Real-time preemptive scheduling of sporadic tasks based on supervisory control of discrete event systems

This paper presents a preemptive scheduling scheme for real-time systems with sporadic tasks based on the supervisory control theory of discrete event systems. In particular, we present a systematic method of computing a schedulable language that includes all achievable sequences that meet the given deadlines of accepted sporadic tasks. A supervisor that achieves the schedulable language corresponds to a scheduler that can secure the deadlines of all accepted tasks. We further show that the schedulable language includes the decisions on whether a scheduler accepts or rejects a newly arrived sporadic task.     

Supervisory control for fault-tolerant scheduling of real-time multiprocessor systems with aperiodic tasks

Supervisory control theory is a well-established theoretical framework for feedback control of discrete event systems whose behaviours are described by automata and formal languages. In this article, we propose a formal constructive method for optimal fault-tolerant scheduling of real-time multiprocessor systems based on supervisory control theory. In particular, we consider a fault-tolerant and schedulable language which is an achievable set of event sequences meeting given deadlines of accepted aperiodic tasks in the presence of processor faults. Such a language eventually provides information on whether a scheduler (i.e., supervisor) should accept or reject a newly arrived aperiodic task. Moreover, we present a systematic way of computing a largest fault-tolerant and schedulable language which is optimal in that it contains all achievable deadline-meeting sequences.     

An exact schedulability test for fixed-priority preemptive mixed-criticality real-time systems

The current literature of fixed-priority scheduling algorithms relies on sufficient tests to determine if a set of mixed-criticality sporadic tasks is schedulable on a single processor. The drawback of these safe tests is their pessimism, a matter that could be solved if an exact schedulability analysis is used. However, because of the non-deterministic behavior of tasks in the mentioned setups, exact quantification of worst-case response times, needed for the test, is a difficult problem; more precisely, such a quantification needs evaluation of enormous sequences of job executions. The core problem is thus to merge such sequences to make the analysis practical. This paper, for the first time, gives an algorithm for exact worst-case response time characterization of mixed-criticality sporadic real-time tasks executing according to a given fixed-priority scheduler. We use a set of techniques which carefully consider the task properties and their relation to the worst scenarios to prune the analysis state space. We also show an interesting result that if an exact schedulability test is used, the Audsley’s optimal priority assignment algorithm is not applicable to the mixed-criticality case. Accordingly, we need new priority assignment algorithms to work with the exact test; we give a simple task priority assignment algorithm to this aim. The performance of the proposed exact test (in terms of time complexity) is examined and the effectiveness of some heuristic priority assignment algorithms using the test (in terms of the ratio of task sets which are deemed schedulable) are compared.     

Sporadic task scheduling with overload conditions

Hard real-time task scheduling in a dynamic environment has been an important area of research, posing difficult problems. In an overloaded system where periodic and sporadic tasks have computational demands that are greater than the CPU time in that interval, the scheduler faces the question of which tasks must really make their deadlines. Assuming that periodic tasks have priority over sporadic ones, we end up with a system where some sporadic tasks may not make their deadlines. It is known that through the assignment of priorities to tasks based on the earliest deadline policy, there is no way to predict which sporadic task will miss the deadline and which will not. In order to prevent important sporadic tasks from missing their deadlines, we assign each task an importance function that is used by the scheduling algorithm. Generally, the summation of important function values must be maximized to allow the most important tasks to meet their timing constraints. We present two novel scheduling algorithms that try to maximize this summation. We show that these algorithms have better performance compared to related algorithms regarding complexity and benefit optimization.     

Handling mixed sets of tasks in combined offline and online scheduled real-time systems

Many industrial applications with real-time demands are composed of mixed sets of tasks with a variety of requirements. These can be in the form of standard timing constraints, such as period and deadline, or complex, e.g., to express application specific or nontemporal constraints, reliability, performance, etc. As many algorithms focus on specific sets of task types and constraints only, system design has to focus on those supported by a particular algorithm, at the expense of the rest. In this paper, we present a method to deal with a combination of mixed sets of tasks and constraints: periodic tasks with complex and simple constraints, soft and firm aperiodic, and sporadic tasks. We propose the use of an offline scheduler to manage complex timing and resource constraints of periodic tasks and transform these into a simple EDF model with start-times and deadlines. At run-time, the execution of the offline scheduled tasks is flexibly shifted in order to allow for feasible inclusion of dynamically arriving sporadic and aperiodic tasks. Sporadic tasks are guaranteed offline based on their worst-case activation frequencies. At run-time, this pessimism is reduced by the online algorithm which uses the exact knowledge about sporadic arrivals to reclaim resources and improve response times and acceptance of firm aperiodic tasks.     

A design fix to supervisory control for fault-tolerant scheduling of real-time multiprocessor systems with aperiodic tasks

In the article ‘Supervisory control for fault-tolerant scheduling of real-time multiprocessor systems with aperiodic tasks’, Park and Cho presented a systematic way of computing a largest fault-tolerant and schedulable language that provides information on whether the scheduler (i.e., supervisor) should accept or reject a newly arrived aperiodic task. The computation of such a language is mainly dependent on the task execution model presented in their paper. However, the task execution model is unable to capture the situation when the fault of a processor occurs even before the task has arrived. Consequently, a task execution model that does not capture this fact may possibly be assigned for execution on a faulty processor. This problem has been illustrated with an appropriate example. Then, the task execution model of Park and Cho has been modified to strengthen the requirement that none of the tasks are assigned for execution on a faulty processor.     

An analysis of EDF schedulability on a multiprocessor

A new schedulability test is derived for preemptive deadline scheduling of periodic or sporadic real-time tasks on a single-queue m-server system. The new test allows the task deadline to be more or less than the task period, and is based on a new analysis concept, called a /spl mu/-busy interval. This generalizes a result of Goossens et al. [2003] that a system of periodic tasks with maximum individual task utilization u/sub max/ is EDF-schedulable on m processors if the total utilization does not exceed m(1 /sup max/)+u/sub max/. The new test allows the analysis of hybrid EDF-US [x] scheduling, and the conclusion that EDF-US[1/2] is optimal, with a guaranteed worst-case schedulable utilization of (m +1)/2.     

Timed Discrete Event Control of Parallel Production Lines with Continuous Outputs

In this contribution we present an approach to formulate and solve certain scheduling tasks for hybrid systems using timed discrete event control methods. To demonstrate our approach, we consider a cyclically operated plant with parallel reactors using common resources and a continuous output. For this class of systems, we show how to pose the control problem within a discrete event framework by modelling system components as multirate timed automata. We propose a supervisory control strategy incorporating off-line optimisation to assure safety and nonconflicting use of resources. These properties have to be achieved in the presence of a class of bounded errors/disturbances and can be verified by applying formal methods.     

Preference-oriented real-time scheduling and its application in fault-tolerant systems

In this paper, we consider a set of real-time periodic tasks where some tasks are preferably executed as soon as possible (ASAP) and others as late as possible (ALAP) while still meeting their deadlines. After introducing the idea of preference-oriented (PO) execution, we formally define the concept of PO-optimality. For fully-loaded systems (with 100% utilization), we first propose a PO-optimal scheduler, namely ASAP-Ensured Earliest Deadline (SEED), by focusing on ASAP tasks where the optimality of ALAP tasks’ preference is achieved implicitly due to the harmonicity of the PO-optimal schedules for such systems. Then, for under-utilized systems (with less than 100% utilization), we show the discrepancies between different PO-optimal schedules. By extending SEED, we propose a generalized Preference-Oriented Earliest Deadline (POED) scheduler that can obtain a PO-optimal schedule for any schedulable task set. The application of the POED scheduler in a dual-processor fault-tolerant system is further illustrated. We evaluate the proposed PO-optimal schedulers through extensive simulations. The results show that, comparing to that of the well-known EDF scheduler, the scheduling overheads of SEED and POED are higher (but still manageable) due to the additional consideration of tasks’ preferences. However, SEED and POED can achieve the preference-oriented execution objectives in a more successful way than EDF.     

Robust supervisory control of timed discrete event systems under partial observation based on eligible time bounds: The existence conditions

This paper addresses a supervisory control problem for uncertain timed discrete event systems (DESs) under partial observation. An uncertain timed DES to be controlled is represented by a set of possible timed models based on the framework of Brandin and Wonham [(1994). Supervisory control of timed discrete event systems. IEEE Transactions on Automatic Control, 39(2), 329-342]. To avoid the state space explosion problem caused by tick events in the timed models, a notion of eligible time bounds is proposed for a single timed model obtained from the set of all possible timed models. Based on this notion, we present the necessary and sufficient conditions for the existence of a robust supervisor achieving a given language specification for the single timed model. Moreover, we show that the robust supervisor can also achieve the specification for any timed model in the set.     

<Emphasis Type="Italic">SetExp</Emphasis>: a method of transformation of timed automata into finite state automata

Real-time discrete event systems are discrete event systems with timing constraints, and can be modeled by timed automata. The latter are convenient for modeling real-time discrete event systems. However, due to their infinite state space, timed automata are not suitable for studying real-time discrete event systems. On the other hand, finite state automata, as the name suggests, are convenient for modeling and studying non-real time discrete event systems. To take into account the advantages of finite state automata, an approach for studying real-time discrete event systems is to transform, by abstraction, the timed automata modeling them into finite state automata which describe the same behaviors. Then, studies are performed on the finite state automata model by adapting methods designed for non real-time discrete event systems. In this paper, we present a method for transforming timed automata into special finite state automata called Set-Exp automata. The method, called SetExp, models the passing of time as real events in two types: Set events which correspond to resets with programming of clocks, and Exp events which correspond to the expiration of clocks. These events allow to express the timing constraints as events order constraints. SetExp limits the state space explosion problem in comparison to other transformation methods of timed automata, notably when the magnitude of the constants used to express the timing constraints are high. Moreover, SetExp is suitable, for example, in supervisory control and conformance testing of real-time discrete event systems.     

EDF统一调度硬实时周期任务和偶发任务的可调度性判定算法

现有的硬实时周期任务和非周期任务的混合调度方法都没有保证非周期任务的实时性,所以不适合调度具有强实时要求的偶发任务.通过分析和计算EDF算法调度偶发任务所占用的空闲时间和挪用时间,以及调度后对空闲时间和最大可挪用时间的影响,提出一种采用EDF算法统一调度硬实时周期任务和偶发任务时的可调度性充分判定算法.最后用仿真实验得出了该算法在不同系统负载下的判定准确率和偶发任务的平均响应时间.     

Trade-Off Analysis of Real-Time Control Performance and Schedulability*

Most real-time computer-controlled systems are developed in two separate stages: controller design followed by its digital implementation. Computational tasks that implement the control algorithms are usually scheduled by treating their execution times and periods as unchangeable parameters. Task schedulability therefore depends only on the limited computing resources available. On the other hand, controller design is primarily based on the continuous-time dynamics of the physical system being controlled. The set of tasks resulting from this controller design may not be schedulable with the limited computing resources available. Even if the given set of tasks is schedulable, their overall performance may not be optimal in the sense that they do not make a full use of the computing resources. In this paper, we propose an integrated approach to controller design and task scheduling. Specifically, task frequencies (or periods) are allowed to vary within a certain range as long as such changes do not affect critical control functions such as the maintenance of system stability. We present an algorithm that determines the task frequencies such that a prescribed aspect of system performance is optimized subject to satisfaction of computing resource constraints. The tasks are then scheduled with the chosen frequencies. The proposed approach also addresses the issue of choosing controller processors.     

Grid automata and supervisory control of dense real-time discrete event systems

We present a generalization of the classical supervisory control theory for discrete event systems to a setting of dense real-time systems modeled by Alur and Dill timed automata. The main problem involved is that in general the state space of a timed automaton is (uncountably) infinite. The solution is to reduce the dense time transition system to an appropriate finite discrete subautomaton, the grid automaton, which contains enough information to deal with the timed supervisory control problem (TSCP). The plant and the specifications region graphs are sampled for a granularity defined in a way that each state has an outgoing transition labeled with the same time amount. We redefine the controllability concept in the context of grid automata, and we provide necessary and sufficient solvability conditions under which the optimal solution to centralized supervisory control problems in timed discrete event systems under full observation can be obtained. The enhanced setting admits subsystem composition and the concept of forcible event. A simple example illustrates how the new method can be used to solve the TSCP.     

一种实时系统中的多任务可预测调度算法

通过研究实时系统中可能出现的任务类型，提出了一种实时系统任务模型和基于这个模型的多任务调度算法，分析了该算法下所有周期任务和非周期任务可调度的条件。该算法结合了DMS(Dcadlinc Monotonic Scheduling)和DD(Deadline Driven)算法，在保证系统中周期任务执行的前提下,也使非周期任务获得了，较好的响应时间。     

Response Time Analysis of Asynchronous Real-Time Systems

In asynchronous real-time systems the time when all events occur can not be predicted beforehand. Systems with sporadic tasks, or that operate a protocol for sharing resources like the priority ceiling protocol, for example, are asynchronous real-time systems. In this paper, we present a sufficient and efficient response time based analysis technique for computing R _i(k), the worst case response time at each invocation k of the periodic tasks of real-time asynchronous systems. In addition, efficient idle time computation for asynchronous systems is presented. This analysis technique can be applied to the analysis of several process models including weakly hard real-time systems, and slack management techniques like aperiodic servers and slack stealing algorithms. It is also shown that the pattern of response times of tasks in a hyperperiod is pseudoperiodic and that the maximum response time instants tend to occur evenly separated within the hyperperiod.     

Formalizing real-time scheduling using priority-based supervisory control of discrete-event systems

In this note, we formalize real-time task scheduling by applying an extension of supervisory control theory (SCT) of discrete-event systems to real-time models. The set of all possible timed traces of the system is specified by a discrete timed automaton where each transition is associated with an event occurrence or the passage of one unit of time. We introduce priorities to SCT, and apply them to the setting of discrete timed automata in order to develop a formal and unified framework for task scheduling on a single CPU.     

Schedulability analysis of fixed-priority systems using timed automata

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$n+1$ extra clocks, where n$n$ 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.     

Parking Can Get You There Faster: Model Augmentation to Speed up Real-Time Model Checking

We present an approximation technique, that can render real-time model checking of safety and universal path properties more efficient. It is beneficial, when loops lead to repetition of control situations. Basically we augment a timed automata model with carefully selected extra transitions. This increases the size of the state-space, but potentially decreases the number of symbolic states to be explored by orders of magnitude.We give a formal definition of a timed automata formalism, enriched with basic data types, hand-shake synchronization, urgency, and committed locations. We prove by means of a trace semantics, that if a safety property can be established in the augmented model, it also holds for the original model.We extend our technique to a richer set of properties, that can be decided via a set of traces (universal path properties). In order for universal path properties to carry over to the original model, the semantics of the timed automata formalism is formulated relative to the applied augmentation.Our technique is particularly useful in systems, where a scheduler dictates repetition of control over elapsing time. As a typical example we mention translations of LEGO® RCX™ programs to Uppaal models, where the Round-Robin scheduler is a static entity. We allow scheduler and associated tasks to “park”, until some timing or environmental conditions are met.We apply our technique on a brick-sorter model for a safety property and report run-time data.     

Reliability-aware low energy scheduling in real time systems with shared resources

Dynamic voltage scaling (DVS) is a technique which is widely used to save energy in a real time system. Recent research shows that it has a negative impact on the system reliability. In this paper, we consider the problem of the system reliability and focus on a periodic task set that the task instance shares resources. Firstly, we present a static low power scheduling algorithm for periodic tasks with shared resources called SLPSR which ignores the system reliability. Secondly, we prove that the problem of the reliability-aware low power scheduling for periodic tasks with shared resources is NP-hard and present two heuristic algorithms called SPF and LPF respectively. Finally, we present a dynamic low power scheduling algorithm for periodic tasks with shared resources called DLPSR to reclaim the dynamic slack time to save energy while preserving the system reliability. Experimental results show that the presented algorithm can reduce the energy consumption while improving the system reliability.