Approximate Mean Value Analysis based on Markov Chain Aggregation by Composition

Markovian performance models are impractical for large systems because their state space grows very rapidly with the system size. This paper derives an approximate Mean Value Analysis (AMVA) solution for Markov models that represent a composition of subsystems. The goal is robust scalable analytical approximation. The approach taken here is to create approximate aggregated Markov chain submodels, each representing a view of the Markov chain for the entire system from the perspective of a selected set D of tagged components, and to derive mean value equations from them. The analytic solutions of submodels are then combined using system-level relationships, which must be identified for each system; this is not automatic but is usually straightforward. The first point of novelty is the method used to create the aggregate submodels for different sets D, building up each submodel by composition of the components in D rather than by aggregating the entire state space. Another point of novelty is the use of partitioned Markov models to obtain analytic solutions.