Adaptive Scheduling of Data Paths using Uppaal Tiga

S. Andova et.al. (Eds.): Workshop on Quantitative Formal Methods: Theory and Applications (QFM’09) EPTCS 13, 2009, pp. 1–11, doi:10.4204/EPTCS.13.1 Adaptive Scheduling of Data Paths using Uppaal Tiga∗ Israa AlAttili Fred Houben Georgeta Igna Steffen Michels Feng Zhu Frits Vaandrager Institute for Computing and Information Sciences Radboud University Nijmegen P.O. Box 9010, 6500 GL Nijmegen, The Netherlands We apply Uppaal Tiga to automatically compute adaptive scheduling strategies for an industrial case study dealing with a state-of-the-art image processing pipeline of a printer. As far as we know, this is the first application of timed automata technology to an industrial scheduling problem with uncertainty in job arrivals. 1 Introduction Scheduling concerns the allocation of resources to activities over time in order to achieve some goals. Scheduling problems occur in many different domains and a vast amount of research has been carried out in this area. However, in the research literature scheduling is usually seen as a function of known, perfect inputs: the set of jobs, their arrival times, the capacities of machines, the duration of activities, and other characteristics of the problem are assumed to be known and static [9]. It has been observed that scheduling processes in practice are driven by uncertainty [13, 15]. This uncertainty may arise due to various sources (machine breakdown, unexpected arrival of new jobs, modification of existing jobs, uncertainty of task durations,..). McKay et al. [14] even claim that the dynamic characteristics of real- world scheduling environments render the bulk of existing solution approaches for the job shop problem unusable when applied to practical problems. The number of scientific publications devoted to schedul- ing in a setting with uncertainty is relatively small and most of them have the flavor of AI planning rather than Operations Research [9, 1]. Altogether the problem of computing optimal scheduling strategies in practical settings with uncertainty is largely open. The present paper aims to address this problem. Within the European AMETIST project [3], steps have been taken in the development of a general theory of scheduling inspired by the methodology of model checking and based on the timed automa- ton model of Alur and Dill [2]. In the AMETIST approach, components of a system are modeled as dynamical systems with a state space and a well-defined dynamics. All that can happen is expressed in terms of behaviors that can be generated by the dynamical systems; these constitute the semantics of the problem. Verification, optimization, synthesis and other design activities explore and modify system structure so that the resulting behaviors are correct, optimal, etc. Using this approach, the project was able to derive schedules that were of comparable quality as those that were provided by an industrial tool [4]. Most of the work within AMETIST did not address scheduling under uncertainty, with the notable exception of [1], which studies uncertainty in task durations. Recently, however, an extension of the timed automata model checker Uppaal [6] has been proposed, called Uppaal Tiga, that implements the first efficient on-the-fly algorithm for solving games based on timed game automata with respect to reachability and safety properties [5, 7]. Although still a prototype, we believe that this extension has ∗The research of Igna and Vaandrager was carried out in the context of the Octopus project, with partial support of the Netherlands Ministry of Economic Affairs under the Senter TS program. This research was also supported by European Community’s Seventh Framework Programme under grant agreement no 214755 (QUASIMODO). 2 Adaptive Scheduling of Data Paths using Uppaal Tiga potential as a tool for solving scheduling problems that involve uncertainty (using the AMETIST ap- proach). In Uppaal Tiga, systems are specified through a network of timed game automata [12]. These are timed automata in the sense of [2] where edges are marked as either controllable or uncontrollable. This defines a two player game with on the one side the controller (mastering the controllable edges) and on the other side the environment (mastering the uncontrollable edges). Winning conditions of the game are specified through TCTL formulas and for instance state that, irrespective of the strategy used by the environment player, the system player can always reach (or always avoid) certain states. In a scheduling context, uncertainty can be modeled using uncontrollable edges. Uppaal Tiga is then able to synthesize strategies for controlling the system such that scheduling objectives are met irrespective of the timing of uncontrollable edges. In order to demonstrate the practical usefulness of Uppaal Tiga for solving scheduling problems with uncertainty, we have applied the tool to an industrial case study from Oc´e Technologies that concerns the scheduling of a state-of-the-art image processing pipel

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