Network Planning Algorithms in CATV Networks

1. 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

2. Outline • Introduction • Problem Formulation • Single-Layered Solution Procedure and Computational Experiments • Multi-Layered Solution Procedure and Computational Experiments • Conclusion and Future Work

3. Outline • Introduction • Problem Formulation • Single-Layered Solution Procedure and Computational Experiments • Multi-Layered Solution Procedure and Computational Experiments • Conclusion and Future Work

4. Overview Research Scope Research Background Introduction Introduction of CATV Communication Networks

5. 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。

6. 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。

7. 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。

8. 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

9. Research Background • CATV Communication Network Technology • Network Architecture • Noise-funneling effect • Traditional Network Planning Methods • Research Methods • Mathematical Programming • Geometric Programming

10. CATV Communication Network Technology Figure 1-1. The Network Structure of CATV Networks

11. Noise Funneling Effect Figure1-7. Noise-funnelling effect

12. 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

13. 幹線系統設計 Figure 1-8. 頭端幹線系統

14. 餽線系統設計 • Figure 1-9

15. 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.

16. Research Methods • Mathematical Programming • Geometric Programming Method • Steepest Descent Method • Enhanced Steepest Descent Method • Surrogate Functions • Projection Method • Integer Programming • Linear Relaxation

17. Geometric Programming Method • Formulation of the Primal Problem

18. Geometric Programming Method • Formulation of the Dual Problem

19. Outline • Introduction • Problem Formulation • Single-Layered Solution Procedure and Computational Experiments • Multi-Layered Solution Procedure and Computational Experiments • Conclusion and Future Work

20. Problem Formulation • Mathematical Formulation of the CATV Network Planning Problem • Reformulation of the original problem • The Dual Problem

21. Mathematical Formulation and Network Optimization • Basic ideas: formulate the network and try to optimize it.

22. 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

23. 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)

24. 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

25. Reformulation of the CATV Network Design Problem • Surrogate Function • Surrogate function of the objective function • Surrogate functions of the constraints

26. Surrogate function of the objective function • Original objective function • Surrogate function of the objective function

27. Surrogate functions of the constraints • Original Constraints for X-Mod • Surrogate function for X-Mod

28. 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

29. Outline • Introduction • Problem Formulation • Single-Layered Solution Procedure and Computational Experiments • Multi-Layered Solution Procedure and Computational Experiments • Conclusion and Future Work

30. Single-Layered Solution Procedure and Computational Experiments • Solution Procedure • Analysis of Starting Points • Analysis of Initial Step Size • Analysis of Computing Time

31. Solution Procedure

32. The Penalty Function Where

33. Comparison of Gradient Methods • Figure 3-2. Comparison of Solution Quality

34. Analysis of Starting Points • Figure 3-7. Comparison of starting point: network example 3.

35. Analysis of Starting Points • Figure3-8. Comparison of starting point: data for network example 3

36. Analysis of Initial Step Size • Figure 3-7. Comparison of starting point: network example 3.

37. Analysis of Initial Step Size • Figure 3-11. Comparison of initial step size: data for network example3

38. Analysis of Initial Step Size • Initial Step Size vs. Number of Nodes on Steiner Tree Constructed

39. Analysis of Initial Step Size • Initial Step Size vs. Penalty Parameter J

40. 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

41. Analysis of Computing Time • Figure 3-12. Number of Network Users versus Computing Time

42. Analysis of Computing Time • Figure 3-13. Network Size versus Computing Time

43. Outline • Introduction • Problem Formulation • Single-Layered Solution Procedure and Computational Experiments • Multi-Layered Solution Procedure and Computational Experiments • Conclusion and Future Work

44. Multi-Layered Solution Procedure and Computational Experiments • Multi-layered Solution Procedure • Adaptive Placement Algorithms for Drop Points • Conclusion

45. Multi-layered Solution Procedure: Concept • Figure 4-1. 階層式規劃：第一層

46. Multi-layered Solution Procedure: Concept (Cont.) • Figure 4-2. 階層式規劃：第二層

47. 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.

48. Network Example for Clustering • Figure 4-4. Network Example for Clustering

49. Network Example after Clustering • Figure 4-5. Network Example after Clustering

50. Adaptive Placement Algorithms for Drop Points • Figure 4-7. Different placement for drop points