A compositional approach to performance modelling
A compositional approach to performance modelling
SIAM Journal on Matrix Analysis and Applications
Markov Decision Processes: Discrete Stochastic Dynamic Programming
Markov Decision Processes: Discrete Stochastic Dynamic Programming
An Efficient Kronecker Representation for PEPA Models
PAPM-PROBMIV '01 Proceedings of the Joint International Workshop on Process Algebra and Probabilistic Methods, Performance Modeling and Verification
Model Checking Continuous-Time Markov Chains by Transient Analysis
CAV '00 Proceedings of the 12th International Conference on Computer Aided Verification
Formal verification of probabilistic systems
Formal verification of probabilistic systems
Theoretical Computer Science - Tools and algorithms for the construction and analysis of systems (TACAS 2004)
ACM SIGMETRICS Performance Evaluation Review
Compositional Abstraction for Stochastic Systems
FORMATS '09 Proceedings of the 7th International Conference on Formal Modeling and Analysis of Timed Systems
Three-valued abstraction for continuous-time Markov chains
CAV'07 Proceedings of the 19th international conference on Computer aided verification
PRISM: a tool for automatic verification of probabilistic systems
TACAS'06 Proceedings of the 12th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Don’t know in probabilistic systems
SPIN'06 Proceedings of the 13th international conference on Model Checking Software
Visualisation for stochastic process algebras: the graphic truth
EPEW'11 Proceedings of the 8th European conference on Computer Performance Engineering
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Stochastic process algebras such as PEPA allow complex stochastic models to be described in a compositional way, but this leads to state space explosion problems. To combat this, there has been a great deal of work in developing techniques for abstracting Markov chains. In particular, abstract -- or interval -- Markov chains allow us to aggregate states in such a way as to safely bound transient probabilities of the original Markov chain. Whilst we can apply this technique directly to a PEPA model, it requires us to obtain the CTMC of the model, whose state space may be too large to construct explicitly. In this paper, we present a compositional application of abstract Markov chains to PEPA, based on a Kronecker representation of the underlying CTMC. This can be used to bound probabilistic reachability properties in the Continuous Stochastic Logic (CSL), and we have implemented this as part of the PEPA plug-in for Eclipse. We conclude with an example application -- analysing the performance of a wireless network--and use this to illustrate the impact of the choice of states to aggregate on the precision of the bounds.