## Abstract

This paper constructs a multistate flow network composed of multistate edges to model a computer network. Each edge has lead time, capacity, and cost parameters. Therefore, the minimum transmission time through a single path is not a fixed number. Under the transmission protocol that the data are sent through p (p ≥ 2) minimal paths simultaneously, the minimum transmission time is also stochastic. This paper is mainly to evaluate the probability that a given amount of data can be sent through p minimal paths simultaneously subject to both time and budget constraints. Such a probability is named network reliability herein, which can be treated as a performance indicator to measure the transmission capability of a computer network. Without knowing all minimal paths, a solution procedure is first proposed to calculate network reliability. Furthermore, the network administrator decides the routing rule indicating the first and the second priority p minimal paths in order to enhance the network reliability. Subsequently, network reliability according to the routing rule is also computed. At last, the expected demand, expected budget, expected time, and the criterion to find an ideal routing rule are presented as well.

Original language | English |
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Pages (from-to) | 4205-4217 |

Number of pages | 13 |

Journal | International Journal of Innovative Computing, Information and Control |

Volume | 8 |

Issue number | 6 |

State | Published - 1 Jun 2012 |

## Keywords

- Budget
- Multiple minimal paths
- Multistate flow network
- Network reliability
- Routing rule
- Transmission protocol