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58
Optimal strategies in priced timed game automata
 In FSTTCS 04, LNCS 3328
, 2004
"... 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 nonzeno ..."
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Cited by 63 (27 self)
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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 nonzenoness 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 statebased winning optimal strategy. 1
Scheduling a Steel Plant with Timed Automata
 In Sixth International Conference on RealTime Computing Systems and Applications (RTCSA’99). IEEE Computer
, 1999
"... 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 ..."
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Cited by 60 (5 self)
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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 takeup 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...
Task Automata: Schedulability, Decidability and Undecidability
, 2008
"... We present a model, task automata, for real time systems with nonuniformly recurring computation tasks. It is an extended version of timed automata with asynchronous processes that are computation tasks generated (or triggered) by timed events. Compared with classical task models for real time syst ..."
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Cited by 58 (9 self)
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We present a model, task automata, for real time systems with nonuniformly recurring computation tasks. It is an extended version of timed automata with asynchronous processes that are computation tasks generated (or triggered) by timed events. Compared with classical task models for real time systems, task automata may be used to describe tasks (1) that are generated nondeterministically according to timing constraints in timed automata, (2) that may have interval execution times representing the best case and the worst case execution times, and (3) whose completion times may influence the releases of task instances. We generalize the classical notion of schedulability to task automata. A task automaton is schedulable if there exists a scheduling strategy such that all possible sequences of events generated by the automaton are schedulable in the sense that all associated tasks can be computed within their deadlines. Our first technical result is that the schedulability for a given scheduling strategy can be checked algorithmically for the class of task automata when the best case and the worst case execution times of tasks are equal. The proof is based on a decidable class of suspension automata: timed automata with bounded subtraction in which clocks may be updated by subtractions within a bounded zone. We shall also study the borderline between decidable and undecidable cases. Our second technical result shows that the schedulability checking problem will be undecidable if the following three conditions hold: (1) the execution times of tasks are intervals, (2) the precise finishing time of a task instance may influence new task releases, and (3) a task is allowed to preempt another running task.
Distributing Timed Model Checking  How the Search Order Matters
, 2000
"... 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 appl ..."
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Cited by 54 (7 self)
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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.
Timed automata with asynchronous processes: schedulability and decidability
 In Proceedings of TACAS 2002
, 2002
"... Abstract. In this paper, we exend timed automata with asynchronous processes i.e. tasks triggered by events as a model for realtime systems. The model is expressive enough to describe concurrency and synchronization, and real time tasks which may be periodic, sporadic, preemptive or nonpreemptive. ..."
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Cited by 51 (11 self)
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Abstract. In this paper, we exend timed automata with asynchronous processes i.e. tasks triggered by events as a model for realtime systems. The model is expressive enough to describe concurrency and synchronization, and real time tasks which may be periodic, sporadic, preemptive or nonpreemptive. 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 automatatheoretic 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 densetime 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
Efficient Guiding Towards CostOptimality in UPPAAL
, 2001
"... 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 ..."
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Cited by 42 (22 self)
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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 branchandbound algorithms which can be used for limiting the search space and for quickly finding nearoptimal solutions. The algorithm has been implemented in the verification tool Uppaal. When applied on a number of experiments the presented techniques reduced the explored statespace with up to 90%.
As Cheap as Possible: Efficient CostOptimal Reachability for Priced Timed Automata
, 2001
"... 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 automat ..."
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Cited by 40 (11 self)
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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 socalled 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 costoptimal reachability using priced zones. We report on experiments with a costoptimizing extension of Uppaal on a number of examples, including a range of aircraft landing problems.
Staying Alive As Cheaply As Possible
 IN PROC. OF 7TH INTL. WORKSHOP ON HYBRID SYSTEMS: COMPUTATION AND CONTROL (HSCC), VOLUME 2993 OF LECT. NOTES IN COMP. SCI
, 2004
"... 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 modellin ..."
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Cited by 39 (21 self)
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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 nonterminating schedules for such doublepriced timed automata is computable. This
Schedulability analysis of fixedpriority systems using timed automata
 Theoretical Computer Science
, 2006
"... In classic scheduling theory, realtime tasks are usually assumed to be periodic, i.e. tasks are released and computed with fixed rates periodically. To relax the stringent constraints on task arrival times, we propose to use timed automata to describe task arrival patterns. In a previous work, it i ..."
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Cited by 32 (5 self)
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In classic scheduling theory, realtime tasks are usually assumed to be periodic, i.e. tasks are released and computed with fixed rates periodically. To relax the stringent constraints on task arrival times, we propose to use timed automata to describe task arrival patterns. In a previous work, it is shown that the general schedulability checking problem for such models is a reachability problem for a decidable class of timed automata extended with subtraction. Unfortunately, the number of clocks needed in the analysis is proportional to the maximal number of schedulable task instances associated with a model, which is in many cases huge. In this paper, we show that for fixed priority scheduling strategy, the schedulability checking problem can be solved using standard timed automata with 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 RateMonotonic Analysis (RMA). The result is further extended to systems with datadependent control, in which the release time of a task may depend on the timepoint at which other tasks finish their execution. For the case when the execution times of tasks are constants, we show that the schedulability problem can be solved using n+ 1 extra clocks, where n is the number of tasks. The presented analysis techniques have been implemented in the Times tool. For systems with only periodic tasks, the performance of the tool is comparable with tools implementing the classic RMA technique based on equationsolving, without suffering from the exponential explosion in the number of tasks.
UPPAAL  Present and Future
, 2001
"... Uppaal is a tool for modelling, simulation and verification of realtime 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 nondeterministic processes wit ..."
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Cited by 29 (3 self)
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Uppaal is a tool for modelling, simulation and verification of realtime 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 nondeterministic processes with finite control structure and realvalued clocks, communicating through channels or shared variables. Typical application areas include realtime 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.