傳統網路可靠度分析皆假定網路中節點與傳輸邊的傳輸時間為固定之常數，而往往實際生活中的傳輸時間卻是具隨機性。更進一步，傳輸時間有可能並非為獨立性，而是具相關性。因此，本研究提出一個新穎的數學模式與演算法，藉以處理上述問題。其中，包含以下三點： 1. 將網路當中的負載量與傳輸時間同時視為隨機變數； 2. 節點與節點之間存在2條以上路徑可以通過； 3. 網路當中節點與傳輸邊彼此間的傳輸時間可具不獨立性。最後，並應用於物流運輸問題與有線通訊問題。

Traditionally, all analysis of network reliability assumes that times of transmission and consumption in regard to arcs and nodes are a fixed constant; however, in reality these transmission times are not fixed and are stochastic. Moreover, the parameters of these transmission times may or may not be statistically independent; it is possible that they may be correlated. Therefore, this study proposes a new
mathematic model and algorithm by which to solve this problem when encountered. This model includes the following three points: 1. It treats both the capacity and transmission times as stochastic. 2. It allows for the possibility of more than 2 paths between each node. 3. It allows for the possibility that the transmission times in
the network need not be statistically independent. Eventually, this new model can be utilized in regard to transportation logistics problems, as well as non-wireless,
network communication problems.

1. 黃培勝(2011), 「混合螞蟻禁忌搜尋之柔性計算於隨機流量網路可靠度最佳化」, 國立臺灣科技大學工業管理系碩士論文。
2. Aggarwal, K. & Gupta, J. & Misra, K. (1975). A simple method for reliability evaluation of a communication system. IEEE Transactions on Communications , 23 (5), pp. 563-566.
3. Dotson, W. & Gobien, J. (1979). A new analysis technique for probabilistic graphs. IEEE Transactions on Circuits and Systems, 26 (10), pp. 855-865.
4. Hansler, E. (1972). A fast recursive algorithm to calculate the reliability of a communication network. IEEE Transactions on Communications, 20 (3), pp. 637-640.
5. Hudson, J. C. & Kapur, K. C. (1985). Reliability bounds for multistate systems with multistate components. Operations Research, 33 (1), pp. 153-160.
6. Hsieh, C. C. & Lin, M. H. (2003). Reliability-oriented multi-resource allocation in a stochastic-flow network. Reliability Engineering and System Safety, 81 (2), pp. 155-161.
7. Hsieh, C. C. & Chen, Y. T. (2005). Reliable and economic resource allocation in an unreliable flow network. Computers & Operations Research, 32 (3), pp. 613-628.
8. Hsieh, C. C. & Lin, M. H. (2006). Simple algorithms for updating multi-resource allocations in an unreliable flow network. Computers & Industrial Engineering, 50 (1-2), pp. 120-129.
9. Jane, C. C. & Laih, Y. W. (2010). A dynamic bounding algorithm for approximating multi-state two-terminal reliability. European Journal of Operational Research, 205 (3), pp. 625-637.
10. Kuo, S. Y. & Lu, S. K. & Yeh, F. M. (1999). Determining terminal pair reliability based on edge expansion diagrams using OBDD. IEEE Transactions on Reliability, 48 (3), pp. 234-46.
11. Lin, Y. K. (2001). A simple algorithm of reliability evaluation of a stochastic-flow network with node failure. Computers & Operations Research, 28 (13), pp. 1277-1285.
12. Lin, Y. K. (2002). Overall-terminal reliability of a stochastic capacitated-flow network. Mathematical and computer modeling, 36 (1-2), pp. 173-181.
13. Lin, Y. K. (2002). Two-commodity reliability evaluation for a stochastic-flow network with node failure. Computers & Operations Research, 29 (13), pp. 1927-1939.
14. Lin, Y. K. (2003). Extend the quickest path problem to the system reliability evaluation for a stochastic-flow network. Computers & Operations Research, 30 (4), pp. 567-575.
15. Lin, Y. K. (2004). Reliability of a stochastic-flow network with unreliable branches & nodes under budget constraints. IEEE Transactions on Reliability, 53 (3), pp. 381-387.
16. Liu, Q. & Zhao, Q. & Zang, W. (2008). Study on multi-objective optimization of flow allocation in a multi-commodity stochastic-flow network with unreliable nodes. Journal of Applied Mathematics and Computing, 28 (1-2), pp. 185-198.
17. Lin, Y. K. (2009). Time version of the shortest path problem in a stochastic-flow network. Journal of computational and applied mathematics, 228 (1), pp. 150-157.
18. Lin, Y. K. (2009). Routing policy of stochastic-flow networks under time threshold and budget constraint. Expert Systems with Applications, 36 (3), pp. 6076-6081.
19. Lin, Y. K. (2010). Reliability of k separate minimal paths under both time and budget constraints. IEEE Transactions on Reliability, 59 (1), pp. 183-190.
20. Lin, Y. K. & Yeh, C. T. (2010). Optimal carrier selection based on network reliability criterion for stochastic logistics networks. International journal of production economics, 128 (2), pp. 510-517.
21. Lin, Y. K. (2011). Network reliability of a time-based multistate network under spare routing with p minimal paths. IEEE Transactions on Reliability, 60 (1), pp. 61-69.
22. Ramirez-Marquez, J. E. & Coit, D. W. (2005). A monte-carlo simulation approach for approximating multi-state two-terminal reliability. Reliability Engineering & System Safety, 87 (2), pp. 253-264.
23. Ramirez-Marquez, J. E. , & Rocco, C. M. , & Gebre, B. A. (2006). New insights on multi-state component criticality and importance. Reliability Engineering and System Safety, 91 (8), pp. 894-904.
24. Satitsatian, S. & Kapur, K. C. (2006). An algorithm for lower reliability bounds of multistate two-terminal networks. IEEE Transactions on Reliability , 55 (2), pp. 199-206.
25. Shrestha, A. & Xing, L. & Coit, D. W. (2010). An Efficient multistate multi-valued decision diagram-based approach for multistate system sensitivity analysis. IEEE Transactions on Reliability, 59 (3), pp. 581-592.
26. Xu, W. & He, S. & Song, R. & Li, J. (2009). Reliability based assignment in stochastic-flow freight network. Applied Mathematics and Computation, 211 (1), pp. 85-94.
27. Yeh, W. C. (2003). Multistate-node acyclic networks reliability evaluation based on mc.Reliability engineering & system safety, 81 (2), pp. 225-231.
28. Yeh, W. C. (2004). Multistate network reliability evaluation under the maintenance cost constraint. International Journal of Production Economics, 88 (1), pp. 73-83.
29. Yeh, W. C. (2008). A simple minimal path method for estimating the weighted multi-commodity multistate unreliable networks reliability. Reliability Engineering
and System Safety, 93 (1), pp. 125-136.
30. Yeh, W. C. & Chang, W. W. & Chiu, C. W. (2009). A simple method for the multi-state quickest path flow network reliability problem. IEEE Transactions on Reliability, pp. 108-110.
31. Yeh, W. C. (2011). 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, 41 (2), pp. 350-355.
32. Zuo, M. J. & Tian, Z. & Huang, H. Z. (2007). An efficient method for reliability evaluation of multistate networks given all minimal path vectors. IIE Transactions, 39 (8), pp. 811-817.