Invariante statlonäre zustandswahrscheinlichkeiten fur eine klasse stochastischer modelle mit f unktionellen abhangigkeiten
- 1 January 1976
- journal article
- research article
- Published by Taylor & Francis in Mathematische Operationsforschung und Statistik
- Vol. 7 (4) , 497-522
- https://doi.org/10.1080/02331887608801314
Abstract
A wide class of stochastic queueing and reliability systems is postulated. Independent randnm variables may be realized with different. speeds depending on the state of the whole system. In this way one may also seize certain functional dependences between elements of the system and temporary interruptions of the realizations of the randam variables. They may also be breaken off. Besides more than one simultaneous redized random variables can be assigned to several elements of the model. A homogeneous MARKOV process is constructed. A property of invariance for the stationary probabilities of states at changing over from exponential to common distributed random variables with given mathematical expectations is defined. Necessary and sufficient pure algebraic criterions for the validity of the property of invsriance are stated. Besides the stationary probabilities of states at arbitrary points of time corresponding stationary quantities at points of time of changing states of the system and the connection between them are investigated. An example is given. Further appiications on several models are included in [10].Keywords
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