### Abstract

Multiclass queuing networks and stochastic loss networks often give rise to a product form solution for their equilibrium probabilities, but the product form solution typically involves a normalization constant calling for a multidimensional summation over an astronomical number of states. The authors propose the application of Monte Carlo summation to the problem of determining the normalization constant and related performance measures. It is shown that if the proper sampling technique is used then the computational effort of Monte Carlo summation is independent of link capacities for loss networks. The application of importance sampling and antithetic variates is then discussed. Importance sampling is shown to give significant variance reduction for a multirate loss network example.

Original language | English (US) |
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Title of host publication | 90 Winter Simulation Conf. |

Publisher | Publ by IEEE |

Pages | 270-275 |

Number of pages | 6 |

ISBN (Print) | 0911801723 |

State | Published - Dec 1990 |

Event | 1990 Winter Simulation Conference Proceedings - New Orleans, LA, USA Duration: Dec 9 1990 → Dec 12 1990 |

### Other

Other | 1990 Winter Simulation Conference Proceedings |
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City | New Orleans, LA, USA |

Period | 12/9/90 → 12/12/90 |

### Fingerprint

### ASJC Scopus subject areas

- Chemical Health and Safety
- Software
- Safety, Risk, Reliability and Quality
- Applied Mathematics
- Modeling and Simulation

### Cite this

*90 Winter Simulation Conf.*(pp. 270-275). Publ by IEEE.

**Solving product form stochastic networks with Monte Carlo summation.** / Ross, Keith; Wang, Jie.

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

*90 Winter Simulation Conf..*Publ by IEEE, pp. 270-275, 1990 Winter Simulation Conference Proceedings, New Orleans, LA, USA, 12/9/90.

}

TY - GEN

T1 - Solving product form stochastic networks with Monte Carlo summation

AU - Ross, Keith

AU - Wang, Jie

PY - 1990/12

Y1 - 1990/12

N2 - Multiclass queuing networks and stochastic loss networks often give rise to a product form solution for their equilibrium probabilities, but the product form solution typically involves a normalization constant calling for a multidimensional summation over an astronomical number of states. The authors propose the application of Monte Carlo summation to the problem of determining the normalization constant and related performance measures. It is shown that if the proper sampling technique is used then the computational effort of Monte Carlo summation is independent of link capacities for loss networks. The application of importance sampling and antithetic variates is then discussed. Importance sampling is shown to give significant variance reduction for a multirate loss network example.

AB - Multiclass queuing networks and stochastic loss networks often give rise to a product form solution for their equilibrium probabilities, but the product form solution typically involves a normalization constant calling for a multidimensional summation over an astronomical number of states. The authors propose the application of Monte Carlo summation to the problem of determining the normalization constant and related performance measures. It is shown that if the proper sampling technique is used then the computational effort of Monte Carlo summation is independent of link capacities for loss networks. The application of importance sampling and antithetic variates is then discussed. Importance sampling is shown to give significant variance reduction for a multirate loss network example.

UR - http://www.scopus.com/inward/record.url?scp=0025533029&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0025533029&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0025533029

SN - 0911801723

SP - 270

EP - 275

BT - 90 Winter Simulation Conf.

PB - Publ by IEEE

ER -