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A simple algorithm for reliability evaluation of a stochastic-flow network with node failure. (English) Zbl 0989.90015
Summary: This paper addresses a stochastic-flow network in which each arc or node has several capacities and may fail. Given the demand $d$, we try to evaluate the system reliability that the maximum flow of the network is not less than $d$. A simple algorithm is proposed firstly to generate all lower boundary points for $d$, and then the system reliability can be calculated in terms of such points. One computer example is shown to illustrate the solution procedure.

MSC:
90B15Network models, stochastic (optimization)
90B25Reliability, availability, maintenance, inspection, etc. (optimization)
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References:
[1] Hudson, J. C.; Kapur, K. C.: Reliability bounds for multistate systems with multistate components. Operations research 33, 153-160 (1985) · Zbl 0571.90028
[2] Lin, Y. K.; Yuan, J.: A new algorithm to generate d-minimal paths in a multistate flow network with noninteger arc capacities. International journal of reliability, quality, and safety engineering 5, 269-285 (1998)
[3] Xue, J.: On multistate system analysis. IEEE transactions on reliability 34, 329-337 (1985)
[4] Yarlagadda, R.; Hershey, J.: Fast algorithm for computing the reliability of communication network. International journal of electronics 70, 549-564 (1991)
[5] Yuan, J.; Ko, K. L.: A factoring method to calculate reliability for systems of dependence components. Reliability engineering and system safety 21, 107-118 (1988)
[6] Aggarwal, K. K.; Gupta, J. S.; Misra, K. B.: A simple method for reliability evaluation of a communication system. IEEE transactions on communications 23, 563-565 (1975) · Zbl 0349.94003
[7] Lee, S. H.: Reliability evaluation of a flow network. IEEE transactions on reliability 29, 24-26 (1980) · Zbl 0428.90024
[8] Ford, L. R.; Fulkerson, D. R.: Flows in networks.. (1962) · Zbl 0106.34802
[9] Aggarwal, K. K.; Chopra, Y. C.; Bajwa, J. S.: Capacity consideration in reliability analysis of communication systems. IEEE trans. Reliability 31, 177-180 (1982) · Zbl 0485.90046
[10] Rueger, W. J.: Reliability analysis of networks with capacity-constraints and failures at branches and nodes. IEEE transactions on reliability 35, 523-528 (1986) · Zbl 0608.90036
[11] Lin, J. S.; Jane, C. C.; Yuan, J.: On reliability evaluation of a capacitated-flow network in terms of minimal pathsets. Networks 25, 131-138 (1995) · Zbl 0828.90038
[12] Jane, C. C.; Lin, J. S.; Yuan, J.: On reliability evaluation of a limited-flow network in terms of minimal cutsets. IEEE transactions on reliability 42, 354-361 (1993) · Zbl 0795.90028
[13] Aven, T.: Reliability evaluation of multistate systems with multistate components. IEEE transactions on reliability 34, 473-479 (1985) · Zbl 0581.90030