中文摘要

在大型分散記憶體多重處理器中，通訊延遲已經成為整個系統的效能瓶頸，而路由器的設計為影響通訊效能最主要的因素，在中等以上的通訊量情況下，因壅塞而造成的排隊延遲可以大量地增加通訊延遲。

我們的研究已提出一種廣域階層式適應性路由方法，此方法能針對網狀網路系統整體交通狀態做動態評量，並依此評量之系統整體交通狀態，做降低壅塞程度的路由選擇，因而改進在中高通訊量時的通訊延遲。此方法採取對網狀網路作階層式切割，以便利作不同範圍層級的交通狀況評量與路由選取。為了有效運用評量之交通狀況於避免壅塞的路由選取。此方法包含了兩種細部路由(self-routing)方法：環視路由(look-around routing)方法與平行近似迷宮路由(parallel approximate maze routing)方法，以用於合適範圍層級上避開壅塞區域的路由選取。

在此論文研究中，我們著重對此廣域階層路由器設計應用於網狀網路的通訊效能評估。我們設計了此系統的模擬軟體，並且規劃了不同均勻程度的通訊模式產生方式，以測試此方法與最短路由及適應性路由方法在不同情況下對降低壅塞的路由能力，並測得通訊效能的比較。由實驗得知，此路由方法由於能有效改進整體壅塞情況，因而能在中高交通量時，有顯著之通訊效能改進。

Abstract
In large-scale distributed multiprocessor systems, communication delay becomes the bottleneck of system performance. A main factor which affects communication delay is the adopted routing method and the router design light traffic, the queuing delay can be increased drastically due to message congestion.

We have developed a hierarchical globally adaptive routing method. The method can poll global traffic status. According to the traffic status, it can select a routing path congestion which can alleviate. Therefore, the queuing delay due to congestion can be reduces significantly non-light traffic globally. We also developed two detail routing methods applied at different hierarchical routing levels：the look around routing method and the parallel approximate maze routing method. They can avoid selecting a routing path via congested regions as much as possible.

In this research, we designed a performance simulator of the globally adaptive mesh router. We also provided a traffic with the different levels of non-uniform traffic distribution. We utilized the performance simulator to exercise minimal routing, adaptive routing and our globally adaptive routing methods. The experiment results show that our globally adaptive method obtains significant performance improvement in non-light traffic.

Contents
1 Introduction --------------------------------------------------------------------------------1
1-1 Overview of Parallel Computer Routing-----------------------------------------1
1-2 Research Motivation----------------------------------------------------------------4
1-3 Organization of the Thesis---------------------------------------------------------5

2 Backupground------------------------------------------------------------------------------6
2-1 Basic types of data routing faults--------------------------------------------------6
2-2 Dynamically Allocated Multi-Queue----------------------------------------------9
2-3 General Routing Method-----------------------------------------------------------10
2-4 Central Buffer for Deadlock Free-------------------------------------------------13

3 The Globally Adaptive Mesh Router Design
3-1 The Basic Architecture of The Globally Adaptive Router ------------------ 17
3-2 Hierarchical Routing Structure---------------------------------------------------19
3-3 Dynamical Traffic Polling in the Hierarchical Routing Structure-----------21
3-4 The Hierarchical Globally Adaptive Routing Method -----------------------25
3-5 The Look-Around Routing Method --------------------------------------------28
3-6 The Parallel Approximate Maze Routing Method ---------------------------30

4 The Design of performance Evaluation Experiment ------------------------------39
4-1 Simulator Designs-----------------------------------------------------------------40
4-2 Multiple Pseudo Random Number Generation -------------------------------43
4-3 Performance Metric and Measurement Method ------------------------------45
4-4 Measurement of a Non-uniformness Degree Metrics------------------------47
4-5 Experimented Result -------------------------------------------------------------50
4-6 Result Analysis -------------------------------------------------------------------60

5 Conclusion -----------------------------------------------------------------------------69

Bibliography ---------------------------------------------------------------------------------70

Bibliography
[1] T. Lee, "A Mesh Routing Method for SPMD Communication", Tech. Rep. No 99-02, CAD Lab., Dept. of Electrical Eng., Nat'l Sun Yat-Sen Univ., Kao-Hsiung, Taiwan,R.O.C., 1999.
[2] T. Lee, "A Congestion-Controlled Adaptive Routing Method", Tech. Rep. CAD-98-01, Dep. of Electrical Eng., Nat'l Sun Yat-Sen Univ., Kao-Hsiung, Taiwan, R.O.C., 1998.
[3] T. Lee, "A Hierarchical Globally Adaptive Mesh Routing Method", Tech. Rep.CAD-00-01, Dep. of Electrical Eng., Nat'l Sun Yat-Sen Univ., Kao-Hsiung, Taiwan, R.O.C., 2000.
[1] Kai Hwang,. Advanced Computer Architecture：Parallelism, Scalability, Programmability. McGraw-Hill, 1993
[5] J. Upadhyay, et al., "A Traffic -Balanced Adaptive Wormhole Routing Scheme for Two-Dimensional Meshes," in IEEE Trans. Computers,Vol. 46, No. 2, Feb. 1997
[6] P. Kermani and L. Kleinrock, "Virtual Cut-Through: A New Communication Switching Technique," in Computer Networks, Vol. 3, No. 4, 1979
[7] T. Nesson, et al., "RIMM Routing: A Class of Efficient Minimal Routing Algorithms, "in Parallel Computer Routing and Communication, Springer-Verlag, 1991
[8] Q. P. Gu and J. Gu, "Two Packet Routing Algorithms on the Mesh-connected Computer," IEEE Trans. On Parallel and Distributed Systems, Vol. 6, No. 4, pp436-440, Apr. 1995
[9] D. Chinn, "The Performance of Adaptive Routers on Worst Case Permutation," IEEE Trans. On Parallel and Distributed Systems, Vol. 9, No. 5, pp 60-71, May 1998
[10] Tamir, Y. and G. L. Frazier. "Dynamicall-Allocated multi-queue buffers for VLSI communication switches". IEEE Trans. On Comput., vol. 41, no.6, pp725-737,June 1992.
[11] STUNKEL, C. B., SHEA, D. G., ABALI,B.,ETAL. The SP2 High-Performance Switch. IBM System Jounal 34,2(1995), 185-204.
[12] Y. W. Lu, Efficient Multiprocessor Communications: Networks, Algorithms, Simulation, and Implementation.. Computer System Laboratory, Dep. Of Electrical Engineering Stanford Univ. CA 94305.
[13] Gregory Lee Frazier, Buffering and Flow Control in Communication Switches for Scalable Multicomputers,. Univ. of California,. Los Angeles.
[14] Emilio Leonardi, Fabio Neri, Politecnico di Torino, Mario Gerla and Prasasth Palnati, "Congestion Control Techniques in Asynchronous Wormhole Routing Networks",. IEEE Communication Magazine, Nov. 1996, pp. 59-69.
[15] Jennifer Rexford and Kang G. Shin,. Support for Multiple Classes of Traffic in Multicomputer Routers,. Real-Time Computing Laboratory Department of Electrical Engineering and Computer Science,. Univ. of Michigan.
[16] Hsing-Lung Chen and Han-Shing Yihng,. Generalized Wormhole Routing Strategies in Hypercubes,. Department of Electronic Enginerring,. National Taiwan Institute of Technology.
[17] S. Konstantinidou On the Effect of Queue Size and Channel Scheduling Policies in the Segment Router,. IBM T.J. Watson Research Center Route 134 Yorktown Heights, NY 10598
[18] Craig B. Stunkel, Rajeev Sivaram, Dhabaleswa K. Panda,. Implementing Multidestination Worms in switch-Based Parallel Systems: Architectural Alternatives and their Impact.
[19] Wu-chang Feng and Kang G. Shin,. Impact of Selection Functions on Routing Algorithm Performance in Multicomputer Networks,. Real-Time Computing Laboratory,. Department of Electrical Engineering and Computer Science, Univ. of Michigan.
[20] Ted Nesson and Lennart Johnsson,. ROMM Routing : A Class of Efficient Minimal Routing Algorithms,. Harvard University, Cambridge, MA 02138, USA. Tinking Machines Corporation, 245 First Street, Cambridge, MA 02142, USA.
[21] Jose Duato A New Theory of Deadlock-Free Adaptive Routing in Wormhole Networks,. Department of Ingenieria.
[22] Christian Roche, Parsasth Palnati, Mario Gerla,. Performance of Congestion Mechanisms in Wormhole Routing Networks. UCLA Computer Science Dept.
[23] Timothy Mark Pinkston,. Sugath Warnakulasuriya,. On Deadlocks in Interconnection Networks. EE-System Dept., University of Southern California, Los Angeles, CA 90089-2562.
[24] Chi-Ming Chiang and Lionel M. Ni,. Multi-Address Encoding for Multicast,. Department of Computer Science, Michigan State University.
[25] Dhabaleswar K. Panda, Sanjay Singal, and Pradeep Prabhakaran,. Multidestination Message Passing Mechanism Conforming to Base Wormhole Routing Scheme,. Depart. Of Computer and Information Science.
[26] Wu-chang Feng, Jennifer Rexford, Stuart Daniel, Ashish Mehra, and Kang Shin,. Tailoring Routing and Switching Schemes to Application Workloads in Multicomputer Networks. Real-Time Computing Laboratory Department of Electrical Engineering and Computer Science. Univ. of Michigan.
[27] Arne Folkestad, Christian Roche,. Deadlock Probability in Unrestricted Wormhole Routing Networks. Dept. of Telematics, Norweigian University of Science and Technology. UCLA Computer Science Dept. 3732H Boelter Hall Los Angeles.
[28] J.W. Dolter, P. Ramanathan, and K.G. Shin A Microprogrammable VLSI Routing Controller for HARTS. Real-Time Computing Laboratory Department of Electrical Engineering and Computer Science. Univ. of Michigan.