Computation of the state probabilities in a class of semi-regenerative queueing models
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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.
KeywordsBusy Period Input Process Service Time Distribution Time Epoch Phase Type Distribution
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- A.G. de Kok (1982), Computational methods for single server queueing systems with repeated attemps. Report, Interfaculteit der Actuariele Wetenschappen en Econometrie, Vrije Universiteit, Amsterdam.Google Scholar
- M.F. Neuts (1981), Matrix-geometric solutions in stochastic models. An algorithmic approach. The John Hopkins University Press. Baltimore.Google Scholar
- H. Schellhaas (1978). On the T-policy for an M/G/1 queue. Operations Research Verfahren 29, 750–763.Google Scholar
- M.H. Van Hoorn (1983), Algorithms and approximations for queueing systems Doctoral thesis. Mathematisch Centrum, Amsterdam.Google Scholar