Performance evaluation:= (Process Algebra + Model Checking) × Markov chains

Abstract

Markov chains are widely used in practice to determine system performance and reliability characteristics. The vast majority of applications considers continuous-time Markov chains (CTMCs). This tutorial paper shows how successful model specification and analysis techniques from concurrency theory can be applied to performance evaluation. The specification of CTMCs is supported by a stochastic process algebra, while the quantitative analysis of these models is tackled by means of model checking. Process algebra provides: (i) a high-level specification formalism for describing CTMCs in a precise, modular and constraint-oriented way, and (ii) means for the automated generation and aggregation of CTMCs. Temporal logic model checking provides: (i) a formalism to specify complexmeasures-of-interest in a lucid, compact and flexible way, (ii) automated means to quantify these measures over CTMCs, and (iii) automated measure-driven aggregation (lumping) of CTMCs. Combining process algebra and model checking constitutes a coherent framework for performance evaluation based on CTMCs.