### Abstract

If networks of queues satisfy certain conditions, then the equilibrium distribution for the number of jobs in the various stations has the so-called product-form. In such cases there are relatively elegant and simple computational procedures for the relevant behavioral characteristics. Quite commonly, however, the conditions are too severe and exact solution is practically impossible for larger problems.

In this paper we will consider iterative approximations for networks of queues which either don't possess product-form solutions or are so large that exact solution becomes intractable even using the product-form of the solution. The approximations are based on a mean value analysis approach and use either aggregation of some sort or decomposition. For the details of the approximations heuristic arguments are used. The approach is worked out for some problem types.

In this paper we will consider iterative approximations for networks of queues which either don't possess product-form solutions or are so large that exact solution becomes intractable even using the product-form of the solution. The approximations are based on a mean value analysis approach and use either aggregation of some sort or decomposition. For the details of the approximations heuristic arguments are used. The approach is worked out for some problem types.

Original language | English |
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Title of host publication | Stochastic Programming |

Editors | F. Archetti, G. Di Pillo, M. Lucertini |

Place of Publication | Berlin |

Publisher | Springer |

Pages | 95-106 |

Number of pages | 12 |

ISBN (Electronic) | 978-3-540-39729-8 |

ISBN (Print) | 3-540-16044-2, 978-3-540-16044-1 |

DOIs | |

Publication status | Published - 1986 |

Event | IFIP Workshop - Gargnano, Italy Duration: 15 Sep 1983 → 21 Sep 1983 |

### Publication series

Name | Lecture Notes in Control and Information Sciences |
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Volume | 76 |

ISSN (Print) | 0170-8643 |

### Conference

Conference | IFIP Workshop |
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Country | Italy |

City | Gargnano |

Period | 15/09/83 → 21/09/83 |

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## Cite this

van Doremalen, J. B. M., & Wessels, J. (1986). Iterative approximations for queueing networks. In F. Archetti, G. Di Pillo, & M. Lucertini (Eds.),

*Stochastic Programming*(pp. 95-106). (Lecture Notes in Control and Information Sciences; Vol. 76). Springer. https://doi.org/10.1007/BFb0006866