Modeling and analysis of switching max-plus linear systems with discrete-event feedback

Switching max-plus linear system (SMPLS) models are an apt formalism for performance analysis of discrete-event systems. SMPLS analysis is more scalable than analysis through other formalisms such as timed automata, because SMPLS abstract pieces of determinate concurrent system behavior into atomic modes with fixed timing. We consider discrete-event systems that are decomposed into a plant and a Supervisory Controller (SC) that controls the plant. The SC needs to react to events, concerning e.g. the successful completion or failure of an action, to determine the future behavior of the system, for example, to initiate a retrial of the action. To specify and analyze such system behavior and the impact of feedback on timing properties, we introduce an extension to SMPLS with discrete-event feedback. In this extension, we model the plant behavior with system modes and capture the timing of discrete-event feedback emission from plant to SC in the mode matrices. Furthermore, we use I/O automata to capture how the SC responds to discrete-event feedback with corresponding mode sequences of the SMPLS. We define the semantics of SMPLS with events using new state-space equations that are akin to classical SMPLS with dynamic state-vector sizes. To analyze the extended models, we formulate a transformation from SMPLS with events to classical SMPLS with equivalent semantics and properties such that performance properties can be analyzed using existing techniques. Our approach enables the specification of discrete-event feedback from the plant to the SC and its performance analysis. We demonstrate our approach by specifying and analyzing the makespan of a flexible manufacturing system.