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**Some order relations in closed networks of queues with multiserver stations.**
*(English)*
Zbl 0612.90042

Consider a closed network of queues of the ”product-form” type, where each station has s servers (s\(\geq 1\) is identical for all stations). We show that the throughput function of the network is Schur concave with respect to the loading of the stations and arrangement increasing with respect to the assignment of server groups. Consequently, different loading/assignment policies can be compared under majorization/arrangement orderings and their relative merits decided according to the yields of throughput. The results can be used to support planning decisions in computer and production systems which are modeled as closed networks of queues.

### MSC:

90B22 | Queues and service in operations research |

90B10 | Deterministic network models in operations research |

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

### Keywords:

multiserver stations; closed network of queues; loading/assignment policies; majorization/arrangement orderings; computer and production systems
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\textit{D. D. Yao} and \textit{S. C. Kim}, Nav. Res. Logist. 34, No. 1--2, 53--66 (1987; Zbl 0612.90042)

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