Analyzing permutation capability of multistage interconnection networks with colored Petri nets

Abstract

In a multistage interconnection network (MIN) the calculation of the number of permutations of the input terminals into the output terminals is a classic difficult problem. In this paper, we introduce an innovative technique based on Colored Petri Nets (known as CP-nets or CPNs) that will allow us to analyze the permutation capability of arbitrary MINs. We show how to verify whether a MIN is rearrangeable through the state space analysis of the associated CP-net and we measure the permutation capability of non-rearrangeable MINs in terms of the permutations that can be generated. The proposed approach takes advantage of powerful existing software tools, particularly, CPNTools, which is used to explore the occurrence graphs of CP-nets and determine the set of permutations performed by the modeled MINs. This new technique is easy to use and can be efficiently applied to MINs made of cross-bar switches.