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A definition of discrete product form distributions

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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.

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

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Schassberger, R. A definition of discrete product form distributions. Zeitschrift für Operations Research 23, 189–195 (1979). https://doi.org/10.1007/BF01919483

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  • DOI: https://doi.org/10.1007/BF01919483

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