### Abstract

System decomposition is a novel technique for modeling the dependability of complex systems without constructing a single-level Markov Chain (MC). This is demonstrated in this paper for the availability computation of a class of multiprocessors that uses 4×4 switching elements for the multistage interconnection network (MIN). The availability model is known as task-based availability, where a system is considered operational as long as the task requirements are satisfied. We develop two simple MC’s for the processors and memories and solve them using a software package, called HARP. The probabilities of i processing elements (PE’s) and j memory modules (MM’s) working at any time t, denoted as P_{i}(t) and Pj(t)_{9} are obtained from their corresponding MC’s. The effect of the MIN is captured in the model by finding the number of switches required for the connection of i PE’s and j MM’s. A third MC is then developed for the switches to find the probability that the MIN provides the required (i x j) connection. Multiplying this term with P_{t}(t) and P_{j}(i), the probability of an (i x j) working group is obtained. The methodology is generalized to model arbitrary as well as larger size systems. Transient and steady state availabilities are computed for a variety of MIN configurations and the results are validated through simulation.

Original language | English (US) |
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Pages (from-to) | 1118-1129 |

Number of pages | 12 |

Journal | IEEE Transactions on Parallel and Distributed Systems |

Volume | 4 |

Issue number | 10 |

DOIs | |

Publication status | Published - Oct 1993 |

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### All Science Journal Classification (ASJC) codes

- Signal Processing
- Hardware and Architecture
- Computational Theory and Mathematics

### Cite this

*IEEE Transactions on Parallel and Distributed Systems*,

*4*(10), 1118-1129. https://doi.org/10.1109/71.246073