Complex Systems

Infinite Petri Nets: Part 2, Modeling Triangular, Hexagonal, Hypercube and Hypertorus Structures Download PDF

Dmitry A. Zaitsev
Vistula University
Warsaw, Poland

Ivan D. Zaitsev
Ershov Institute of Informatics Systems
Novosibirsk, Russia

Tatiana R. Shmeleva
National Academy of Telecommunications
Odessa, Ukraine

Abstract

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 ill-intentioned traffic revealed. Prospective directions for future research of infinite Petri nets are formulated and hypotheses advanced.