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**Some properties of the throughput function of closed networks of queues.**
*(English)*
Zbl 0569.90029

The throughput function of a closed network of queues is shown to be Schur concave and arrangement increasing. As a consequence of these properties, loading and server-assignment policies can be compared based on the majorization and the arrangement orderings. Implications of the results are discussed.

### MSC:

90B22 | Queues and service in operations research |

60K25 | Queueing theory (aspects of probability theory) |

60K20 | Applications of Markov renewal processes (reliability, queueing networks, etc.) |

90B10 | Deterministic network models in operations research |

### Keywords:

Schur convexity; throughput function; closed network of queues; arrangement increasing; majorization
Full Text:
DOI

### References:

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[2] | Gelenbe, E.; Mitrani, I., Analysis and Synthesis of Computer Systems (1980), Academic Press: Academic Press London · Zbl 0484.68026 |

[3] | Gross, D.; Miller, D. R.; Soland, R. M., A closed queueing network model for multi-echelon repairable item provisioning, AIIE Transactions, 15, 344-352 (1983) |

[4] | Marshall, A. W.; Olkin, I., Inequalities: Theory of Majorization and its Applications (1979), Academic Press: Academic Press New York · Zbl 0437.26007 |

[5] | Price, T. G., Probability models of multi-programmed computer systems, (Ph.D. Dissertation (1974), Department of Electrical Engineering, Stanford University: Department of Electrical Engineering, Stanford University Stanford, CA) |

[6] | Shanthikumar, J. G., On the superiority of balanced load in a flexible manufacturing system (1982), Department of Industrial Engineering and Operations Research, Syracuse University: Department of Industrial Engineering and Operations Research, Syracuse University Syracuse, NY |

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