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Practical sequential bounds for approximating two-terminal reliability

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  • Jane, Chin-Chia
  • Shen, Wu-Hsien
  • Laih, Yih-Wenn

Abstract

With increasing emphases on better and more reliable services, network systems have incorporated reliability analysis as an integral part in their planning, design and operation. This article first presents a simple exact decomposition algorithm for computing the NP-hard two-terminal reliability, which measures the probability of successful communication from specified source node to sink node in the network. Then a practical bounding algorithm, which is indispensable for large networks, is presented by modifying the exact algorithm for obtaining sequential lower and upper bounds on two-terminal reliability. Based on randomly generated large networks, computational experiments are conducted to compare the proposed algorithm to the well-known and widely used edge-packing approximation model and to explore the performance of the proposed bounding algorithm. Computational results reveal that the proposed bounding algorithm is superior to the edge-packing model, and the trade-off of accuracy for execution time ensures that an exact difference between upper and lower bounds on two-terminal reliability can be obtained within an acceptable time.

Suggested Citation

  • Jane, Chin-Chia & Shen, Wu-Hsien & Laih, Yih-Wenn, 2009. "Practical sequential bounds for approximating two-terminal reliability," European Journal of Operational Research, Elsevier, vol. 195(2), pages 427-441, June.
    • Handle: RePEc:eee:ejores:v:195:y:2009:i:2:p:427-441
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    References listed on IDEAS

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    1. Jane, Chin-Chia & Yuan, John, 2001. "A sum of disjoint products algorithm for reliability evaluation of flow networks," European Journal of Operational Research, Elsevier, vol. 131(3), pages 664-675, June.
    2. Cook, Jason L. & Ramirez-Marquez, Jose Emmanuel, 2007. "Two-terminal reliability analyses for a mobile ad hoc wireless network," Reliability Engineering and System Safety, Elsevier, vol. 92(6), pages 821-829.
    3. Malinowski, Jacek, 2007. "Node-pair reliability of network systems with small distances between adjacent nodes," Reliability Engineering and System Safety, Elsevier, vol. 92(4), pages 479-489.
    4. D. Klingman & A. Napier & J. Stutz, 1974. "NETGEN: A Program for Generating Large Scale Capacitated Assignment, Transportation, and Minimum Cost Flow Network Problems," Management Science, INFORMS, vol. 20(5), pages 814-821, January.
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    1. Sebastio, Stefano & Trivedi, Kishor S. & Wang, Dazhi & Yin, Xiaoyan, 2014. "Fast computation of bounds for two-terminal network reliability," European Journal of Operational Research, Elsevier, vol. 238(3), pages 810-823.
    2. Jane, Chin-Chia & Laih, Yih-Wenn, 2010. "A dynamic bounding algorithm for approximating multi-state two-terminal reliability," European Journal of Operational Research, Elsevier, vol. 205(3), pages 625-637, September.
    3. Reed, Sean & Löfstrand, Magnus & Andrews, John, 2019. "An efficient algorithm for computing exact system and survival signatures of K-terminal network reliability," Reliability Engineering and System Safety, Elsevier, vol. 185(C), pages 429-439.
    4. Yeh, Wei-Chang, 2022. "Novel self-adaptive Monte Carlo simulation based on binary-addition-tree algorithm for binary-state network reliability approximation," Reliability Engineering and System Safety, Elsevier, vol. 228(C).
    5. Niu, Yi-Feng & Wang, Jun-Feng & Xu, Xiu-Zhen & Xu, Qian-Xin, 2025. "Reliability evaluation for a multi-commodity multi-state distribution network under transportation emission consideration," Reliability Engineering and System Safety, Elsevier, vol. 254(PA).
    6. Cui, Hongjun & Wang, Fei & Ma, Xinwei & Zhu, Minqing, 2022. "A novel fixed-node unconnected subgraph method for calculating the reliability of binary-state networks," Reliability Engineering and System Safety, Elsevier, vol. 226(C).

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