A composition and analysis technique was developed for investigation of infinite Petri nets with regular structure, introduced for modeling networks, clusters and computing grids, that also concerns cellular automata and biological systems. A case study of a square grid structure composition and analysis is presented. Parametric description of Petri nets, parametric representation of infinite systems for the calculation of place/transition invariants, and solving them in parametric form allowed the invariance proof for infinite Petri net models. Complex deadlocks were disclosed and a possibility of network blocking via ill-intentioned traffic revealed.
An overview of works, early published by the authors, has been done that explains peculiarities of composition and analysis technique developed for investigation of infinite Petri nets with regular structure which were introduced for modeling networks, clusters, and computing grids. Parametric description of Petri nets, parametric representation of infinite systems for calculation place/transition invariants, and solving them in parametric form allowed the invariance proof for infinite Petri net models. Complex deadlocks were disclosed and a possibility of the network blocking via ill-intended traffic revealed. Prospective directions for future research of infinite Petri nets were formulated.
A composition and analysis technique was developed for investigation of infinite Petri nets with regular structure introduced for modeling networks, clusters and computing grids that also concerns cellular automata and biological systems. A case study of a hypercube structure composition and analysis is presented; particularities of modeling other structures are discussed: triangular and hexagonal structures on a plane and a hypertorus in a multidimensional space. Parametric description of Petri nets, parametric representation of infinite systems for the calculation of place/transition invariants and solving them in parametric form allow the invariance proof for infinite Petri net models. Complex deadlocks are disclosed and a possibility of the network blocking via illintentioned traffic revealed. Prospective directions for future research of infinite Petri nets are formulated and hypotheses advanced.
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