Numerical Solution of Non-Homogeneous Markov Processes through Uniformization

Abstract

Numerical algorithms based on uniformization have been proven to be numerically stable and computationally attractive to compute transient state distributions in homogeneous continuous-time Markov chains. Recently, Van Dijk [van Dijk 1992] formulated uniformization for non-homogeneous Markov processes, and it is of interest to investigate numerical algorithms based on uniformization for non-homogeneous models as well. We will introduce three different uniformization-based algorithms for non-homogeneous Markov processes. We implement all three algorithms, and use an example of a duplex safety model to compare the algorithms with respect to accuracy, memory use and speed. Based on these results, we provide guidelines for the implementation and application of uniformization-based algorithms for nonhomogeneous Markov processes. 1 INTRODUCTION Computing and communication systems often exhibit time-dependent behavior that can be modeled naturally by non-homogeneous continuous-time Markov ...