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研究生： 謝明益
Ming-I Hsieh
論文名稱： 對應IP網路上的既時群播演算法
Algorithms to Real-time Multicast Applications over IP Network
指導教授： 吳曉光
Hsiao-Kuang Wu
口試委員:
學位類別： 博士
Doctor
系所名稱： 資訊電機學院 - 資訊工程學系
Department of Computer Science & Information Engineering
畢業學年度： 95
語文別： 英文
論文頁數： 155
中文關鍵詞： 既時 、群播演算法
外文關鍵詞： Multicast, ADSL Downlink, Fair Queuing, Steiner Tree
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    • 近十年來, 人們之間溝通的方式隨著科技的進步迅速地改變中. 隨著快速成長且便宜化的網路頻寬及無線網路的普及, 人們之間溝通的快速地從早期昂貴具特制的設備及架構, 如 H323及PSTN, 移向便宜且通用的架構, 如IP及VoIP. 特別是在peer-to-peer(P2P)架構的想法在提出及普及化後. 隨著更新且便宜的網路架構, 目前一部份幾乎免費的溝通方式己經實現在人們的生活中. 然而在新的架構上, 依然有許多的問題隨著新的架構而出現. 特別是當這類型的網路頻寛是被多種應用同時分享, 在對於每個應用的品質保證上會無法保證且影響到一部份應用的運行. 特別是既時性應用程式無法在long-delay的網路上運作, 這將會造成這類的應用在實現上的困難. 除此之外, 在新型態的P2P架構中, 節點的運作能力將比之前標準的IP network來的多且其頻寛在其運算能力下, 相對地就比較少. 在這方面, 如果有效地利用其特性來轉送封包將會是這類應用服務的另一個難題. 在這篇博士論文中, 作者將專注在這方面的問題來解決提供既時群播應用服務所遇到的部份問題. 在服務品質部份, 由於大多傳輸的瓶頸發生在last-mile(最後一哩的網路), 在這方面我們提供了postgate, LLEPS及QGPS來在無ISP支援的情況下, 保證其封包可以快速地傳輸以提高其服務的品質. 在另一方面, 群播, 作者提供了一個更有效率的演算法以在有限地時間內找出更有效率的傳輸路徑. 基於我們結果, 相信一個便宜且可行的既時群播服務應是可以在現有的IP網路上實現.

    In recent ten years, the communication between people are acculturated quickly. With the rapidly growth and cheaper of network bandwidth and wireless access, the communication was being moved gradually from the dedicated and expensive architecture, e.g. H323 and PSTN switch, to the common and cheaper ones, e.g. IP and VoIP. Especially, the notion of peer-to-peer(P2P) architecure was addressed and become popular in the applications of file distributions and voice communications. With the new cheaper network access and architectures, some almost-free communications between humans are available today. However, in this moment some problems were also incurred from new architectures. Since the cheaper bandwidth are shared and may be used by many applications in the same time, the quality of service for each application is not guaranteed by the service provider. Since the real-time applications could not be able over the long-delay network, it would be a challenge to such applications. Besides, the node in new P2P architecture would obtain more computing power and less bandwidth compared with the traditional PSTN switch. Hence, how to route and forward the packets from the source node to the multiple destinations would be another challenge to provide a real-time multicast services on such network. In this dissertation, the author focuses this issue that supports the real-time multicast applications over Internet. In the quality of service issue, since the bottleneck nodes are located at last-mile in most cases, we provide our solutions, postgate, LLEPS, and QGPS, to guarantee the delay and jitter for the real-time packets without ISP supports. In another issue, multicast delivery, we provide an efficient multicast algorithm which could find out a low cost distribution tree to delivery packets in an acceptable time. Based on our results, a cheap and feasible multicast real-time application should be possible over current Internet.

    1 Introduction 1 1.1 Quality of Service and Fair Queueing . . . . . . . . . . . . . . . . . 4 1.2 Multicast Routing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.3 Organization of this Dissertation . . . . . . . . . . . . . . . . . . . 15 2 Related Work and Background Knowledge 17 2.1 Bandwidth Management for ADSL Downlink . . . . . . . . . . . . . 18 2.1.1 Partition solution (…xed rate solution) . . . . . . . . . . . . 19 2.1.2 Weighted fair queueing solution . . . . . . . . . . . . . . . . 20 2.2 Fair Queueing Algorithms . . . . . . . . . . . . . . . . . . . . . . . 20 2.2.1 General Processor Sharing (GPS) . . . . . . . . . . . . . . . 21 2.2.2 Weighted Fair Queueing (WFQ) . . . . . . . . . . . . . . . . 22 2.2.3 Delay Optimized Worst Case Fair WFQ (WF2Q) Packet Scheduling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.2.4 Low Latency Queueing (LLQ) . . . . . . . . . . . . . . . . . 25 2.2.5 De…cit Round Robin (DRR) /Nested De…cit Round Robin (NDRR) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.2.6 A Dynamic Regulation and Scheduling Scheme for Real- Time Tra￠ c Management (RCSP) . . . . . . . . . . . . . . 27 2.3 Analysis for Alignment Problem of Virtual Time . . . . . . . . . . . 27 2.3.1 Generalize Processor Sharing (GPS) . . . . . . . . . . . . . . 28 2.3.2 Low Bound of Computational Complexity . . . . . . . . . . 31 2.3.3 L-GPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 2.4 Directed Steiner Tree Problem . . . . . . . . . . . . . . . . . . . . . 35 2.4.1 TM Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . 36 2.4.2 Charikar et al’s algorithm . . . . . . . . . . . . . . . . . . . 41 2.4.3 Roos’algorithm . . . . . . . . . . . . . . . . . . . . . . . . . 43 I Quality of Service 47 3 ADSL downlink bandwidth management 49 3.1 Postgate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 3.1.1 Throughput estimation . . . . . . . . . . . . . . . . . . . . . 50 3.1.2 Weight estimation . . . . . . . . . . . . . . . . . . . . . . . . 52 3.2 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 3.2.1 Queueing delay and throughput . . . . . . . . . . . . . . . . 56 3.2.2 Bandwidth, burst index and weight of each class . . . . . . . 59 3.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 4 Scheduler for Real-time Application 63 4.1 The Bu¤er Underrun Problem . . . . . . . . . . . . . . . . . . . . . 64 4.2 Detailed Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 4.3 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 4.3.1 Bandwidth Reservation . . . . . . . . . . . . . . . . . . . . . 73 4.3.2 Queueing Delay Comparison of LLEPS, SFQ, SCFQ,WF2Q+... 74 4.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 5 Analysis for the Alignment Problem of Virtual Time 79 5.1 QGPS: Virtual Time Function and Algorithm . . . . . . . . . . . . 79 5.1.1 Virtual Time Function . . . . . . . . . . . . . . . . . . . . . 80 5.1.2 An algorithm to …nd out the backlogged set in (log n) times 83 5.2 QGPS: Practical Issues and Solutions . . . . . . . . . . . . . . . . . 86 5.2.1 How many bits does a timestamp require? . . . . . . . . . . 87 5.2.2 Fairness and relative deviation . . . . . . . . . . . . . . . . . 91 5.2.3 Bits requirements . . . . . . . . . . . . . . . . . . . . . . . . 95 5.2.4 A Practicable GPS Simulator . . . . . . . . . . . . . . . . . 100 5.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 II Multicast Routing 109 6 Solutions for the Multicast Distribution Tree 111 6.1 FasterDSP Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . 111 6.1.1 approximation guarantee of the l-restricted Steiner tree . . . 112 6.1.2 Select operator and special graph H . . . . . . . . . . . . . . 117 6.1.3 algorithm to construct a FasterDSP tree . . . . . . . . . . . 118 6.1.4 Approximation Guarantee for 2-level Steiner tree of FasterDSP120 6.2 Algorithm Detail . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 6.2.1 FasterDSP Vertices Function . . . . . . . . . . . . . . . . . . 122 6.2.2 FasterDSP Forest Function . . . . . . . . . . . . . . . . . . . 123 6.2.3 FasterDSPTree Function . . . . . . . . . . . . . . . . . . . . 125 6.2.4 Analysis for Time Complexity and Space Complexity . . . . 126 6.3 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 6.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 7 Conclusion 131 References 133

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