Timed Rebeca schedulability and deadlock freedom analysis using bounded floating time transition system

Abstract

Timed Rebeca is an extension of the actor-based modeling language Rebeca that supports timing features. Rebeca is purely actor-based with no shared variables and asynchronous message passing with no explicit receive. Both computation time and network delays can be modeled in Timed Rebeca. In this paper, we propose a new approach for checking schedulability and deadlock freedom of Timed Rebeca models. The key features of Timed Rebeca, asynchrony of actors and absence of shared variables, and the focus on events instead of states in the selected properties, led us to a significant reduction in the state space. In the proposed method, there is no unique time value for each state, instead of that we store the local time of each actor separately. We prove the bisimilarity of the generated transition system, called floating time transition system, and the state space generated from the original semantics of Timed Rebeca. In addition, to avoid state space explosion because of time progress, we define a type of equivalency among states called shift equivalency. The shift equivalence relation between states can be used for Timed Rebeca as the timing features are based on relative values. We developed a tool, and the experimental results show that our approach mitigates the state space explosion problem of the former methods and allows model checking of larger systems.