Sufficient Schedulability Condition Research Articles

Periodic Scheduling Optimization for Dual-Arm Cluster Tools with Arm Task and Residency Time Constraints via Petri Net Model

In order to improve quality assurance in wafer manufacturing, there are strict process requirements. Besides the well-known residency time constraints (RTCs), a dual-arm cluster tool also requires each robot arm to execute a specific set of tasks. We call such a tool an arm task-constrained dual-arm cluster tool (ATC-DACT). To do this, one of the arms is identified as the dirty one and the other as the clean one. The dirty one can deal with raw wafers, while the clean one can deal with processed wafers. This requirement raises a new problem for scheduling a cluster tool. This paper discusses the scheduling problem of ATC-DACTs with RTCs. Due to the arm task constraints, the proven, effective swap strategy is no longer applicable to ATC-DACTs, making the scheduling problem difficult. To address this problem, we explicitly describe the robot waiting as an event and build a Petri net (PN) model. Then, we propose a hybrid task sequence (HTS) as an operation strategy by combining the swap and backward strategies. Based on the HTS, the necessary and sufficient conditions for schedulability are established; also, a linear programming model is developed. We then develop an algorithm using these results to optimally schedule the system. Industrial case studies demonstrate the application of this method.

Energy aware fixed priority scheduling in mixed-criticality systems

Most of studies about energy management for MC systems are based on dynamic priority scheme. The disadvantages of dynamic priority scheme are high system overhead and poor predictability. Unlike previous studies, we focus on the problem of scheduling mixed-criticality (MC) periodic tasks with minimizing energy consumption in MC systems based on fixed priority scheme. Firstly, we explain a criticality rate monotonic scheduling (CRMS) and propose the sufficient schedulability condition of CRMS. Secondly, we compute the energy minimization uniform scaled speed and present an optimal static solution algorithm based on CRMS. The extra workload of the high criticality level (HI) task executes with the maximum processor speed in the high criticality mode (HI-mode). But this algorithm does not exploit the slack time generated from the HI task in the low criticality mode (LO-mode). For energy efficiency, we propose a dynamic fixed priority energy minimization algorithm which exploits the slack time generated from the HI task in LO-mode to save energy. In addition, it combines a dynamic voltage and frequency scaling technique and a dynamic power management technique to reduce energy consumption. Finally, the experiments are applied to evaluate the performance of the proposed algorithm and the experimental results show that the proposed algorithm can save up 23.89% energy compared with other existing algorithms.

Improving the Schedulability of Real-Time Tasks Using Fog Computing

Due to the significant communication delay to user tasks, the cloud is not ideal for executing real-time tasks with stringent deadlines. Fog computing consists of low computation capability fog nodes, or cloudlets located in proximity to the source of the data generation: the users. These cloudlets are ideal for executing tasks that have early deadlines. In this paper, we propose algorithms that schedule a set of real-time tasks on such an embedded-fog-cloud architecture. We consider hard, firm and soft tasks. The execution framework consists of embedded, fog and cloud processors. Tasks are scheduled on appropriate processors based on their deadline requirements. In general, hard real-time tasks are executed on embedded processors, firm real-time tasks on fog processors, and soft real-time tasks on cloud processors. We also propose a sufficient schedulability condition. Simulation results from the CERIT trace as well as test-bed results show that the proposed algorithms offer superior performance as compared to algorithms that do not employ fog processors. Employing an <inline-formula><tex-math notation="LaTeX">$Embedded-fog-cloud$</tex-math></inline-formula> architecture offers an improvement of 62.37 percent for real-time Success Ratio (SR) and 35 percent for Average Response Time as compared to scheduling tasks on the <inline-formula><tex-math notation="LaTeX">$cloud$</tex-math></inline-formula> alone.

Temporal consistency maintenance on multiprocessor platforms with instance skipping

Maintaining temporal consistency of real-time data is important for cyber-physical systems. Most of the previous studies focus on uniprocessor systems. In this paper, the problem of temporal consistency maintenance on multiprocessor platforms with instance skipping was formulated based on the (m,k)-constrained model. A partitioned scheduling method SC-AD was proposed to solve the problem. SC-AD uses a derived sufficient schedulability condition to calculate the initial value of m for each sensor transaction. It then partitions the transactions among the processors in a balanced way. To further reduce the average relative invalid time of real-time data, SC-AD judiciously increases the values of m for transactions assigned to each processor. Experiment results show that SC-AD outperforms the baseline methods in terms of the average relative invalid time and the average valid ratio under different system workloads.

Exact response time analysis of fixed priority systems based on sporadic servers

Abstract Real-time servers have been widely explored in the scheduling literature to predictably execute aperiodic activities, as well as to allow hierarchical scheduling settings. As they facilitate timing isolation between different software components, there is a renewed interest for the adoption of fixed priority real-time servers in the automotive domain, as a way to implement more efficient reservation mechanisms than TDMA-based methods. In this paper, we focus on the Sporadic Server, which is the only fixed priority server supported by the POSIX standard. Despite its popularity, we realized that only sufficient schedulability conditions exist for real-time systems scheduled with a Sporadic Server. Thus, we develop a formal characterization of an exact response time analysis for fixed priority systems based on Sporadic Servers in a multi-level scheduling setting under preemptive scheduling. We then provide an experimental characterization of the schedulabilty improvement that can be obtained with respect to existing sufficient schedulability tests, proving the effectiveness of the proposed exact analysis.

Polynomial Time Schedulability Test for Periodic Non-Preemptive 2-Task System

Non-preemptive scheduling of tasks is often preferred in safety-critical systems because of its simplicity in implementation. But, one of the major issues with non-preemptive scheduling is that no known polynomial time schedulability condition exists. The general problem of schedulability of a set of tasks on a single processor under such scheme is known to be NP-Hard [1]. People have attempted to propose different sufficient or necessary conditions for schedulability of a set of tasks under various constrained scenarios. In this work, we explore schedulability condition for 2-task systems when the tasks are scheduled non-preemptively and periodically using work conserving model of execution. We assume that the tasks are released at the same point of time initially. We show that the proposed condition for 2-task systems can be evaluated in polynomial time.

Robust Scheduling of Time-Constrained Dual-Arm Cluster Tools With Wafer Revisiting and Activity Time Disturbance

Wafer revisiting and residency time constraints complicate the scheduling problem of cluster tools in semiconductor manufacturing. Random disturbance to the activity time in operating a tool further complicates such a scheduling problem. To solve this challenging problem, this paper proposes a robust real-time schedule which consists of a real-time controller (RTC) and an off-line schedule. The former is developed to offset the activity time disturbance such that the wafer sojourn time fluctuation in a process module is minimized. With the RTC, to find the off-line schedule, necessary and sufficient schedulability conditions under which a feasible schedule exists are derived and these conditions can be easily checked. Then, the off-line schedule can be efficiently found by the proposed algorithms based on nondisturbed activity time if a feasible schedule exists. With the obtained real-time schedule, it is shown that the productivity of the system is maximized. Finally, examples are used to illustrate the proposed approach.

Cooperative control and communication of connected vehicles considering packet dropping rate

ABSTRACTThis paper investigates cooperative control and communication scheduling of a platoon of connected vehicles. Considering the effect of packet dropout and the network access limitation, the vehicular platoon is modelled as a discrete-time switching system. We obtain a set of sufficient conditions (where the rate of different platoon control modes is factored in) for string stability and schedulability of the vehicular platoon. A unified framework of network access scheduling and platoon control is proposed, which can guarantee string stability of the platoon of vehicles and resolve network access conflicts among them. Both numerical simulations and experimental studies with laboratory-scale cars have demonstrated the effectiveness of the presented co-design algorithm.

Schedulability analysis and efficient scheduling of rate constrained messages in the TTEthernet protocol

SummaryOver time, cyber‐physical systems are becoming mixed criticality systems. As the complexity and the size of these systems grow, computation/communication resources should be more efficient than with traditional systems. TTEthernet is a communication infrastructure that enables the use of a single physical communication infrastructure for distributed mixed criticality applications while providing timely determinism. TTEthernet distinguishes between two traffic categories: the standard event triggered and the time triggered. The latter, for which higher priority is granted, is subject to strong timing guarantees because of strict periodicity constraint that fixes start‐time cycles of time‐triggered messages. In addition, event‐triggered traffic includes rate‐constrained messages that are of lower priority and have a minimum time interval between their transmission. The paper proposes both an on‐line efficient scheduling algorithm and a necessary and sufficient schedulability condition based on the worst case response time computation for rate‐constrained messages while taking into account time‐triggered messages transmission. Copyright © 2017 John Wiley &amp; Sons, Ltd.

Schedulability and Scheduling Analysis of Dual-Arm Cluster Tools with Wafer Revisiting and Residency Time Constraints Based on a Novel Schedule

Some wafer fabrication processes require a wafer to visit some processing modules in a cluster tool multiple times, leading to a wafer revisiting process. They may pose wafer residency time constraints, i.e., a wafer can stay in a module for a limited time after it is processed. Although techniques exist for scheduling cluster tools with either wafer residency time constraints or wafer revisiting, it is much more challenging to schedule tools with both of them. Considering that atomic layer deposition is a typical wafer revisiting process, this paper intends to schedule a dual-arm cluster tool dealing with it. Based on the analysis of such a tool's properties, a novel scheduling strategy called modified 1-wafer cyclic scheduling is derived. With this strategy, necessary and sufficient schedulability conditions are presented. If schedulable, highly efficient scheduling algorithms are developed to obtain a feasible and optimal schedule together with a way to implement the obtained one. Illustrative examples are given to show the application of the proposed approach.

Scheduling of Single-Arm Multi-cluster Tools With Wafer Residency Time Constraints in Semiconductor Manufacturing

This paper studies the challenging problem of scheduling single-arm multi-cluster tools with wafer residency time constraints. They have a linear topology and their bottleneck tool is process-bound. This work aims to find an optimal one-wafer cyclic schedule. With the Petri net model developed in our previous work and the minimal cycle time for a multicluster tool without wafer residency time constraints, it derives the necessary and sufficient schedulability conditions for multicluster tools with wafer residency time constraints for the first time. Then, it gives an algorithm to find an optimal one-wafer cyclic schedule if schedulable. This is done by simply setting the robots' waiting time for each tool. Thus, it is very computationally efficient and applicable to practical problems. An example is presented to illustrate the proposed method.

An Efficient Test Method for Rate Monotonic Schedulability

Rate Monotonic scheduling algorithm has been widely used in real-time systems for its optimality in fixed priority scheduling. Determining the Rate Monotonic schedulability of tasks is an important problem when designing a real-time system. There are exact schedulability test methods for Rate Monotonic scheduling, but the worst case response time analysis on which the exact tests are based is NP-hard. So the exact tests are often too complex to be executed on-line for large numbers of tasks. For practical use, polynomial time sufficient conditions for the Rate Monotonic schedulability have been studied. However, existing polynomial time tests are often too pessimistic. In this paper, we propose a new polynomial time sufficient condition based on the response time analysis, which is less pessimistic than existing ones. Simulation results show that our test significantly outperforms the existing tests and has performance close to the exact test.

Schedulability Analysis of DeferrableScheduling Algorithms for MaintainingReal-Time Data Freshness

Although the deferrable scheduling algorithm for fixed priority transactions ( DS-FP) has been shown to provide a better performance compared with the More-Less (ML) method, there is still a lack of any comprehensive studies on the necessary and sufficient conditions for the schedulability of DS-FP. In this paper, we first analyze the necessary and sufficient schedulability conditions for DS-FP, and then propose a schedulability test algorithm for DS-FP by exploiting the fact that there always exists a repeating pattern in a DS-FP schedule. To resolve the limitation of fixed priority scheduling in DS-FP, we then extend the deferrable scheduling to a dynamic priority scheduling algorithm called DS-EDF by applying the earliest deadline first (EDF) policy to schedule update jobs. We also propose a schedulability test for DS-EDF and compare its performance with DS-FP and ML through extensive simulation experiments. The results show that the schedulability tests are effective. Although the schedulability of DS-EDF is lower than DS-FP and the repeating patterns in DS-EDF schedules are longer than those in DS-FP due to the use of dynamic priority scheduling, the performance of DS-EDF is better than both DS-FP and ML in terms of CPU utilization and impact on lower priority application transactions.

Utilisation bounds of P-FRP tasks

Priority-based functional reactive programming (P-FRP) is a new functional programming formalism for developing safety-critical embedded systems. P-FRP allows static priority assignment and guarantees real-time response by preempting lower priority tasks. Due to the state-less nature of functional programmes, preempted tasks in P-FRP are aborted and have to restart after the higher priority tasks have completed execution. Since the execution semantics of P-FRP are different from the classical preemptive model of execution, existing utilisation-based sufficient conditions cannot be applied. In this paper, we derive a new utilisation-based sufficient schedulability condition for P-FRP, and validate it using experimental task sets. We then compare the sufficient schedulability condition of P-FRP with that of the preemptive model to demonstrate the severe restrictions on task set sizes in P-FRP. Effect on the utilisation bound under conditional preemption has also been analysed.

An SRP-based energy-efficient scheduling algorithm for dependent real-time tasks

In this paper, we are interested in the energy-efficient scheduling of dependent real-time tasks which may access multiunit resources. Based on the well-known stack resource policy (SRP), we propose the blocking-time stealing (BTS) algorithm to schedule dynamic-priority and fixed-priority tasks on a non-ideal dynamic voltage scaling (DVS) processor. Under the BTS algorithm, tasks are scheduled to be executed at proper processor speeds which are determined according to the sufficient schedulability conditions of the earliest deadline first (EDF) and the rate monotonic (RM) algorithms. The BTS algorithm measures dynamically the slack between the actual blocking time of a task and its estimated worst-case blocking time. The slack is then exploited to lower the processor speed guaranteeing that the feasibility of tasks is not affected. As a result, the energy consumption can be reduced while satisfying the timing constraints of real-time tasks.

Utilization Bound Scheduling Analysis for Nonpreemptive Uniprocessor Architecture Using UML-RT

The key for adopting the utilization-based schedulability test is to derive the utilization bound. Given the computation times, this paper proposes two utilization bound algorithms to derive interrelease times for nonpreemptive periodic tasks, using a new priority scheme, “Rate Monotonic Algorithm-Shortest Job First.” The obtained task set possesses the advantage of Rate Monotonic Algorithm and Shortest Job First priority scheme. Further, the task set is tested for schedulability, by first deriving a general schedulability condition from “problem window” analysis and, a necessary and sufficient schedulability condition for a task to be scheduled, at any release time are also derived. As a technical contribution, success ratio and effective processor utilization are analyzed for our proposed utilization bound algorithms on a uniprocessor architecture modeled using UML-RT.

Schedulability Analysis of Distributed Real-Time Applications under Dependence and Several Latency Constraints

This paper focuses on the analysis of real-time non preemptive multiprocessor scheduling with precedence and several latency constraints. It aims to specify a schedulability condition which enables a designer to check a priori -without executing or simulating- if its scheduling of tasks will hold the precedences between tasks as well as several latency constraints imposed on determined pairs of tasks. It is shown that the required analysis is closely linked to the topological structure of the application graph. More precisely, it depends on the configuration of tasks paths subject to latency constraints. As a result of the study, a sufficient schedulability condition is introduced for precedences and latency constraints in the hardest configuration in term of complexity with an optimal number of processors in term of applications parallelism. In addition, the proposed conditions provides a practical lower bounds for general cases. Performances results and comparisons with an optimal approach demonstrate the effectiveness of the proposed approach.

Efficient computation of response time bounds for preemptive uniprocessor deadline monotonic scheduling

The deadline-monotonic (DM) scheduling of sporadic task systems upon a preemptive uniprocessor is considered. A technique is derived for determining upper bounds on the response time of the jobs of each task, when a constrained-deadline sporadic task system is scheduled. This technique yields a generalization to a load-based sufficient schedulability condition for DM, the generalization being the added ability to account for blocking in the presence of non-preemptable serially re-usable resources.

Optimizing Distributed Real-Time Embedded System Handling Dependence and Several Strict Periodicity Constraints

This paper focuses on real-time nonpreemptive multiprocessor scheduling with precedence and strict periodicity constraints. Since this problem is NP-hard, there exist several approaches to resolve it. In addition, because of periodicity constraints our problem stands for a decision problem which consists in determining if, a solution exists or not. Therefore, the first criterion on which the proposed heuristic is evaluated is its schedulability. Then, the second criterion on which the proposed heuristic is evaluated is its execution time. Hence, we performed a schedulability analysis which leads to a necessary and sufficient schedulability condition for determining whether a task satisfies its precedence and periodicity constraints on a processor where others tasks have already been scheduled. We also present two multiperiodic applications.

Utilization Bound of Non-preemptive Fixed Priority Schedulers

It is known that the schedulability of a non-preemptive task set with fixed priority can be determined in pseudo-polynomial time. However, since Rate Monotonic scheduling is not optimal for non-preemptive scheduling, the applicability of existing polynomial time tests that provide sufficient schedulability conditions, such as Liu and Layland's bound, is limited. This letter proposes a new sufficient condition for non-preemptive fixed priority scheduling that can be used for any fixed priority assignment scheme. It is also shown that the proposed schedulability test has a tighter utilization bound than existing test methods.