即時與非即時分散式系統容錯能力之研究｜國立清華大學博碩士論文庫

簡易檢索 / 詳目顯示

回結果列表

研究生：	黃珮琪
論文名稱：	即時與非即時分散式系統容錯能力之研究 The Study of k-fault Tolerance Issues on Real-time/Non-real-time Distributed Systems
指導教授：	石維寬
口試委員:	石維寬陳朝欽賴尚宏呂政修衛信文
學位類別：	博士 Doctor
系所名稱：	電機資訊學院 - 資訊工程學系 Computer Science
論文出版年：	2012
畢業學年度：	100
語文別：	英文
論文頁數：	102
中文關鍵詞：	分散式系統、即時排程、容錯能力
相關次數：	點閱：3 下載：0
分享至:	分享至facebook 分享至twitter

查詢本校圖書館目錄查詢臺灣博碩士論文知識加值系統勘誤回報

即時系統像是多媒體系統與嵌入式系統非常普遍出現在許多應用，有許多專家研究如何將其技術延伸應用於多核心處理器的即時系統上，但對於這樣的系統，主要的挑戰之一在於在許多工作同時進行時，如何設計一個好的排程演算法使得所有的工作都可以在時間的限制內如期完成，因此，一些特殊應用系統是可以准許有些許短暫的錯誤發生，這樣的系統稱之為k-fault tolerant模式。不管何時任何錯誤被偵測後，系統會進入復原機制，因此，這些額外的復原工作也必須和目前的所有工作一起做排程，同樣因仍必須在規定時間限制內完成，增加對其問題的複雜度。
本論文首先探討的就是在k-fault tolerant系統下，如何改善提升這系統的效能，並利用EDF(Earliest Deadline First) 發展出一套可行性檢查演算法，結果顯示此演算法的確有大大的提升效能。本論文的第二部分，若將此系統應用在多核心處理器系統下，可將問題定義成undirected graph問題，即每個處理器可對應成一個vertex，在兩兩成對的處理器之間有可用的溝通頻道可對應成一條edge，此問題可被定義成Connectivity Augmentation problem，本論文首先探討 bipartite graphs，指的是在這graph中只會有兩個不同的群組，在不同的群組中可加上edge，但先決條件就是所加的edge數一定要是最少的，再者，將問題複雜化，假設有k種不同的群組，但仍必須要在不同的群組中加上edge，同樣地所加上的edge數仍然要最少。對於兩者，我們分別提出了一系列的演算法和證明，經由我們的證明可得知，提出的演算法加得edge數是optimal最少的，同時也可以滿足對所有的vertex而言，即使少掉一個溝通頻道edge，仍然可以互相傳遞訊息。

Real-time systems such as multimedia systems and embedded systems are appearing in many applications. Many researchers have been extensively working on multiprocessor real-time systems. The main challenge for these systems is to design a scheduling algorithm for the task system T such that all tasks in T can meet their timing constraints. In some applications, task systems allow few transient faults. This kind of task systems is characterized by the “k-fault tolerant” model. Whenever a fault is detected, the system enters the recovery mode. Some extra recovery tasks must be scheduled and finished before the deadline of the current task. In this dissertation, first, we have done research to improve the performance of the systems, and develop a feasible-checking algorithm for k-fault tolerant systems under the “Earliest Deadline First” schedule. Also, a multiprocessor system can be modeled as an undirected graph G; each processor corresponds to the vertex and each communication channel available between pairs of processors corresponds to the edge. Therefore, second, we propose a number of simple algorithms for solving connectivity augmentation problem related to bipartite graphs. In these algorithms, we add a set of edges with the smallest possible cardinality so that the resulting graph is 2-edge-connected. Third, the vertices of a graph G are partitioned into k groups by adding the smallest number of edges to G such that the resulting graph is 2-vertex connected. The above augmentation problems are solved in linear time in the size of the input graph.

Acknowledgments : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : iii
Abstract : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : iv
List of Tables : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : ix
List of Figures : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : x
Introduction : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 1
1. Real-time Distributed Systems . . . . . . . . . . . . . . . . . . . . . . . . 2
2. Non-real-time Distributed Systems . . . . . . . . . . . . . . . . . . . . . . 3
3. Organization of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . 4
k-fault Tolerance for Real-time Distributed Systems under the “Earliest Deadline
First” Schedule : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 5
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2. Model and Notations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
3. The Dominating Task . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
4. Feasibility Test for a Task System Under any Fault Pattern . . . . . . . . . 10
5. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
vi
k-fault Tolerance for Real-time Disk Scheduling Problem : : : : : : : : : : : 13
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2. Problem Descriptions and Definitions . . . . . . . . . . . . . . . . . . . . 14
2.1. Disk Service Model in a Real-time Multimedia Environment . . . . 14
2.2. Real-time Disk-scheduling Problem . . . . . . . . . . . . . . . . . 15
3. Related Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
4. NP-complete Proof of the General Disk-scheduling Problem with Linear
Seek-cost Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4.1. Problem Definition . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4.2. The NP-hardness Proof . . . . . . . . . . . . . . . . . . . . . . . . 18
5. Real-time Disk-scheduling Algorithm . . . . . . . . . . . . . . . . . . . . 20
5.1. The Basic Approach: EDF-SCAN . . . . . . . . . . . . . . . . . . 20
5.2. Shortest-Task-First-DM (STF-DM) . . . . . . . . . . . . . . . . . 23
5.3. Speed up Shortest-Task-First-DM (SSTFDM) . . . . . . . . . . . . 23
6. Performance Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
6.1. Experimental Environment . . . . . . . . . . . . . . . . . . . . . . 24
6.2. The Minimum, the Maximum, and the Average Schedule Fulfill-time 25
6.3. Number of Supported Real-time Tasks . . . . . . . . . . . . . . . . 26
7. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
k-fault Tolerance for Non-real-time Distributed Systems with a Bipartite Augmentation
Problem : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 27
1. Related Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2. Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3. Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.1. Graph-theoretical Definitions . . . . . . . . . . . . . . . . . . . . . 30
3.2. Block Forests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
vii
4. Case 1: When BB(G) is a tree . . . . . . . . . . . . . . . . . . . . . . . . 35
4.1. Lower bound on aug2e(BB(G)) . . . . . . . . . . . . . . . . . . . 35
4.2. Case 1.1: When BB(G) is an easy tree . . . . . . . . . . . . . . . . 36
4.3. Case 1.2: When BB(G) is a general tree . . . . . . . . . . . . . . . 42
5. Case 2: When BB(G) is a forest . . . . . . . . . . . . . . . . . . . . . . . 44
5.1. Case 2.1: When BB(G) contains no isolated vertices . . . . . . . . 45
5.2. Case 2.2: When BB(G) contains isolated vertices . . . . . . . . . . 52
6. Componentwise 2-edge-connectivity Augmentation . . . . . . . . . . . . . 56
k-fault Tolerance for Non-real-time Distributed Systems with with a Partition
Augmentation Problem : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 58
1. Lower Bound on jaug2v(BT(G))j . . . . . . . . . . . . . . . . . . . . . . 58
2. Recolor Vertices of Degree < 2 with Three Colors . . . . . . . . . . . . . . 60
2.1. BT(G) is Color-saturated . . . . . . . . . . . . . . . . . . . . . . 60
2.2. BT(G) is Color-safe . . . . . . . . . . . . . . . . . . . . . . . . . 61
3. BT(G) Is Color-safe with 3 Colors among Vertices of degree < 2 . . . . . 65
3.1. BT(G) is Set-saturated . . . . . . . . . . . . . . . . . . . . . . . . 66
3.2. BT(G) is Set-safe . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4. Adding Edges to Make a Forest into a Tree . . . . . . . . . . . . . . . . . 87
4.1. High-level Description of the Algorithm . . . . . . . . . . . . . . . 87
4.2. Finding a Valid Pair . . . . . . . . . . . . . . . . . . . . . . . . . 88
4.3. Implementation Issues and Time Complexity . . . . . . . . . . . . 90
4.4. Proof of Correctness . . . . . . . . . . . . . . . . . . . . . . . . . 92
Conclusion : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 94
Bibliography : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 96
                                

[1] C. Krishna and K. Shin., “On scheduling tasks with a quick recovery from failure.,” IEEE Trans. Computers, vol. 35, no. 5, pp. 448–455, 1986.
[2] A. Liestman and R. Campbell., “A fault-tolerant scheduling problem.,” IEEE Trans. Software Eng., vol. 12, no. 11, pp. 1,089–1,095, 1986.
[3] R. M. F. Liberato, S. Lauzac and D. Moss´e., “Global fault tolerant real-time scheduling on multiprocessors.,” in Proceedings of the Euromicro Conf. Real-Time Systems, 1999.
[4] R. M. S. Ghosh and D. Moss´e., “Fault-tolerance through scheduling of aperiodic tasks in hard real-time multiprocessor systems.,” IEEE Trans. Parallel and Distributed Systems, vol. 8, no. 3, pp. 272–284, 1997.
[5] R. M. S. Ghosh and D. Moss´e., “Fault-tolerant scheduling on a hard real-time multiprocessor
system.,” in Proceedings of the 16th IEEE Real-Time Systems Symposium, 1994.
[6] R. M. S.Ghosh and D. Moss´e., “Enhancing real-time schedules to transient faults.,” in Proceedings of the 16th IEEE Real-Time Systems Symposium, 1995.
[7] R. M. F. Liberato and D. Moss´e., “Tolerance to multiple transient faults for aperiodic tasks in hard real-time systems,” IEEE Trans. Computers, vol. 49, no. 9, 2000.
[8] S. M. X. Castillo and D. Siewiorek., “Derivation and caliberation of a transient error reliability model.,” IEEE Trans. Computers, vol. 31, no. 7, pp. 658–671, 1982.
[9] K. P. Eswaran and R. E. Tarjan., “Augmentation problems.,” SIAM Journal on Computing, vol. 5, pp. 653–665, 1976.
[10] T. sheng Hsu., “Undirected vertex-connectivity structure and smallest four-vertexconnectivity augmentation (extended abstract).,” in Lecture Notes in Computer Science
1004: Proceedings of the 6th International Symposium on Algorithms and Computation (J. Staples, ed.), (New York, NY), pp. 274–283, Springer-Verlag, 1995.
[11] T. sheng Hsu., “On four-connecting a triconnected graph.,” Journal of Algorithms, vol. 35, pp. 202–234, 2000.
[12] T. sheng Hsu., “Simpler and faster vertex-connectivity augmentation algorithms (extended abstract).,” in Lecture Notes in Computer Science 1879: Proceedings of the 8th
European Symposium on Algorithms (M. Paterson, ed.), (New York, NY), pp. 278–289, Springer-Verlag, 2000.
[13] T. sheng Hsu., “Simpler and faster biconnectivity augmentation.,” Journal of Algorithms, vol. 45(1), pp. 55–71, 2002.
[14] T. sheng Hsu. and M. Y. Kao., “Optimal augmentation for bipartite componentwise biconnectivity in linear time.,” SIAM Journal on Discrete Mathematics, vol. 19(2), pp. 345–362, 2005.
[15] T. sheng Hsu. and V. Ramachandran., “On finding a smallest augmentation to biconnect a graph.,” SIAM Journal on Computing, vol. 22, pp. 889–912, 1993.
[16] A. Rosenthal and A. Goldner., “Smallest augmentations to biconnect a graph.,” SIAM Journal on Computing, vol. 6, pp. 55–66, 1977.
[17] A. N. Toshimasa Watanabe, “A minimum 3-connectivity augmentation of a graph.,” Journal of Computer and System Sciences, vol. 46, pp. 91–128, 1993.
[18] J. L. W.K. Shih and J. Chung., “Fast algorithms for scheduling imprecise computationss.,” in Proceedings of the Real-Time Systems Symposium, pp. 12–19, 1989.
[19] J. W.-S. L. W. K. Shih, “On-line scheduling of imprecise computations to minimize error.,” SIAM J. Computing, vol. 25, no. 5, pp. 1105–1121, 1996.
[20] D. K. P. R. D.J. Gemmell, H.M. Vin, “Multimedia storage servers: a tutorial,” IEEE Computer, vol. 28, no. 5, pp. 40–49, 1995.
[21] D. S. A. Dan and P. Shahabuddin., “Scheduling policies for an on-demand video server with batching.,” in Proceedings of the 2nd ACM Multimedia Conference, pp. 5–22,
1994.
[22] D. Gemmell and S. Christodoulakis., “Principles of delay sensitive multimedia data storage and retrieval.,” ACM Trans. on Information Systems, vol. 10, no. 1, pp. 51–90,
1992.
[23] R. Steinmetz., “Multimedia file systems survey: approaches for continuous media disk scheduling.,” Computer Communication, vol. 18, no. 3, pp. 133–144, 1995.
[24] J. Lehoczky., “Fixed priority scheduling of periodic task sets with arbitrary deadlines.,” in Proceedings of the 11th IEEE Real-Time Systems Symposium, pp. 201–212, 1990.
[25] A. Reddy and J.Wyllie., “I/o issues in a multimedia system.,” IEEE Computer, vol. 27, no. 3, pp. 69–76, 1994.
[26] W. S. H.P. Chang, R.I. Chang and R. Chang., “Enlarged-maximum-scannable-groups for real-time disk scheduling in a multimedia system.,” in Proceedings of the 24th IEEE International Computer Software and Application Conference (COMPSAC), pp. 383–388, 2000.
[27] D. S. K. Jellay and C. Martel., “On nonpreemptive scheduling of periodic and sporadic tasks.,” in Proceedings of the 12th IEEE Real-Time Systems Symposium, pp. 129–139, 1991.
[28] C.Wong., “Minimizing expected head movement in one dimension and two dimensions mass storage system.,” Computer Survey, vol. 12, no. 2, pp. 167–178, 1980.
[29] M. B. M. Andrews and L. Zhang., “New algorithms for the disk scheduling problem.,” in Proceedings of the 37th Annual Symposium on Foundations of Computer Science, p. 500, 1996.
[30] P. Denning., “Effects of scheduling on file memory operations.,” in Proceedings of the AFIPS SJCC, pp. 9–21, 1967.
[31] T. Chen andW. Yang., “Amortized analysis of disk scheduling algorithm v (r).,” Journal of Information Science and Engineering, vol. 8, no. 2, pp. 223–242, 1992.
[32] A. Reddy and J.Wyllie., “Disk scheduling in a multimedia i/ o system.,” in Proceedings of the 1st ACM Multimedia Conference, pp. 225–233, 1993.
[33] R. I. C. M. C. C. J. M. H. Y. C.Wang, S. L. Tsao and M. T. Ko., “A fast data placement scheme for video server with zoned-disks.,” in Proceedings of the SPIE VVDC, pp. 92–102, 1997.
[34] P. C. Huang, H. W. Wei, W. C. Lu, W. K. Shih, and T. sheng Hsu., “Smallest bipartite bridge-connectivity augmentation.,” Algorithmica, vol. 54(3), pp. 353–378, 2009.
[35] J. B. Jensen, H. N. Gabow, T. Jordan, and Z. Szigeti., “Edge-connectivity augmentation with partition constraints.,” SIAM Journal on Discrete Mathematics, vol. 12, pp. 160–207, 1999.
[36] A. Frank., “Connectivity augmentation problems in network design.,” in Mathematical Programming: State of the Art 1994 (J. R. Birge and K. G. Murty., eds.), pp. 34–63,
The University of Michigan, 1994.
[37] T. sheng Hsu., Graph Augmentation and Related Problems: Theory and Practice. PhD thesis, University of Texas at Austin, 1993.
[38] G. Kant., Algorithms for Drawing Planar Graphs. PhD thesis, Utrecht University, the Netherlands, 1993.
[39] H. Nagamochi., “Recent development of graph connectivity augmentation algorithms.,” IEICE Transactions on Information and System, vol. E83-D, pp. 372–383, 2000.
[40] M. Y. Kao., “Linear-time optimal augmentation for componentwise bipartitecompleteness of graphs.,” Information Processing Letters, vol. 54, pp. 59–63, 1995.
[41] N. R. Adam and J. C.Wortmann., “Security-control methods for statistical database: A comparative study.,” ACM Computing Surveys, vol. 21, pp. 515–556, 1989.
[42] F. Y. Chin and G. O¨ zsoyogˇlu., “Auditing and inference control in statistical databases.,” IEEE Transactions Software Engineering, vol. 8, pp. 574–582, 1982.
[43] L. H. Cox., “Suppression methodology and statistical disclosure control.,” Journal of the American Statistical Association, vol. 75, pp. 377–385, 1980.
[44] D. E. Denning and J. Schl¨orer., “Inference controls for statistical databases.,” IEEE Computer, vol. 16, no. 7, pp. 69–82, 1983.
[45] A. A. A. James P. Kelly, Bruce L. Golden, “Cell suppression: Disclosure protection for sensitive tabular data.,” Networks, vol. 22, pp. 397–417, 1992.
[46] D. Gusfield., “A graph theoretic approach to statistical data security.,” Journal on Computing, vol. 17, pp. 552–571, 1988.
[47] T. sheng Hsu. and M. Y. Kao., “Security problems for statistical databases with general cell suppressions.,” in Proceedings of the 9th International Conference on Scientific and Statistical Database Management, pp. 155–164, 1997.
[48] M. Y. Kao., “Data security equals graph connectivity.,” Journal on Discrete Mathematics, vol. 9, pp. 87–100, 1996.
[49] M. Y. Kao., “Total protection of analytic-invariant information in cross-tabulated tables.,” Journal on Computing, vol. 26, pp. 231–242, 1997.
[50] F. M. Malvestuto and M. Moscarini., “Censoring statistical tables to protect sensitive information: Easy and hard problems.,” in Proceedings of the 8th International Conference on Scientific and Statistical Database management, pp. 12–21, 1996.
[51] F. M. Malvestuto and M. Moscarini., “Suppressing marginal totals from a twodimensional table to protect sensitive information.,” Statistics and Computing, vol. 7,
pp. 101–114, 1997.
[52] M. M. F. M. Malvestuto and M. Rafanelli., “Suppressing marginal cells to protect sensitive information in a two-dimensional statistical table.,” in Proceedings of the 10th ACM SIGACT-SIGMOD-SIGACT Symposium on Principles of Database Systems, pp. 252–258, 1991.
[53] F. Harary., Graph Theory. Reading, Massachusetts: Addison-Wesley, 1969.
[54] A. M. Gibbons., Algorithmic Graph Theory. Cambridge University Press, 1985.
[55] R. E. Tarjan., “Depth-first search and linear graph algorithms.,” SIAM Journal on Computing, vol. 1, pp. 146–160, 1972.
[56] R. E. Tarjan and U. Vishkin., “An efficient parallel biconnectivity algorithm.,” SIAM Journal on Computing, vol. 14, pp. 862–874, 1985.
[57] T.-W. L. Ka Wong Chong, Yijie Han, “Concurrent threads and optimal parallel minimum spanning trees algorithm.,” J.ACM, vol. 48(2), pp. 297–323, 2001.
[58] R. Cole and U. Vishkin., “Approximate parallel scheduling. Part II: Applications to logarithmic-time optimal graph algorithms.,” Information and Computation, vol. 92, pp. 1–47, 1991.
[59] V. Ramachandran., “Parallel open ear decomposition with applications to graph biconnectivity and triconnectivity.,” in Synthesis of Parallel Algorithms (J. H. Reif, ed.), ch. 1, pp. 275–340, Morgan Kaufmann, 1993.
[60] R. E. Tarjan and U. Vishkin., “An efficient parallel biconnectivity algorithm.,” Journal on Computing, vol. 14, pp. 862–874, 1985.

全文公開日期本全文未授權公開 (校內網路)
全文公開日期本全文未授權公開 (校外網路)

簡易檢索 / 詳目顯示

相關論文