### Abstract

In the probabilistic single processor scheduling problem, there are n tasks, each with a start time, a length, a deadline, and a probability of occurrence. When tasks occur independently with the known probabilities, the task reliability is the probability that all occurring tasks can be completed, each by its deadline. The processor reliability is the probability that the occurring tasks keep the processor as busy as possible. A set of tasks is nonoverlapping whenever for any two tasks, if the start time of the first precedes the start time of the second, the deadline of the first is no later than the deadline of the second. Pseudopolynomial time algorithms are developed for computing task and processor reliabilities for nonoverlapping sets of tasks; when all tasks have unit length, these algorithms are polynomial time. Efficient algorithms for counting bases, circuits, and cocircuits in doubly convex scheduling matroids are also developed.

Original language | English (US) |
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Pages (from-to) | 101-112 |

Number of pages | 12 |

Journal | Discrete Applied Mathematics |

Volume | 27 |

Issue number | 1-2 |

DOIs | |

State | Published - May 1990 |

Externally published | Yes |

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Applied Mathematics

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## Cite this

*Discrete Applied Mathematics*,

*27*(1-2), 101-112. https://doi.org/10.1016/0166-218X(90)90132-V