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研究生: 林宜珊
Yi-Shan Lin
論文名稱: 隨機流量網路敏感度分析
Sensitivity Analysis for Stochastic-flow Networks
指導教授: 林義貴
Yi-Kuei Lin
口試委員: 王逸琳
I-Lin Wang
郭人介
Ren-Jieh Kuo
學位類別: 碩士
Master
系所名稱: 管理學院 - 工業管理系
Department of Industrial Management
論文出版年: 2012
畢業學年度: 100
語文別: 英文
論文頁數: 75
中文關鍵詞: 敏感度分析隨機流量網路隨機專案網路最小路徑遞迴不交和法
外文關鍵詞: Sensitivity analysis, Stochastic-flow network, Stochastic project network, Minimal paths, Recursive Sum of Disjoint Products
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  • 對於真實世界中的許多系統,可藉由模擬成網路型式以分析該系統之績效,如通信網路、物流網路、電腦網路與電力網路等,在該網路是邊(arc)及節點(node)所組成的。其中網路可靠度為許多系統重要績效指標之一。因此,可靠度敏感度分析是大多數系統管理者所欲達成之目標。近年來,如何建立有效方案來提升或穩固網路可靠度是個重要議題。例如,如何提高網路可靠度?如何減少網路可靠度降低?另外每一個邊容量視為隨機性,此網路可稱之隨機流量網路(stochastic-flow network)。
    近年來的文獻大部分利用可靠度重要度量方法(importance measure)以探討影響網路可靠度的重要因素。在此,本研究提出三個敏感度分析技巧來探討邊的變化對網路可靠度的影響情形,包括機率的改變(changes in probability)、邊容量的改變(changes in arc capacity)以及改善的潛力(improvement potential)。然而,其主要目標是藉由這些分析結果找出提升網路可靠度的要點以及找出高度影響網路可靠度的邊。所有網路可靠度的計算方式結合最小路徑(Minimal Paths)與遞回不交和法(Recursive Sum of Disjoint Product)演算法。
    本研究針對四個網路模型進行敏感度分析,分別為隨機流量網路、電力網路、電腦網路與專案網路。隨機流量網路是其它網路的基本模型,因此在隨機流量網路的敏感度分析將網路條件(傳輸邊容量、機率分配)設置相同。另外三個與日常生活息息相關的網路,藉由敏感度分析找出關鍵性的邊並提出有效的改善方法來提高或穩固網路可靠度。


    For real world systems can be modeled a network for analyzing its performance, such as a logistics network, a computer network, an electric power network, in which the network is constructed by a set of arcs and a set of nodes. Therefore, sensitivity analysis of network reliability is the goal which most managers pursue. Recently, determine a plan for improving network reliability is a crucial issue. How to improve the network reliability and reduce decrease of network reliability? In addition, each arc/node owns several capacities with a probability distribution and may fail should be regarded as stochastic-flow networks.
    In the past, most of researches extended importance measure to explore the important factor of network reliability. This study addresses three sensitivity analysis techniques to analyze the changes of arcs that will affect the network reliability, including changes in probability, changes in arc capacity and improvement potential. The main goal is to apply these solutions to obtain the characteristic of network and plan for improving network reliability. In addition, the network reliability is evaluated by Minimal Paths (MPs) and Recursive Sum of Disjoint Product (RSDP) algorithm.
    Furthermore, sensitivity analysis techniques is applied to four network models, including stochastic-flow network, stochastic electric power network, time-based computer network and stochastic project network. The condition is set the same for sensitivity analysis in stochastic-flow network model. Other three network models related with our daily life, utilizing sensitivity analysis to figure out the way of improving network reliability or stably keeping network reliability.

    摘要 I ABSTRACT II ACKNOWLEDGMENTS III CONTENTS IV LIST OF FIGURES VI LIST OF TABLES VII Chapter 1 INTRODUCTION 1 1.1. Background and motivation 1 1.2. Research objectives 1 1.3. Overview of this thesis 3 Chapter 2 LITERATURE REVIEW 5 2.1. Network reliability analysis 5 2.2. Extension of network research 6 2.2.1 Network reliability optimization 6 2.2.2 Quickest path analysis 7 2.2.3 Project network analysis 9 2.3. Sensitivity analysis of network reliability 10 Chapter 3 FOUR ADDRESSED PROBLEMS 12 3.1. Model I: Stochastic-flow network model 13 3.1.1. Flow vector and capacity vector 15 3.1.2. Stochastic-flow network reliability evaluation 15 3.1.3. Generate all d-MPs 16 3.2. Model II: Stochastic electric power network 18 3.2.1. GA-based algorithm development 20 3.3. Model III: Time-based computer network model 23 3.3.1. The transmission time 24 3.3.2. The lower boundary point for (d, T) 24 3.3.3. Network reliability on two disjoint MPs evaluation 25 3.4. Model IV: Stochastic project network model 26 3.4.1. Introduction of project network 28 3.4.2. Generate all upper boundary vectors for (T, B) 28 3.4.3. Generate all lower boundary vectors for (T, B) 29 3.4.4. Evaluation of reliability in stochastic project network 30 Chapter 4 SENSITIVITY ANALYSIS 32 4.1. Changes in probability 32 4.2. Changes in arc capacity 36 4.3. Improvement potential 39 Chapter 5 NUMERICAL EXPERIMENTS 41 5.1. Sensitivity analysis on Model I 41 5.2. Sensitivity analysis on Model II 48 5.3. Sensitivity analysis on Model III 53 5.4. Sensitivity analysis on Model IV 56 Chapter 6 CONCLUSIONS AND FUTURE RESEARCH 59 REFERENCES 61

    Aven, T. and Ostebo, R., “Two new importance measures for a flow network system”, Reliability Engineering, Vol. 14, pp. 75-80 (1986).
    Ball, M. O., Hagstrom, J., and Provan, J. S., “Threshold reliability of networks with small failure sets”, Networks, Vol. 25, pp. 101-115 (1995).
    Bodin, L. D., Golden, B. L., Assad, A. A. and Ball, M. O., “Routing and scheduling of vehicles and crews: the state of the art”, Computers and Operations Research, Vol. 10, pp. 63-211 (1982).
    Chen, G. H. and Hung, Y. C., “On the quickest path problem”, Information Processing Letters, Vol. 46, pp. 125-128 (1993).
    Chen, G. H. and Hung, Y. C., “Algorithms for the constrained quickest path problem and the enumeration of quickest paths”, Computers and Operations Research, Vol. 21, pp. 113-118 (1994).
    Chen, Y. L. and Chin, Y. H., “The quickest path problem”, Computers and Operations Research, Vol. 17, pp. 153-161 (1990).
    Chen, Y. L. and Tang, K., “Minimum time paths in a network with mixed time constraints”, Computers and Operations Research, Vol. 25, pp. 793-805 (1998).
    Cheng, S. T. “Topological optimization of a reliable communication network”, IEEE Transactions on Reliability, Vol. 47, pp. 225-233 (1998).
    Chen, A., Yang, H., Lo, H. K. and Tang, W. H., “Capacity reliability of a road network: an assessment methodology and numerical results”, Transportation Research Part B, Vol. 36, pp. 225-252 (2002).
    Clímaco, J. C. N., Pascoal, M. M. B., Craveirinha, J. M. F. and Captivo, M. E. V., “Internet packet routing: Application of a K-quickest path algorithm”, European Journal of Operational Research, Vol. 181, pp. 1045-1054 (2007).
    Gido, J. and Clements, J. P., Successful Project Management South-western college publishing, Ohio (1999).
    Golden, B. L. and Magnanti, T. L., “Deterministic network optimization: a bibliography”, Networks, Vol. 7, pp. 149-183 (1977).
    Golenko-Ginzburg, D. and Gonik, A., “Stochastic network project scheduling with non-consumable limited resources”, International Journal of Production Economics, Vol. 48, pp. 29-37 (1997).
    Harold, K., Project Management A Systems Approach to Planning, Scheduling, and Controlling, John Wiley & Sons, Inc., NJ (2009).
    Hiller, F. S. and Liberman, G. J., Introduction to Operations Research 8/e McGraw-Hill, NY (2005).
    Hsieh, C. C. and Chen, Y. T., “Reliable and economic resource allocation in an unreliable flow network”, Computer and Operations Research, Vol. 32, pp. 613-628 (2005a).
    Hsieh, C. C. and Chen, Y. T., “Resource allocation decisions under various demands and cost requirements in an unreliable flow network”, Computer and Operations Research, Vol. 32, pp. 2771-2784 (2005b).
    Hsieh, C. C. and Lin, M. H., “Reliability-oriented multi-resource allocation in a stochastic-flow network”, Reliability Engineering and System Safety, Vol. 81, pp. 155-161 (2003).
    Hsieh, C. C. and Lin, M. H., “Simple algorithms for updating multi-resource allocations in an unreliable flow network”, Computers and Industrial Engineering, Vol. 50, pp. 120-129 (2006).
    Hung, Y. C. and Chen, G. H., “Distributed algorithms for the quickest path problem”, Parallel Computing, Vol. 18, pp. 823-834 (1992)
    Jane, C. C. and Laih, Y. W., “Algorithms to determine the threshold reliability of flow networks”, IIE Transactions, Vol. 36, pp. 469-479 (2004).
    Jane, C. C., Lin, J. S. and Yuan, J., “On reliability evaluation of a limited-flow network in terms of minimal cutsets”, IEEE Transactions on Reliability, Vol. 42, pp. 354-361 (1993).
    Jane, C. C. and Yuan, J., “A sum of disjoint products algorithm for reliability evaluation of flow networks”, European Journal of Operational Research, Vol. 131, pp. 664-675 (2001).
    Lee, D. T. and Papadopoulou, E., “The all-pairs quickest path problem”, Information Processing Letters, Vol. 45, pp. 261-267 (1993).
    Levitin, G. and Lisnianski, A., “Importance and sensitivity analysis of multi-state systems using the universal generating function method”, Reliability Engineering and System Safety, Vol. 65, pp. 271-82 (1999).
    Levitin, G., “Reliability evaluation for acyclic consecutively connected networks with multiatate elements”, Reliability Engineering and System Safety, Vol. 73, pp. 137-143 (2001).
    Levitin, G. and Lisnianski, A., “A new approach to solving problems of multi-state system reliability optimization”, Quality Reliability Engineering International, Vol. 17, pp. 93-104 (2001).
    Lin, J. S., Jane, C. C. and Yuan, J., “On reliability evaluation of a capacitated-flow network in terms of minimal pathsets”, Networks, Vol. 25, pp. 131-138 (1995).
    Lin, Y. K., “A simple algorithm for reliability evaluation of a stochastic-flow network with node failure”, Computer and Operations Research, Vol. 28, pp. 1277-1285 (2001a).
    Lin, Y. K., “Study on the multicommodity reliability of a capacitated-flow network”, Computers and Mathematics with Applications, Vol. 42, pp. 255-264 (2001b).
    Lin, Y. K., “Using minimal cuts to evaluate the system reliability of a stochastic-flow network with failures at nodes and arcs”, Reliability Engineering and System Safety, Vol. 75, pp. 41-46 (2002a).
    Lin, Y.K., “Find all longer and shorter boundary duration vectors under project time and budget constraints”, Journal of the Operations Research Society of Japan, Vol.45 pp. 260-267 (2002b).
    Lin, Y. K. “Extend the quickest path problem to the system reliability evaluation for a stochastic-flow network”, Computers and Operations Research, Vol. 30, pp. 567-575 (2003).
    Lin, Y. K., “Reliability of a stochastic-flow network with unreliable branches and nodes under budget constraints”, IEEE Transactions on Reliability, Vol. 53, pp. 381-387 (2004).
    Lin, Y. K., “Reliability evaluation for an information network with node failure under cost constraint”, IEEE Transactions on Systems, Man and Cybernetics – Part A: Systems and Humans, Vol. 37, pp. 180-188 (2007a).
    Lin, Y. K., “On a multicommodity stochastic-flow network with unreliable nodes subject to budget constraint”, European Journal of Operational Research, Vol. 176, pp. 347-360 (2007b).
    Lin, Y.K., “Study on longer and shorter boundary duration vectors with arbitrary duration and cost values”, Journal of the Operations Research Society of Japan, Vol. 50 pp. 73-81 (2007c).
    Lin, Y.K., “Time version of the shortest path problem in a stochastic-flow network”, Journal of Computational and Applied Mathematics, Vol. 228 pp. 150-157 (2009).
    Lin, Y. K., “System reliability of a stochastic-flow network through two minimal paths under time threshold”, International Journal of Production Economics, Vol. 124, pp. 382-387 (2010a).
    Lin, Y. K., “Spare routing reliability for a stochastic flow network through two minimal paths under budget constraint”, IEEE Transactions on Reliability, Vol. 59, pp. 2-10 (2010b).
    Lin, Y. K. and Yeh, C. T., “Optimal resource assignment to maximize multistate network reliability for a computer network”, Computers and Operations Research, Vol. 37, no. 12, pp. 2229-2238 (2010a).
    Lin, Y. K. and Yeh, C. T., “Evaluation of optimal network reliability under components-assignments subject to a transmission budget”, IEEE Transactions on Reliability, Vol. 59, pp. 539-550 (2010b).
    Lin, Y. K. and Yeh, C. T., “Computer network reliability optimization under double-resource assignments subject to a transmission budget”, Information Sciences, Vol. 181, no. 3, pp. 582-599 (2011a).
    Lin, Y. K. and Yeh, C. T., “Maximal network reliability with optimal transmission line assignment for stochastic electric power network via genetic algorithms”, Applied Soft Computing, Vol. 11, no. 2, pp. 2714-2724 (2011b).
    Lisnianski, A. and Levitin, G., Multi-state system reliability: assessment, optimization and application, Vol. 6, World Scientific, Singapore (2003).
    Liu, Q., Zhang, H., Ma, X., and Zhao, Q., “Genetic algorithm-based study on flow allocation in a multi-commodity stochastic-flow network with unreliable nodes”, Proceedings of The 8th ACIS International Conference on Software Engineering, Artificial Intelligence, Networking, and Parallel/Distributed Computing, Tsinan, pp. 576-581 (2007).
    Liu, Q., Zhao, Q., and Zang, W., “Study on multi-objective optimization of flow allocation in a multi-commodity stochastic-flow network with unreliable nodes”, Journal of Applied Mathematics and Computing, Vol. 28, pp. 185-198 (2008).
    Martins, E. D. Q. V. and Santos, J. L. E. D., “An algorithm for the quickest path problem”, Operations Research Letters, Vol. 20, pp. 195-198 (1997).
    Painton, L. and Campbell, J., “Genetic algorithms in optimization of system reliability”, IEEE Transactions on Reliability, Vol. 44, pp. 172-178 (1995).
    Park, C. K., Lee, S. and Park, S., “A label-setting algorithm for finding a quickest path”, Computers and Operations Research, Vol. 31, pp. 2405-2418 (2004).
    Pascoal, M. M. B., Captivo, M. E. V. and Cl´ımaco, J. C. N., “An algorithm for ranking quickest simple paths”, Computers and Operations Research, Vol. 32, pp. 509-520 (2005).
    Pierre, S. and Legault, G., “A genetic algorithm for designing distributed computer network topologies”, IEEE Transactions on Systems, Man, and Cybernetics – Part B: Cybernetics, Vol. 28, pp. 249-258 (1998).
    Ramirez-Marquez, J. E. and Coit, D., “Composite importance measures for multistate systems with multistate components”, IEEE Transactions on Reliability, Vol. 54, pp. 517-29 (2005).
    Ramirez-Marquez, J. E., Rocco, C., Assefa, B., Coit, D.and Tortorella, M., “New insights on multi-state component criticality and importance”, Reliability Engineering and System Safety, Vol. 91, pp. 894-904 (2006).
    Ramirez-Marquez, J. E. and Coit, D., “Multi-state component criticality analysis for reliability improvement in multi-state systems”, Reliability Engineering and System Safety, Vol. 92, pp. 1608-1619 (2007).
    Ramirez-Marquez, J. E. and Rocco S., C. M., “Stochastic network interdiction optimization via capacitated network reliability modeling and probabilistic solution discovery”, Reliability Engineering and System Safety, Vol. 94, pp. 913-921 (2009).
    Ramirez-Marquez, J. E., Rocco S., C. M., and Levitin, G., “Optimal protection of general source-sink networks via evolutionary techniques”, Reliability Engineering and System Safety, Vol. 94, pp. 1676-1684 (2009).
    Rueger, W. J., “Reliability analysis of networks with capacity constraints and failure at branches and nodes, IEEE Transactions on Reliability, Vol. 35, pp. 523-528 (1986).
    Shrestha, A., Xing, L., and Coit, D. W., “An efficient multistate multivalued decision diagram-based approach for multistate systems sensitivity analysis”, IEEE Transactions on Reliability, Vol. 59, pp. 581-592 (2010).
    Soh, S. and Rai, S., “An efficient cutset approach for evaluating communication-network reliability with heterogeneous link-capacities”, IEEE Transactions on Reliability, Vol. 54, pp. 133-144 (2005).
    Wu, S. and Chan, L., “Performance utility—analysis of multi-state systems”, IEEE Transactions on Reliability, Vol. 52, pp. 14-21 (2003).
    Xu, W., He, S., Song, R., and Li, J., “Reliability based assignment in stochastic-flow freight network”, Applied Mathematics and Computation, Vol. 211, pp. 85-94 (2009).
    Yeh, W. C., “A simple algorithm to search for all d-MPs with unreliable nodes”, Reliability Engineering and System Safety, Vol. 73, pp. 49-54 (2001).
    Yeh, W. C., “Multistate network reliability evaluation under the maintenance cost constraint”, International Journal of Production Economics, Vol. 88, pp. 73-83 (2004).
    Yeh, W. C., “A simple algorithm to search for all MCs in networks”, European Journal of Operational Research, Vol. 174, pp. 1694-1705 (2006).
    Yeh, W. C., “An improved sum-of-disjoint-products technique for the symbolic network reliability analysis with known minimal paths”, Reliability Engineering and System Safety, Vol. 92, pp. 260-268 (2007).
    Yeh, W. C., “A simple minimal path method for estimating the weighted multi-commodity multistate unreliable networks reliability”, Reliability Engineering and System Safety, Vol. 93, pp. 125-136 (2008).
    Yeh, W. C., “A simple universal generating function method to search for all minimal paths in networks”, IEEE Transactions on Systems, Man, and Cybernetics Part A: Systems and Humans, Vol. 39, pp. 1247-1254 (2009).
    Yeh, W. C., “An improved method for multistate flow network reliability with unreliable nodes and a budget constraint based on path set”, IEEE Transactions on Systems, Man, and Cybernetics Part A: Systems and Humans, Vol. 41, pp. 350-355 (2011).
    Zio, E. and Podofillini, L., “Monte-Carlo simulation analysis of the effects on different system performance levels on the importance on multistate components”, Reliability Engineering & System Safety, Vol. 82, pp. 63-73 (2003).
    Zio, E., Podofillini, L. and Levitin, G., “Estimation of the importance measures of multi-state elements by Monte Carlo simulation”, Reliability Engineering & System Safety, Vol. 86, pp. 191-7204 (2004).
    Zuo, M. J., Tian, Z., and Huang, H. Z., “An efficient method for reliability evaluation of multistate networks given all minimal path vectors”, IIE Transactions, Vol. 39, pp. 811-817 (2007).

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