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Analysis of stochastic Petri nets by the concept of near-complete decomposability

 
: Giglmayr, J.

Czech Academy of Sciences, Praha:
Tenth Prague Conference on Information Theory, Statistical Decision Functions, Random Processes 1988. Vol.A : Held at Prague, from July 7 to 11, 1986
Dordrecht: Reidel, 1988
ISBN: 90-277-2480-6
pp.337-344
Prague Conference on Information Theory, Statistical Decision Functions, Random Processes <10, 1986, Praha>
English
Conference Paper
Fraunhofer HHI ()
petri nets; queueing theory; state-space methods; stochastic processes; switching theory; real systems modelling; stochastic petri nets; near-complete decomposability; state space explosion; transition rate matrix; stationary marking probabilities; broadband switching control

Abstract
The crucial problem when modelling real systems by stochastic Petri nets is the state space explosion and consequently the increase of the size of the transition rate matrix representing the stochastic Petri net. A stochastic Petri net is analysed by decomposing the transition rate matrix. In particular, the stationary marking probabilities are determined by solving several smaller matrix equations instead of solving the large equation system made up of the transition rate matrix. The applicability of the approach is shown by the simplified Petri net model of a broadband switching control. For this example rules for the decomposition providing exact results for the stationary marking probabilities are presented.

: http://publica.fraunhofer.de/documents/N-13869.html