### Abstract

Iterative aggregation/disaggregation (IAD) methods are powerful tools for solving Markov chain models whose transition probability matrices are nearly completely decomposable (NCD). Such models arise frequently during the performance and reliability analysis of computer and telecommunication systems. IAD methods require the solution of a stochastic coupling matrix whose elements denote transition probabilities among blocks. The coupling matrices are often large and in NCD models necessarily have diagonal elements close to one and small off-diagonal elements. This makes their solution by either iterative or direct methods rather difficult. In this paper we propose a modification of the coupling matrix that allows us to accurate and efficiently compute its stationary probability vector.

Original language | English |
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Title of host publication | Proceedings of the IEEE International Workshop on Modeling, Analysis, and Simulation of Computer and Telecommunication Systems |

Editors | Vijay Madisetti, Erol Gelenbe, Jean Walrand |

Publisher | Publ by IEEE |

Pages | 255-262 |

Number of pages | 8 |

ISBN (Print) | 0818652926 |

Publication status | Published - 1994 |

Event | Proceedings of the 2nd International Workshop on Modeling, Analysis, and Simulation of Computer and Telecommunication Systems - Durham, NC, USA Duration: Jan 31 1994 → Feb 2 1994 |

### Other

Other | Proceedings of the 2nd International Workshop on Modeling, Analysis, and Simulation of Computer and Telecommunication Systems |
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City | Durham, NC, USA |

Period | 1/31/94 → 2/2/94 |

### Fingerprint

### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*Proceedings of the IEEE International Workshop on Modeling, Analysis, and Simulation of Computer and Telecommunication Systems*(pp. 255-262). Publ by IEEE.

**On solving stochastic coupling matrices arising in iterative aggregation/disaggregation methods.** / Stewart, William J.; Touzene, A.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the IEEE International Workshop on Modeling, Analysis, and Simulation of Computer and Telecommunication Systems.*Publ by IEEE, pp. 255-262, Proceedings of the 2nd International Workshop on Modeling, Analysis, and Simulation of Computer and Telecommunication Systems, Durham, NC, USA, 1/31/94.

}

TY - GEN

T1 - On solving stochastic coupling matrices arising in iterative aggregation/disaggregation methods

AU - Stewart, William J.

AU - Touzene, A.

PY - 1994

Y1 - 1994

N2 - Iterative aggregation/disaggregation (IAD) methods are powerful tools for solving Markov chain models whose transition probability matrices are nearly completely decomposable (NCD). Such models arise frequently during the performance and reliability analysis of computer and telecommunication systems. IAD methods require the solution of a stochastic coupling matrix whose elements denote transition probabilities among blocks. The coupling matrices are often large and in NCD models necessarily have diagonal elements close to one and small off-diagonal elements. This makes their solution by either iterative or direct methods rather difficult. In this paper we propose a modification of the coupling matrix that allows us to accurate and efficiently compute its stationary probability vector.

AB - Iterative aggregation/disaggregation (IAD) methods are powerful tools for solving Markov chain models whose transition probability matrices are nearly completely decomposable (NCD). Such models arise frequently during the performance and reliability analysis of computer and telecommunication systems. IAD methods require the solution of a stochastic coupling matrix whose elements denote transition probabilities among blocks. The coupling matrices are often large and in NCD models necessarily have diagonal elements close to one and small off-diagonal elements. This makes their solution by either iterative or direct methods rather difficult. In this paper we propose a modification of the coupling matrix that allows us to accurate and efficiently compute its stationary probability vector.

UR - http://www.scopus.com/inward/record.url?scp=0028026503&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0028026503&partnerID=8YFLogxK

M3 - Conference contribution

SN - 0818652926

SP - 255

EP - 262

BT - Proceedings of the IEEE International Workshop on Modeling, Analysis, and Simulation of Computer and Telecommunication Systems

A2 - Madisetti, Vijay

A2 - Gelenbe, Erol

A2 - Walrand, Jean

PB - Publ by IEEE

ER -