Performance-model abstraction in a synthesis-centric model-driven systems engineering framework

Supervisory control theory deals with automated synthesis of models of supervisory controllers that coordinate and control discrete-event high-level system behavior. These controllers ensure safe and nonblocking functioning of the system, but there do not exist efficient synthesis procedures for controllers that can ascertain complex liveness and performance guarantees. To this end, the supervised system must be validated to ensure that the desired functionality and performance is preserved. To verify that the supervised system also satisfies the performance requirements, a performance model is derived by abstracting the model of the supervised system. The latter is modeled by stochastic extensions of discrete-events systems with Markovian (exponential) delays. The resulting performance model is a continuous-time Markov chain with state labels. There exist algorithms for extraction of the Markov process, which optimize the number of states of the performance model. We show that this optimization leads to an abstraction that is not always suitable for performance evaluation by stochastic model checking. The abstracted states form paths that are not justifiable in the original system, which may lead to wrong performance metrics. We formalize the relationship between the original stochastic discrete-event and the performance model, and we propose a new abstraction that does not introduce these insupportable properties in the performance model.