Behavioural equivalences for timed systems

Timed transition systems are behavioural models that include an explicit treatment of time flow and are used to formalise the semantics of several foundational process calculi and automata. Despite their relevance, a general mathematical characterisation of timed transition systems and their behavioural theory is still missing. We introduce the first uniform framework for timed behavioural models that encompasses known behavioural equivalences such as timed bisimulations, timed language equivalences as well as their weak and time-abstract counterparts. All these notions of equivalences are naturally organised by their discriminating power in a spectrum. We prove that this result does not depend on the type of the systems under scrutiny: it holds for any generalisation of timed transition system. We instantiate our framework to timed transition systems and their quantitative extensions such as timed probabilistic systems

Performance analysis using timed Petri Nets

Petri Nets have been successfully used to model and evaluate the performance of distributed systems. Several researchers have extended the basic Petri Net model to include time, and have demonstrated that restricted classes of Petri Nets can be analyzed efficiently. Unfortunately, the restrictions prohibit the techniques from being applied to many interesting systems, e.g. communication protocols. This paper proposes a version of timed Petri Nets which accurately models communication protocols, and which can be analyzed using Timed Reachability Graphs. Procedures for constructing and analyzing these graphs are presented. The analysis is shown to be applicable to a larger class of Timed Petri Nets than previously thought. The model and the analysis technique are demonstrated using a simple communication protocol

Modelling and Simulation of Asynchronous Real-Time Systems using Timed Rebeca

In this paper we propose an extension of the Rebeca language that can be used to model distributed and asynchronous systems with timing constraints. We provide the formal semantics of the language using Structural Operational Semantics, and show its expressiveness by means of examples. We developed a tool for automated translation from timed Rebeca to the Erlang language, which provides a first implementation of timed Rebeca. We can use the tool to set the parameters of timed Rebeca models, which represent the environment and component variables, and use McErlang to run multiple simulations for different settings. Timed Rebeca restricts the modeller to a pure asynchronous actor-based paradigm, where the structure of the model represents the service oriented architecture, while the computational model matches the network infrastructure. Simulation is shown to be an effective analysis support, specially where model checking faces almost immediate state explosion in an asynchronous setting.Comment: In Proceedings FOCLASA 2011, arXiv:1107.584

Schedulability analysis of timed CSP models using the PAT model checker

Timed CSP can be used to model and analyse real-time and concurrent behaviour of embedded control systems. Practical CSP implementations combine the CSP model of a real-time control system with prioritized scheduling to achieve efficient and orderly use of limited resources. Schedulability analysis of a timed CSP model of a system with respect to a scheduling scheme and a particular execution platform is important to ensure that the system design satisfies its timing requirements. In this paper, we propose a framework to analyse schedulability of CSP-based designs for non-preemptive fixed-priority multiprocessor scheduling. The framework is based on the PAT model checker and the analysis is done with dense-time model checking on timed CSP models. We also provide a schedulability analysis workflow to construct and analyse, using the proposed framework, a timed CSP model with scheduling from an initial untimed CSP model without scheduling. We demonstrate our schedulability analysis workflow on a case study of control software design for a mobile robot. The proposed approach provides non-pessimistic schedulability results