved by single-layered solution procedure.
    • The placement of drop points
      • Different placement algorithms for different total costs.
      • Globally adaptive and Partially adaptive
outline5
Outline
  • Introduction
  • Problem Formulation
  • Single-Layered Solution Procedure and Computational Experiments
  • Multi-Layered Solution Procedure and Computational Experiments
  • Conclusion and Future Work
conclusion and future work
Conclusion and Future Work
  • Conclusion
    • Mathematical Model
      • Mathematical formulation for the CATV network planning problem is constructed.
      • The mathematical formulation is re-formulated to conform the posynomial form.
      • By applying the Geometric Programming Method, the dual problem is formulated.
    • Single-layered solution procedure
      • Gradient-based methods
        • Steepest descent method
        • Enhanced steepest descent method
      • Initial value for dual variables
      • Initial step size
      • Adjustment procedure for Initial step size and penalty parameter J.
      • Analysis of computing time
conclusion and future work1
Conclusion and Future Work
  • Conclusion
    • Multi-layered solution procedure
      • Clustering
        • Modified agglomerative hierarchical clustering algorithm
      • Placement of drop points
        • Different placement strategy
        • Adaptive placement algorithm
          • Global adaptive
          • Partial adaptive
future work
Future Work
  • Locally adjustment of network parameters may improve the total cost of networks.
  • How to apply our work to CATV networks with more different constraints and cost structure
    • Multimedia applications
    • Network expansion problems
  • Hybrid network elements
    • Hybrid Fiber-Optical(HFC) network model
    • Other possibility.