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Zeitschrift für Operations Research

, Volume 23, Issue 5, pp 189–195 | Cite as

A definition of discrete product form distributions

  • R. Schassberger
Article

Summary

A number of important applied probability models, many of which can be interpreted as networks of queues, lead to a discrete probability distribution of states exhibiting a so-called “product form”. This phenomenon is explained by a certain form of “decomposability”, and a definition of the notion of product form emerges.

Keywords

Probability Distribution Probability Model Product Form Applied Probability Form 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.

Zusammenfassung

Bei einer Reihe von wichtigen Modellen aus dem Anwendungsbereich der Wahrscheinlichkeitstheorie, viele davon als Netzwerke von Warteschlangen interpretierbar, treten diskrete Wahrscheinlichkeitsverteilungen auf, deren Gestalt von einer „Produktform” ist. Dieses Phänomen wird durch eine gleichzeitig auftretende Art der „Zerlegbarkeit“ erklärt, woraus eine Definition des Begriffs der „Produktform“ resultiert.

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References

  1. Baskett, F., K.M. Chandy, R.R. Muntz andF.G. Palacios: Open Closed, and Mixed Networks of Queues with Different Classes of Customers. Journal of the ACM, 1975, 248–260.Google Scholar
  2. Courtois, P.J.: Decomposability. New York 1977.Google Scholar
  3. Gordon, W.T., andG.F. Newell: Closed Queueing Systems with Exponential Servers. Operations Res.15, 1967, 252–265.Google Scholar
  4. Schassberger, R.: Insensitivity of steady-state distributions of generalized semi-Markov processes. Part I, Ann. Prob.5, 1977, 87–99.Google Scholar
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Copyright information

© Physica-Verlag 1979

Authors and Affiliations

  • R. Schassberger
    • 1
  1. 1.Fachbereich MathematikTU BerlinBerlin 12

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