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Analysis of Busy Period and Response Time Distributions in Queuing Networks

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Messung, Modellierung und Bewertung von Rechensystemen

Part of the book series: Informatik-Fachberichte ((INFORMATIK,volume 61))

Abstract

Queuing networks are widely used for modeling computer and communications systems. In recent years, efficient algorithms have been developed for the stationary state analysis from which the performance can be evaluated in terms of throughput and average delays. In this paper, the method of first passage times is used to analyze time-dependent processes within Markovian queuing networks as busy periods and response (cycle) times. Closed-form expressions are derived for the cyclic queuing system with two service stations. Generalizations to more complex networks are finally discussed. The analysis of life-time processes leads to a much deeper insight in the behavior of queuing networks compared to the stationary state analysis allowing for individual customer delay distributions or distributions of periods of continuous or simultaneous service. The method of first passage times is of particular advantage for cases with higher degrees of dependence as, e.g., networks with state- dependent service rates, queue disciplines other than FIFO, or cycle paths with overtaking.

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Author information

Authors and Affiliations

  1. Institute of Switching and Data Technics, University of Stuttgart, 7000, Stuttgart, Germany

    P. J. Kuehn

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  1. P. J. Kuehn
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Editors and Affiliations

  1. Institut für Nachrichtenvermittlung und Datenverarbeitung, Universität Stuttgart, Seidenstraβe 36, 7000, Stuttgart 1, Deutschland

    Paul J. Kühn

  2. Abt. 3144,7030-19, IBM Entwicklung und Forschung, Schönaicher Straβe 220, 7030, Böblingen, Deutschland

    Klaus M. Schulz

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© 1983 Springer-Verlag Berlin Heidelberg

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Kuehn, P.J. (1983). Analysis of Busy Period and Response Time Distributions in Queuing Networks. In: Kühn, P.J., Schulz, K.M. (eds) Messung, Modellierung und Bewertung von Rechensystemen. Informatik-Fachberichte, vol 61. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-68830-0_10

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  • DOI: https://doi.org/10.1007/978-3-642-68830-0_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11990-6

  • Online ISBN: 978-3-642-68830-0

  • eBook Packages: Springer Book Archive

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