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Computation of the state probabilities in a class of semi-regenerative queueing models

  • Helmut Schellhaas

Abstract

One of the standard problems in queueing analysis concerns the computation of the steady state probabilities. In recent years significant contributions to this problem have been made. Important research papers by M.F. Neuts in the context of phase type distributions and by H.C. Tijms and M.H. Van Hoorn in the context of regenerative processes were very stimulating for our investigations. We refer to Neuts (1981), (1984) and the literature cited there and to Tijms and Van Hoorn (1981) and Van Hoorn (1983). In thie paper we consider the unifying queueing model including several well known models as special cases. Using a semi-regenerative analysis we develop an efficient and stable algorithm for the computation of the steady state probabilities. The usefulness of the results is demonstrated by applications to several modifications of state dependent M/G/1 queues.

Keywords

Busy Period Input Process Service Time Distribution Time Epoch Phase Type Distribution 
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.

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Copyright information

© Springer Science+Business Media New York 1986

Authors and Affiliations

  • Helmut Schellhaas
    • 1
  1. 1.Fachbereich MathematikTechnische Hichschule DarmstadtDarmstadtGermany

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