Symbolic Solution of Kronecker-Based Structured Markovian Models

Abstract

This paper describes a method to obtain symbolic solution of large stochastic models using Gauss-Jordan elimination. Such solution is an efficient alternative to standard simulations and it allows fast and exact solution of very large and complex models that are hard to be dealt even with iterative numerical methods. The proposed method assumes the system described as a structured (modular) Markovian system with discrete states for each system module and transitions among those states ruled by Markovian processes. The mathematical representation of such system is made by a Kronecker (Tensor) formula, i.e., a tensor formulation of small matrices representing each system module transitions and occasional dependencies among modules. Preliminary results of the proposed solution indicate the expected efficiency of the proposed solution.