### Abstract

When the "length" of a link is not deterministic and is governed by a stochastic process, the "shortest" path between two points in the network is not necessarily always composed of the same links and depends on the state of the network. For example, in communication and transportation networks, the travel time on a link is not deterministic and the fastest path between two points is not fixed. This paper presents an algorithm to compute the expected shortest travel time between two nodes in the network when the travel time on each link has a given independent discrete probability distribution. The algorithm assumes the knowledge of all the paths between two nodes and methods to determine the paths are referenced. In reliability (i.e. the probability that two given points are connected by a path) computations, associated with each link is a probability of "failure" and a probability of "success". Since "failure" implies infinite travel time, the algorithm simultaneously computes reliability. The paper also discusses the algorithm's capability to simultaneously compute some other performance measures which are useful in the analysis of emergency services operating on a network.

Original language | English (US) |
---|---|

Pages (from-to) | 347-355 |

Number of pages | 9 |

Journal | Computers and Operations Research |

Volume | 3 |

Issue number | 4 |

DOIs | |

State | Published - 1976 |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

- Information Systems and Management
- Management Science and Operations Research
- Applied Mathematics
- Modeling and Simulation
- Transportation

### Cite this

**Shortest distance and reliability of probabilistic networks.** / Mirchandani, Pitu.

Research output: Contribution to journal › Article

*Computers and Operations Research*, vol. 3, no. 4, pp. 347-355. https://doi.org/10.1016/0305-0548(76)90017-4

}

TY - JOUR

T1 - Shortest distance and reliability of probabilistic networks

AU - Mirchandani, Pitu

PY - 1976

Y1 - 1976

N2 - When the "length" of a link is not deterministic and is governed by a stochastic process, the "shortest" path between two points in the network is not necessarily always composed of the same links and depends on the state of the network. For example, in communication and transportation networks, the travel time on a link is not deterministic and the fastest path between two points is not fixed. This paper presents an algorithm to compute the expected shortest travel time between two nodes in the network when the travel time on each link has a given independent discrete probability distribution. The algorithm assumes the knowledge of all the paths between two nodes and methods to determine the paths are referenced. In reliability (i.e. the probability that two given points are connected by a path) computations, associated with each link is a probability of "failure" and a probability of "success". Since "failure" implies infinite travel time, the algorithm simultaneously computes reliability. The paper also discusses the algorithm's capability to simultaneously compute some other performance measures which are useful in the analysis of emergency services operating on a network.

AB - When the "length" of a link is not deterministic and is governed by a stochastic process, the "shortest" path between two points in the network is not necessarily always composed of the same links and depends on the state of the network. For example, in communication and transportation networks, the travel time on a link is not deterministic and the fastest path between two points is not fixed. This paper presents an algorithm to compute the expected shortest travel time between two nodes in the network when the travel time on each link has a given independent discrete probability distribution. The algorithm assumes the knowledge of all the paths between two nodes and methods to determine the paths are referenced. In reliability (i.e. the probability that two given points are connected by a path) computations, associated with each link is a probability of "failure" and a probability of "success". Since "failure" implies infinite travel time, the algorithm simultaneously computes reliability. The paper also discusses the algorithm's capability to simultaneously compute some other performance measures which are useful in the analysis of emergency services operating on a network.

UR - http://www.scopus.com/inward/record.url?scp=0001008059&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001008059&partnerID=8YFLogxK

U2 - 10.1016/0305-0548(76)90017-4

DO - 10.1016/0305-0548(76)90017-4

M3 - Article

VL - 3

SP - 347

EP - 355

JO - Computers and Operations Research

JF - Computers and Operations Research

SN - 0305-0548

IS - 4

ER -