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Operations-Research-Spektrum

, Volume 11, Issue 2, pp 97–100 | Cite as

Monotonicity of the throughput of a closed exponential queueing network in the number of jobs

  • J. van der Wal
Theoretical Papers

Summary

It is shown that the throughput of a closed exponential queueing network is nondecreasing in the number of jobs in the system if the service rate in each station is nondecreasing in the number of jobs in that queue. The line of proof seems to be extendable to a variety of networks without a product form equilibrium.

Keywords

Product Form Service Rate Form Equilibrium Queueing Network Exponential Queueing 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Zusammenfassung

Es wird gezeigt, daß der Durchsatz eines geschlossenen exponentiellen Warteschlangen-Netzwerks hinsichtlich der Anzahl der Aufträge im System nicht fällt, wenn die Bedienungsrate in jeder Station hinsichtlich der Anzahl der Aufträge in dieser Warteschlange nicht fällt. Die Beweisführung scheint erweiterbar auf eine Vielzahl von Netzwerken ohne Produktionsgleichgewicht.

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References

  1. Doremalen JBM van de Waal PR (1985) An approximation method for closed queueing networks with two-phase servers. Eindhoven University of Technology, Department of Mathematics and Computing Science, Memorandum COSOR 85–15Google Scholar
  2. Robertazzi TG, Lazar AA (1985) On the modeling and optimal flow control on the Jacksonian network. Perform Eval 5:29–43Google Scholar
  3. Suri R (1985) A concept of monotonicity and its characterization for closed queueing networks. Oper Res 33:606–624Google Scholar
  4. Yao DD (1985) Some properties of the throughput function of closed networks of queues. Oper Res Lett 3:313–317Google Scholar

Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • J. van der Wal
    • 1
  1. 1.Department of Mathematics and Computing ScienceEindhoven University of TechnologyEindhovenThe Netherlands

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