Abstract. In this paper we show how the classical job-shop scheduling problem can bemodeled as a special class of acyclic timed automata. Finding an optimal schedule corresponds, then, to nding a shortest (in terms of elapsed time) path in the timed automaton. This representation provides new techniques for solving the optimization problem and, more importantly, it allows to model naturally more complex dynamic resource allocation problems which are not captured so easily in traditional models of operation research. We present several algorithms and heuristics for nding the shortest paths in timed automata and test their implementation in the tool Kronos on numerous be n c hmark examples.
In this paper we show how the problem of job-shop scheduling where the jobs are preemptible can be modeled naturally as a shortest path problem defined on an extension of timed automata, namely stopwatch automata where some of the clocks might be freezed at certain states. Although general verification problems on stopwatch automata are known to be undecidable, we show that due to particular properties of optimal schedules, the shortest path in the automaton belongs to a finite subset of the set of acyclic paths and hence the problem is solvable. We present several algorithms and heuristics for finding the shortest paths in such automata and test their implementation on numerous benchmark examples. This work was partially supported by the European Community Project IST-2001-35304 AME-TIST http://ametist.cs.utwente.nl 1 By a qualitative run of a timed automaton we mean a sequence of states and transitions without metric timing information.
The paper addresses the real-time fixed-priority scheduling problem for battery-powered embedded systems whose energy storage unit is replenished by an environmental energy source. In this context, a task may meet its deadline only if its cost of energy can be satisfied early enough. Hence, a scheduling policy for such a system should account for properties of the source of energy, capacity of the energy storage unit and tasks cost of energy. Classical fixed-priority schedulers are no more suitable for this model. Based on these motivations, we propose P F PASAP an optimal scheduling algorithm that handles both energy and timing constraints. Furthermore, we state the worst case scenario for non concrete tasksets 1 scheduled with this algorithm and build a necessary and sufficient feasibility condition for non concrete tasksets. Moreover, a minimal bound of the storage unit capacity that keeps a taskset schedulable with P F PASAP is also proposed. Finally, we validate the proposed theory with large scale simulations and compare our algorithm with other existing ones.
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