Stochastic Evaluation of Large Interdependent Composed Models Through Kronecker Algebra and Exponential Sums

Abstract

The KAES methodology for efficient evaluation of dependability-related properties is proposed. KAES targets systems representable by Stochastic Petri Nets-based models, composed by a large number of submodels where interconnections are managed through synchronization at action level. The core of KAES is a new numerical solution of the underlying CTMC process, based on powerful mathematical techniques, including Kronecker algebra, Tensor Trains and Exponential Sums. Specifically, advancing on existing literature, KAES addresses efficient evaluation of the Mean-Time-To-Absorption in CTMC with absorbing states, exploiting the basic idea to further pursue the symbolic representation of the elements involved in the evaluation process, so to better cope with the problem of state explosion. As a result, computation efficiency is improved, especially when the submodels are loosely interconnected and have small number of states. An instrumental case study is adopted, to show the feasibility of KAES, in particular from memory consumption point of view.