Approximate steady-state analysis of large Markov models based on the structure of their decision diagram encoding

Abstract

We propose a new approximate numerical algorithm for the steady-state solution of general structured ergodic Markov models. The approximation uses a state–space encoding based on multiway decision diagrams and a transition rate encoding based on a new class of edge-valued decision diagrams. The new method retains the favorable properties of a previously proposed Kronecker-based approximation, while eliminating the need for a Kronecker-consistent model decomposition. Removing this restriction allows for a greater utilization of event locality, which facilitates the generation of both the state–space and the transition rate matrix, thus extends the applicability of this algorithm to larger and more complex models.