## Abstract

Traditionally, many researchers solved the multicommodity maximum flow problem by assuming that the arcs of the flow network are deterministic. When the arcs are stochastic (i.e., the capacity of each arc has several values), this article studies how to calculate the probability that a capacitated-flow network with a unique source node satisfies a demand (d^{1}, d^{2},..., d^{p}) at the unique sink node, where d^{k} is the demand of commodity k. Such a probability is named the multicommodity reliability and is dependent on capacities of arcs. One solution procedure is proposed to evaluate the multicommodity reliability, which includes two parts: an algorithm to generate all (d^{1}, d^{2},...,d^{p})MPs and a method to calculate the multicommodity reliability in terms of (d^{1}, d^{2},..., d^{p})-MPs. Two illustrative examples are given.

Original language | English |
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Pages (from-to) | 255-264 |

Number of pages | 10 |

Journal | Computers and Mathematics with Applications |

Volume | 42 |

Issue number | 1-2 |

DOIs | |

State | Published - 1 Jul 2001 |

## Keywords

- Capacitated-flow network
- Demand
- Minimal path
- Multicommodity reliability