Restructuring tensor products to enhance the numerical solution of structured Markov chains

Kronecker descriptors are an efficient option to store the underlying Markov chain of a model in a structured and compact fashion. The basis of classical numerical solutions for Kronecker descriptors represented models is the VectorDescriptor Product (VDP). The Shuffle algorithm is the most popular VDP method to handle generalized descriptors, i.e., descriptors with functional elements. Recently, the Split algorithm was proposed as a flexible optimization for VDP, but it cannot be used to generalized descriptors. This paper addresses an extension of Split algorithm dealing with generalized tensor products considering matrices aggregations and permutations to reduce the computational cost of operations. We present a heuristic for restructuring tensor products tailored for the Split algorithm considering descriptors with functional rates. The proposed heuristic balances the memory usage and CPU demand in order to achieve a time-efficient solution according to the available memory. Finally, this paper presents further alternatives for restructuring tensor products.