A simple algorithm for reliability evaluation of a stochastic-flow network with node failure.

*(English)*Zbl 0989.90015Summary: 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:

90B15 | Stochastic network models in operations research |

90B25 | Reliability, availability, maintenance, inspection in operations research |

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\textit{Y.-K. Lin}, Comput. Oper. Res. 28, No. 13, 1277--1285 (2001; Zbl 0989.90015)

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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), Princeton University Press NJ · Zbl 0139.13701 |

[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 |

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