A criterion of insensitivity for a class of queueing systems with random marked point processes

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Abstract
For a wide class of queueing models which is described by a formalism the problem is searched that the steady state probabilities are insensitive with respect to the distributions of the sequences of certain basic random variables (e.g. service on a fixed device) of the queueing model. The random variables in such a sequence may be dependent. Moreover functional dependences described by speeds for the working off of the basic random variables are allowed. In the paper a stationary distribution for the models and its attached Palm distribution in such points where they change their “macrostates” are given, if an algebraic criterion is fulfilled by the models. Thus earlier papers which deal with the insensitivity pro mem are generalized. Also a new idea for the proof of the sufficiency of the algebraic criterion is used. Some formulas for imbedded steady state probabilities and mean sojourn times in certain state sets are concluded.