Spatial specification of hypertorus interconnect by infinite and reenterable coloured Petri nets

Abstract

Multidimensional torus interconnect finds wide application in modern exascale computing. For models design in high-performance computing, grid and cloud computing, and also systems biology, two basic ways of specifying spatial structures with Petri nets are considered – an infinite Petri net specified by a parametric expression (PE) and a reenterable coloured Petri net (CPN). The paper studies a composition of hypertorus grid models in the form of a PE and a reenterable CPN, their mutual transformations, and unfolding into a place/transition net; the parameters are the number of dimensions and the size of grid. A grid is composed via connection of neighbouring cells by dedicated transitions modelling channels. Reenterable model peculiarities are explained on step-by-step simulation examples. The rules of mutual transformations of Petri net spatial specifications are specified. Comparative investigation of two mentioned forms of spatial specifications is implemented, including analysis techniques and tools. CPNs are convenient for the state space analysis. The main advantage of PEs is the ability to obtain linear invariants and other structural constructs of Petri nets, for instance, siphons and traps, in parametric form that allows us to draw conclusions on Petri net properties for any values of parameters.