A Component-Based Solution Method for Non-ergodic Markov Regenerative Processes

This paper presents a new technique for the steady state solution of non-ergodic Markov Regenerative Processes (MRP), based on a structural decomposition of the MRP. Each component may either be a CTMC or a (smaller) MRP. Classical steady state solution methods of MRP are based either on the computation of the embedded Markov chain (EMC) defined over regenerative states, leading to high complexity in time and space (since the EMC is usually dense), or on an iterative scheme that does not require the construction of the EMC. The technique presented is particularly suited for MRPs that exhibit a semi-sequential structure. In this paper we present the new algorithm, its asymptotic complexity, and its performance in comparison with classical MRP techniques. Results are very encouraging, even when the MRP only loosely exhibits the required semi-sequential structure.