Scheduling by Timed Automata under Resource Conflicts

Theoretical Computer Science, 2006

In classic scheduling theory, real-time 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 Rate-Monotonic Analysis (RMA). The result is further extended to systems with data-dependent control, in which the release time of a task may depend on the time-point 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 equation-solving, without suffering from the exponential explosion in the number of tasks.

Formal Methods in System Design, 2008

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. This is done by a reduction of the problem to the determination of optimal mean-cycles in finite graphs with weighted edges. This reduction is obtained by introducing the so-called corner-point abstraction, a powerful abstraction technique of which we show that it preserves optimal schedules.

2014 IEEE 20th International Conference on Embedded and Real-Time Computing Systems and Applications, 2014

Formal methods (e.g. Timed Automata or Linear Hybrid Automata) can be used to analyse a real-time system by performing a reachability analysis on the model. The advantage of using formal methods is that they are more expressive than classical analytic models used in schedulability analysis. For example, it is possible to express state-dependent behaviour, arbitrary activation patterns, etc. In this paper we use the formalism of Linear Hybrid Automata to encode a hierarchical scheduling system. In particular, we model a dynamic server algorithm and the tasks contained within, abstracting away the rest of the system, thus enabling component-based scheduling analysis. We prove the correctness of the model and the decidability of the reachability analysis for the case of periodic tasks. Then, we compare the results of our model against classical schedulability analysis techniques, showing that our analysis performs better than analytic methods in terms of resource utilisation. We further present two case studies: a component with state-dependent tasks, and a simplified model of a real avionics system. Finally, through extensive tests with various configurations, we demonstrate that this approach is usable for medium-size components.

Discrete Applied Mathematics, 1983

In deterministic sequencing and scheduling problems, jobs are to be processed on machines of limited capacity. We consider an extension of this class of problems, in which the jobs require the use of additional scarce resources during their execution. A classification scheme for resource constraints is proposed and the computational complexity of the extended problem class is investigated in terms of this classification. Models involving parallel machines, unit-time jobs and the maximum completion time criterion are studied in detail; other models are briefly discussed.

2011

In this paper we discuss an extension of a recent approach to solve batch scheduling problems using reachability analysis for timed automata (TA) by embedding lower bound computations in the reachability algorithm. We propose an extension of the embedded LP-formulation to handle scheduling problems with NIS policy and an improved minimum remaining processing time (MRPT) procedure to compute the lower bounds. The proposed bounding procedures are tested on typical batch scheduling problems. The comparative study shows that the MRPT-based bounding procedure is efficient and increases the overall performance significantly in comparison to the LPbased bounding procedure.

2009

Abstract This paper presents a conservative approximation method for the real-time verification of asynchronous event-driven distributed systems. This problem is known to be undecidable in the generic setting. The proposed approach is based on composable timed automata models that provide a sufficient condition to determine schedulability. We demonstrate the method on a real-time CORBA avionics design.

1998

Extended Abstract. In this paper we develop and analyse CSP-based procedures for solving scheduling problems with metric temporal constraints (e.g. jobs’ deadlines or separation constraints between couple of consecutive activities in a job) and multiple capacitated resources, referred to formally as the Multiple Capacitated Metric Scheduling Problem (MCM-SP). This work follows two different solution approaches used to identify resource capacity conflicts. (1) Proffle-based approaches (e.g. [1]) - They consist of characterizing a resource demand as a function of time, identifying periods of overallocation in this demand proffle, and incrementally performing “eveling actions” to (hopefully) ensure that resource usage peaks fall below the total capacity of the resource. (2) Clique-based approaches [3, 2] - Given a current schedule, this approach builds up a conflicts graph whose nodes are activities and whose edges represent overlapping resource capacity requests of the connected activities. Fully connected subgraphs (cliques) are identiffed and if the number of nodes in the clique is greater than resource capacity a conflict is detected Clique-based approaches perform more global analysis and offer greater accuracy in conflict detection in comparison with local pairwise proffle-based analysis, but at a potentially much higher computational cost. In a previous paper [1], several proffle-based solution procedures were developed and evaluated (in particular the ESTA algorithm), some of them descending from an approach proposed in the planning literature.

2000

This dissertation presents a set of techniques for representing the high-level b ior of a digital subsystem as a collection of nondeterministic finite automata, N Desired behavioral and implementation dynamics: dependencies, repet bounded resources, sequential character, and control state, can also be sim modeled. All possible system execution sequences, obeying imposed constr are encapsulated in a composed NFA. Technology similar to that used in sym model checking enables implicit exploration and extraction of best-possible ex tion sequences. This provides a very general, systematic procedure to pe exact high-level synthesis of cyclic, control-dominated behaviors constraine arbitrary sequential constraints. This dissertation further demonstrates that techniques are scalable to practical problem sizes and complexities. Exact sch ing solutions are constructed for a variety of academic and industrial proble including a pipelined RISC processor. The ability to represent and sche sequen...

2000

In recent years, research of software agents has gained a tremendous amount of attention. To date, very little of the research has involved agents that possess real-time constraints or operate within real-time systems. A real-time multi-agent system (RTMAS) would have certain unique characteristics versus both traditional real-time systems and multi-agent systems. More specifically, the scheduling algorithm for such a system would be capable of exhibiting a more robust scheduling algorithm than previously implementations. This stems directly from an agent's ability to possess multiple execution times for a given task. The change in execution time of these methods is proportional to the "quality" of the result produced. In such a system, before a set of tasks is declared "non schedulable", the quality of the results of scheduled tasks can be reduced in an attempt to achieve total "schedulability" for all tasks seeking execution. The greatest system utility is gained by executing all requested tasks while returning the best possible result within the assigned time slot. An exact definition of "quality" in regards to this paper is offered further in the reading. We have developed such an algorithm based on a heuristic that determines which tasks are the least costly to reduce in order to minimize the reduction in quality. We have also developed a model for realtime agents as well as a model for real-time agent scheduling. iii Acknowledgement I would like to thank Colleen and my parents for providing me with the endless support and love that is necessary to be truly successful at an endeavor such as this.

2017

We consider dynamic scheduling for heterogeneous resources in flexible manufacturing systems. The resources are mobile robots with different capabilities and/or people with different skills. The tasks in the system arise over time and each has a time window for completion. We have developed a method for dynamic scheduling based on mixed integer programming and rolling horizon. The results show it can solve practical scheduling problems fast, and can significantly reduce the cost when compared to current practice.