### 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) |
---|---|

Pages (from-to) | 1118-1129 |

Number of pages | 12 |

Journal | IEEE Transactions on Parallel and Distributed Systems |

Volume | 4 |

Issue number | 10 |

DOIs | |

State | Published - Jan 1 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

}

*IEEE Transactions on Parallel and Distributed Systems*, vol. 4, no. 10, pp. 1118-1129. https://doi.org/10.1109/71.246073

**An Availability Model for MIN-Based Multiprocessors.** / Das, Chitaranjan; Mohapatra, Prasant; Tien, Lei; Bhuyan, Laxmi N.

Research output: Contribution to journal › Article

TY - JOUR

T1 - An Availability Model for MIN-Based Multiprocessors

AU - Das, Chitaranjan

AU - Mohapatra, Prasant

AU - Tien, Lei

AU - Bhuyan, Laxmi N.

PY - 1993/1/1

Y1 - 1993/1/1

N2 - 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 Pi(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 Pt(t) and Pj(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.

AB - 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 Pi(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 Pt(t) and Pj(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.

UR - http://www.scopus.com/inward/record.url?scp=0027677297&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0027677297&partnerID=8YFLogxK

U2 - 10.1109/71.246073

DO - 10.1109/71.246073

M3 - Article

VL - 4

SP - 1118

EP - 1129

JO - IEEE Transactions on Parallel and Distributed Systems

JF - IEEE Transactions on Parallel and Distributed Systems

SN - 1045-9219

IS - 10

ER -