Scheduling in an environment with constraints of many different types is known to be a hard problem. We tackle this problem for an integrated steel plant in Ghent, Belgium, using UPPAAL, a model checker for networks of timed automata. We show how to translate schedulability to reachability, enabling us to use UPPAAL's model checking algorithms. 1. Introduction This report is a result of the participation of CSI Nijmegen in the European Union Esprit long term research project Verification of Hybrid Systems (http://wwwverimag. imag.fr//VHS/). The Esprit program was set up to improve the take-up of modern information technologies in industry. The VHS project in particular is meant to stimulate research in the area of hybrid systems. These systems typically consist of digital components in a continuous environment. The correct behavior depends strongly on the interaction between the digital components, say the controller, and the controlled process. Hybrid systems are important in numero...

Abstract. Priced timed (game) automata extend timed (game) automata with costs on both locations and transitions. In this paper we focus on reachability games for priced timed game automata and prove that the optimal cost for winning such a game is computable under conditions concerning the non-zenoness of cost and we prove that it is decidable. Under stronger conditions (strictness of constraints) we prove that in case an optimal strategy exists, we can compute a state-based winning optimal strategy. 1

In this paper we address the problem of distributing model checking of timed automata. We demonstrate through four real life examples that the combined processing and memory resources of multiprocessor computers can be effectively utilized. The approach assumes a distributed memory model and is applied to both a network of workstations and a symmetric multiprocessor machine. However, certain unexpected phenomena have to be taken into account. We show how in the timed case the search order of the state space is crucial for the effectiveness and scalability of the exploration. An effective heuristic to counter the effect of the search order is provided. Some of the results open up for improvements in the single processor case.

In this paper we present an algorithm for efficiently computing the minimum cost of reaching a goal state in the model of Uniformly Priced Timed Automata (UPTA). This model can be seen as a submodel of the recently suggested model of linearly priced timed automata, which extends timed automata with prices on both locations and transitions. The presented algorithm is based on a symbolic semantics of UTPA, and an efficient representation and operations based on difference bound matrices. In analogy with Dijkstra's shortest path algorithm, we show that the search order of the algorithm can be chosen such that the number of symbolic states explored by the algorithm is optimal, to be optimal, in the sense that the number of explored states can not be reduced by any other search order. We also present a number of techniques inspired by branch-and-bound algorithms which can be used for limiting the search space and for quickly finding near-optimal solutions. The algorithm has been implemented in the verification tool Uppaal. When applied on a number of experiments the presented techniques reduced the explored state-space with up to 90%.

Abstract. In this paper, we exend timed automata with asynchronous processes i.e. tasks triggered by events as a model for real-time systems. The model is expressive enough to describe concurrency and synchronization, and real time tasks which may be periodic, sporadic, preemptive or non-preemptive. We generalize the classic notion of schedulability to timed automata. An automaton is schedulable if there exists a scheduling strategy such that all possible sequences of events accepted by the automaton are schedulable in the sense that all associated tasks can be computed within their deadlines. We believe that the model may serve as a bridge between scheduling theory and automata-theoretic approaches to system modeling and analysis. Our main result is that the schedulability checking problem 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. The crucial observation is that the schedulability checking problem can be encoded as a reachability problem for such automata. Based on the proof, we have developed a symbolic technique and a prototype tool for schedulability analysis. 1

In this paper we present an algorithm for efficiently computing optimal cost of reaching a goal state in the model of Linearly Priced Timed Automata (LPTA). In recent papers, this problem have been shown to be computable using a priced extention of the traditional notion of regions for timed automata. However, for efficiency it is imperative that the computation is based on so-called zones (i.e. convex set of clock valuations) rather than regions. The central contribution of this paper is a priced extension of zones. This, together with a notion of facets of a zone, allows the entire machinery for symbolic reachability in terms of zones to be lifted to cost-optimal reachability using priced zones. We report on experiments with a cost-optimizing extension of Uppaal on a number of examples, including a range of aircraft landing problems.

This paper is concerned with the derivation of infinite schedules for timed automata that are in some sense optimal. To cover a wide class of optimality criteria we start out by introducing an extension of the (priced) timed automata model that includes both costs and rewards as separate modelling features. A precise definition is then given of what constitutes optimal infinite behaviours for this class of models. We subsequently show that the derivation of optimal non-terminating schedules for such double-priced timed automata is computable.

Uppaal is a tool for modelling, simulation and verification of real-time systems, developed jointly by BRICS at Aalborg University and the Department of Computer Systems at Uppsala University. The tool is appropriate for systems that can be modelled as a collection of non-deterministic processes with finite control structure and real-valued clocks, communicating through channels or shared variables. Typical application areas include real-time controllers and communication protocols in particular, those where timing aspects are critical. In this paper, we review the status of the currently distributed version of the tool as well as facilities to be found in upcoming releases.

Abstract. In off-line schedulability tests for real time systems, tasks are usually assumed to be periodic, i.e. they are released with fixed rates. To relax the assumption of complete knowledge on arrival times, we propose to use timed automata to describe task arrival patterns. In a recent work, it is shown that for fixed priority scheduling strategy and tasks with only timing constraints (i.e. execution time and deadline), the schedulability of such models can be checked by reachability analysis on timed automata with two clocks. In this paper, we extend the above result to deal with precedence and resource constraints. This yields a unified task model, which is expressive enough to describe concurrency, synchronization, and tasks that may be periodic, aperiodic, preemptive or non-preemptive with (or without) combinations of timing, 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 technique. The presented results have been implemented in the TIMES tool for automated schedulability analysis. 1

Abstract. We study schedulability problems of timed systems with nonuniformly recurring computation tasks. Assume a set of real time tasks whose best and worst execution times, and deadlines are known. We use timed automata to describe the arrival patterns (and release times) of tasks. From the literature, it is known that the schedulability problem for a large class of such systems is decidable and can be checked efficiently. In this paper, we provide a summary on what is decidable and what is undecidable in schedulability analysis using timed automata. Our main technical contribution is that the schedulability problem will be undecidable if these two conditions hold: (1) the execution times of tasks are intervals and (2) a task is allowed to reset clocks. We show that if one of the above two conditions is dropped, the problem will be decidable again. Thus our result can be used as an indication in identifying classes of timed systems that can be analysed efficiently. 1