A Generic Approach to Schedulability Analysis of Real-Time Systems

This thesis presents a framework for design, analysis, and implementation of embedded systems. We adopt a model of timed automata extended with asynchronous processes i.e. tasks triggered by events. A task is an executable program characterized by its worst-case execution time and deadline, and possibly other parameters such as priorities etc. for scheduling. The main idea is to associate each location of an automaton with a task (or a set of tasks). A transition leading to a location denotes an event triggering the tasks and the clock constraint on the transition specifies the possible arrival times of the event. This yields a model for real-time systems expressive enough to describe concurrency and synchronization, and tasks with (or without) combinations of timing, precedence and resource constraints, which may be periodic, sporadic, preemptive and (or) non-preemptive. We believe that the model may serve as a bridge between scheduling theory and automata-theoretic approaches to system modelling and analysis. Our main result is that the schedulability checking problem for this model is decidable. To our knowledge, this is the first general decidability result on dense-time models for real time scheduling without assuming that preemptions occur only at integer time points. The proof is based on a decidable class of updatable automata: timed automata with subtraction in which clocks may be updated by subtractions within a bounded zone. As the second contribution, we show that for fixed priority scheduling strategy, the schedulability checking problem can be solved by reachability analysis on standard timed automata using only two extra clocks in addition to the clocks used in the original model to describe task arrival times. The analysis can be done in a similar manner to response time analysis in classic Rate-Monotonic Scheduling. We believe that this is the optimal solution to the problem. The third contribution is an extension of the above results to deal with precedence and resource constraints. We present an operational semantics for the model, and show that the related schedulability analysis problem can be solved efficiently using the same techniques. Finaly, to demonstrate the applicability of the framework, we have modelled, analysed, and synthesised the control software for a production cell. The presented results have been implemented in the Times tool for automated schedulability analysis and code synthesis