Exploiting Modal Logic to Express Performance Measures

Abstract

Abstract. Stochastic process algebras such as PEPA provide ample support for the component-based construction of models. Tools compute the numerical solution of these models; however, the stochastic process algebra methodology has lacked support for the specification and calculation of complex performance measures. In this paper we present a stochastic modal logic which can aid the construction of a reward structure over the model. We discuss its relationship to the underlying theory of PEPA. We also present a performance specification language which supports high level reasoning about PEPA models, and allows queries about their equilibrium behaviour. The meaning of the specification language has its foundations in the stochastic modal logic. We describe the implementation of the logic within the PEPA Workbench and a case study is presented to illustrate the approach.

Performance investigation of an on‐line auction system

“…It detects faults such as deadlocks and cooperations which do not involve active participants. In the most recent version, it includes support for a modal logic, allowing behavioural requirements of a model to be formally expressed and automatically checked [12].…”

Trust domains in system models: algebra, logic, utility, and combinators

“…The use of process calculi for decision support is a well established technique. The Performance Evaluation Process Algebra (PEPA) [21,22,23] establishes a compositional theory of Markov Processes, separable product-form distributions for efficient storage, congruence results, and model checking tool support [10,30,23]. This technology can be used to model performance for different designs, enabling decisions to be made at a meta level between such designs.…”

“…Intuitively, a trust domain based on the general nursing skills should be replaceable by a trust domain based on the heart and lungs nursing skills, which include the general skills. Alternatively, we can write this as (10) T D(A, * φ sn ∧ φ nu , ψ su , n su ) ⊆ T D(A, * φ nu , ψ su , n su ).…”

Derivation of passage-time densities in PEPA models using ipc: the imperial PEPA compiler

“…As future developments and to provide further analysis possibilities, we are looking to using ipc to compile full PML (Probabilistic Modal Logic for PEPA models [5,6]) specifications into DNAmaca, as an alternative way of expressing passage start and termination points.…”