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Mean value analysis of closed queueing networks with Erlang service time distributions

Mittelwertanalyse für geschlossene Bedienungssysteme mit Erlang-verteilten Bedienungszeiten

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Abstract

The classical mean value analysis approach is extended to single class closed queueing networks containing Erlang service time distributions and FCFS scheduling disciplines. A new formula for the mean residence time of jobs is derived. Each iteration provides self-checks for validity, and is repeated whenever invalid results are detected. On the average, the solutions obtained vary by less than five percent from their respective simulation results.

Zusammenfassung

Die klassische Mittelwertanalyse wird auf geschlossene Warteschlangennetze mit einer Auftragsklasse, Erlang-verteilten Bedienungszeiten und FCFS Zuteilungsmechanismen erweitert. Eine neue Formel für die mittlere Verweilzeit wird hergeleitet. Jede Iteration sieht Gültigkeitskontrollen vor und wird bei Feststellung ungültiger Ergebnisse wiederholt. Die so gewonnenen Lösungen unterscheiden sich im Durchschnitt um weniger als 5% von entsprechenden Simulationsergebnissen.

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Authors and Affiliations

  1. School of Information and Computer Science, Georgia Institute of Technology, 30332, Atlanta, GA, U.S.A.

    I. F. Akyildiz

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  1. I. F. Akyildiz
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Akyildiz, I.F. Mean value analysis of closed queueing networks with Erlang service time distributions. Computing 39, 219–232 (1987). https://doi.org/10.1007/BF02309556

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  • DOI: https://doi.org/10.1007/BF02309556

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