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Note for Telecommunication Network and Optimization - TNO by Abhishek Apoorv

  • Telecommunication Network and Optimization - TNO
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OPTIMIZATION TECHNIQUES IN COMMUNICATION NETWORKS 1

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TABLE OF CONTENTS page ACKNOWLEDGMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 CHAPTER 1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.1 1.2 1.3 2 OPTIMIZING NETWORK OBJECTIVES IN COLLABORATIVE CONTENT DISTRIBUTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3 Research Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Why Optimization Framework? . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 Research Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Problem Formulation and Motivation . . . . . . . . . . . . . . . . . . . . . . 2.2.1 Optimal Flow Assignment Problem . . . . . . . . . . . . . . . . . . . 2.2.2 Motivation: Performance Gain . . . . . . . . . . . . . . . . . . . . . Subgradient Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Barrier Method with Gradient Projection . . . . . . . . . . . . . . . . . . . . 2.4.1 Nonlinear Approximation of the Min-Congestion Problem with Barrier 2.4.2 Gradient Projection Algorithm . . . . . . . . . . . . . . . . . . . . . 2.4.3 Analysis of Convergence . . . . . . . . . . . . . . . . . . . . . . . . Diagonally Scaled Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.1 Ill-Conditioned Problem . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.2 Diagonally Scaled Gradient Projection Algorithm . . . . . . . . . . . 2.5.3 Asynchronous Algorithm . . . . . . . . . . . . . . . . . . . . . . . . Performance Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6.1 Gradient Projection vs. Subgradient Algorithm . . . . . . . . . . . . 2.6.2 Scaled vs. Unscaled Algorithm . . . . . . . . . . . . . . . . . . . . . Additional Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Proof of Convergence Results for the Synchronous Algorithm (Algorithm 1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 23 23 26 27 31 31 34 37 40 41 41 42 46 46 47 48 50 52 OPTIMAL PEER-TO-PEER TECHNIQUE FOR MASSIVE CONTENT DISTRIBUTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 3.1 3.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 Problem Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 3.2.1 Optimal Multicast Tree Packing . . . . . . . . . . . . . . . . . . . . . . 64 5

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3.3 3.4 3.5 3.6 3.7 3.8 4 3.2.2 Fixed Overlay Link Bandwidth . . . . . . . . . . . . . . . . . . . 3.2.3 Optimally Allocated Overlay Bandwidth . . . . . . . . . . . . . . Distributed Algorithm: Diagonally Scaled Gradient Projection . . . . . . 3.3.1 Fixed Overlay Link Bandwidth . . . . . . . . . . . . . . . . . . . 3.3.2 Optimally Allocated Overlay Bandwidth . . . . . . . . . . . . . . 3.3.3 Convergence Results . . . . . . . . . . . . . . . . . . . . . . . . Column Generation Method . . . . . . . . . . . . . . . . . . . . . . . . 3.4.1 Introduction of Column Generation Method . . . . . . . . . . . . 3.4.2 Apply the Gradient Projection Algorithm to the Restricted Problem 3.4.3 Gap between the Master Problem and the Restricted Problem . . . 3.4.4 Introduce One More Column (Tree) . . . . . . . . . . . . . . . . 3.4.5 Summary of the Algorithm . . . . . . . . . . . . . . . . . . . . . 3.4.6 Convergence Result . . . . . . . . . . . . . . . . . . . . . . . . . Practical Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5.1 Overlapping Content . . . . . . . . . . . . . . . . . . . . . . . . 3.5.2 Mixed Architecture of Fixed and Allocated Bandwidth . . . . . . 3.5.3 Network Dynamics and Churn . . . . . . . . . . . . . . . . . . . 3.5.4 Scalability and Hierarchical Partition of Sessions . . . . . . . . . 3.5.5 Asynchronous Algorithm . . . . . . . . . . . . . . . . . . . . . . Performance Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6.1 Performance Evaluation Metrics . . . . . . . . . . . . . . . . . . 3.6.2 Bottleneck at the Access Links (Profiles 1 to 4) . . . . . . . . . . 3.6.3 Bottleneck at the Internal of ISP Backbone (Profile 5) . . . . . . . 3.6.4 Bottleneck at the Cross-ISP Links (Profile 6-7) . . . . . . . . . . . 3.6.5 Introduce Trees at Varying Degree of Frequency (Profile 5) . . . . 3.6.6 Arrival and Departure Dynamics (Profile 8) . . . . . . . . . . . . Additional Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 68 69 69 77 78 81 81 82 82 84 84 85 86 86 86 87 88 88 88 89 90 92 94 96 97 97 98 A CLASS OF CROSS-LAYER OPTIMIZATION ALGORITHMS FOR PERFORMANCE AND COMPLEXITY TRADE-OFFS IN WIRELESS NETWORKS . . . . . 105 4.1 4.2 4.3 4.4 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Problem Description . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1 Network Model . . . . . . . . . . . . . . . . . . . . . . . 4.2.2 Dual of Master Problem . . . . . . . . . . . . . . . . . . . Two-Timescale Algorithm . . . . . . . . . . . . . . . . . . . . . 4.3.1 Solve Problem MP-A with the Subgradient Method . . . . 4.3.2 Update Time Fraction on a Slower Timescale . . . . . . . 4.3.3 Summary of the Two-Timescale Algorithm . . . . . . . . . Column Generation Method With Imperfect Global Scheduling . . 4.4.1 Column Generation Method . . . . . . . . . . . . . . . . . 4.4.2 Apply the Two-Timescale Algorithm to the RMP . . . . . 4.4.3 Bounding the Gap between the MP and the q th -RMP . . . 4.4.4 Introduce One More Extreme Point (Column or Schedule) . 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 107 108 110 110 111 112 117 118 118 119 120 121

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4.5 4.6 4.4.5 Column Generation by Imperfect Global Scheduling . . . . . . . . . . . . 122 Performance Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 BIOGRAPHICAL SKETCH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 7

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