Efficient Parametric Model Checking Using Domain Knowledge

Abstract

We introduce an efficient parametric model checking (ePMC) method for the analysis of reliability, performance and other quality-of-service (QoS) properties of software systems. ePMC speeds up the analysis of parametric Markov chains modelling the behaviour of software by exploiting domain-specific modelling patterns for the software components. To this end, ePMC precomputes closed-form expressions for key QoS properties of such patterns, and uses these expressions in the analysis of whole-system models.To evaluate ePMC, we show that its application to service-based systems and multi-tier software architectures reduces analysis time by several orders of magnitude compared to current parametric model checking methods.

Fast Parametric Model Checking through Model Fragmentation

“…We summarise the concept of a pDTMC fragment and its exploitation by the PMC approach introduced in [4], where the results from this section are taken from. As shown in Fig.…”

“…The theoretical framework from [4] shows that, if a fragment F of a pDTMC D is identified, then the "monolithic", onestep PMC of reachability, unbounded until and (not covered in our paper) reward properties [24] of D can be replaced by the following equivalent steps: 1) Compute PMC formulae for the probabilities of reaching all the output states of fragment F starting from its input state z 0 ; this amounts to the PMC of #Z out reachability properties of a pDTMC built from F removing the incoming transitions of z 0 and by replacing the outgoing transitions of each output state in Z out with a "self-loop" transition of probability 1. 2) Build an abstract pDTMC model D ′ from D by replacing the states in Z and their internal transitions with a single state z ′ whose incoming transitions (and transition probabilities) are those of z 0 .…”

“…Our paper introduces a fast PMC (fPMC) technique that complements the advances from [1]- [3], enabling the efficient parametric model checking of reachability properties for parametric discrete-time Markov chains (pDTMCs) of systems with more complex behaviour and larger numbers of parameters than previously possible. fPMC extends and automates a recently proposed theoretical framework for efficient parametric model checking [4].…”

“…Parametric model checking (PMC) [1]- [4] is a formal technique for analysing the reliability and performance of systems with stochastic behaviour. The underlying concepts are very simple.…”

“…1) The first model fragmentation algorithm for the automated partition of pDTMCs into fragments with the characteristics defined by our theoretical framework from [4], which shows how model fragments can be exploited, but does not provide a generally applicable model fragmentation technique. 2) New theoretical results that allow the formation of model fragments from subsets of pDTMC states that do not (initially) meet the definition of a fragment.…”