### Abstract

Although many closed multichain queuing networks give rise to a product-form solution for their equilibrium probabilities, evaluating performance measures remains nontrivial due to the presence of a normalization constant. The authors propose the application of Monte Carlo summation in order to determine the normalization constant, throughputs, and gradients of throughputs. The rough idea is to randomly sample the product-form solution over the state space and then average to obtain a consistent estimate. The Monte Carlo summation method has computational requirements that grow polynomially in the problem size, in some cases linearly, and can be adapted to arbitrary product-form networks.

Original language | English (US) |
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Title of host publication | Proceedings of the IEEE Conference on Decision and Control |

Publisher | Publ by IEEE |

Pages | 483-484 |

Number of pages | 2 |

ISBN (Print) | 0780304500 |

State | Published - Jan 1992 |

Event | Proceedings of the 30th IEEE Conference on Decision and Control Part 1 (of 3) - Brighton, Engl Duration: Dec 11 1991 → Dec 13 1991 |

### Other

Other | Proceedings of the 30th IEEE Conference on Decision and Control Part 1 (of 3) |
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City | Brighton, Engl |

Period | 12/11/91 → 12/13/91 |

### Fingerprint

### ASJC Scopus subject areas

- Chemical Health and Safety
- Control and Systems Engineering
- Safety, Risk, Reliability and Quality

### Cite this

*Proceedings of the IEEE Conference on Decision and Control*(pp. 483-484). Publ by IEEE.

**Monte Carlo summation applied to multichain queueing networks.** / Ross, Keith; Wang, Jie.

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

*Proceedings of the IEEE Conference on Decision and Control.*Publ by IEEE, pp. 483-484, Proceedings of the 30th IEEE Conference on Decision and Control Part 1 (of 3), Brighton, Engl, 12/11/91.

}

TY - GEN

T1 - Monte Carlo summation applied to multichain queueing networks

AU - Ross, Keith

AU - Wang, Jie

PY - 1992/1

Y1 - 1992/1

N2 - Although many closed multichain queuing networks give rise to a product-form solution for their equilibrium probabilities, evaluating performance measures remains nontrivial due to the presence of a normalization constant. The authors propose the application of Monte Carlo summation in order to determine the normalization constant, throughputs, and gradients of throughputs. The rough idea is to randomly sample the product-form solution over the state space and then average to obtain a consistent estimate. The Monte Carlo summation method has computational requirements that grow polynomially in the problem size, in some cases linearly, and can be adapted to arbitrary product-form networks.

AB - Although many closed multichain queuing networks give rise to a product-form solution for their equilibrium probabilities, evaluating performance measures remains nontrivial due to the presence of a normalization constant. The authors propose the application of Monte Carlo summation in order to determine the normalization constant, throughputs, and gradients of throughputs. The rough idea is to randomly sample the product-form solution over the state space and then average to obtain a consistent estimate. The Monte Carlo summation method has computational requirements that grow polynomially in the problem size, in some cases linearly, and can be adapted to arbitrary product-form networks.

UR - http://www.scopus.com/inward/record.url?scp=0026618524&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0026618524&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0026618524

SN - 0780304500

SP - 483

EP - 484

BT - Proceedings of the IEEE Conference on Decision and Control

PB - Publ by IEEE

ER -