Shared Transaction Markov Chains for fluid analysis of massively parallel systems

Abstract

We introduce a low-level performance modelling formalism, Shared Transaction Markov Chains (STMCs), specifically designed for the capture and analysis of massively parallel stochastic systems through fluid techniques. We introduce the notion of a shared transaction between concurrently running Markov chains which allows a multi-phase synchronisation to accurately represent complex cooperation between modelling components in a compositional manner. We demonstrate the new modelling formalism on four distinct models and show how fluid analysis may be performed, with results, where appropriate. Our contribution is that this is the first such system tailored to the fluid performance analysis of transaction-based systems as found in computing applications such as peer-to-peer networks, web architectures and Publish-Subscribe networks. The second contribution is that STMCs permit composed phase-type distributed synchronisation which is more useful from a transaction modelling perspective.