Modeling Multidimensional Communication Lattices with Moore Neighborhood by Infinite Petri Nets

Multidimensional torus topology plays a key role as a topology of the communication system of supercomputers and clusters as well as networks on chip. An infinite Petri net model of multidimensional torus communication grid with Moore neighborhood and combined cut-through and store-and-forward switching device has been constructed, its place invariance proven based on solving infinite linear Diophantine systems of equations in parametric form. For specifying Moore neighborhood, that traverses all hypercube bounds of lesser dimension, we use designation of the switching device ports by the coordinate difference. It is mentioned that the obtained results are applicable for modeling brain and processes of spreading insects and viruses.