Xingliang Zou

Minimal Schedulability Testing Interval for Real-Time Periodic Tasks with Arbitrary Release Offsets

The concept of feasibility (or schedulability) interval plays a very important role in the schedulability analysis in real-time systems. Existing results on the schedulability testing interval of real-time task sets under fixed priority scheduling with arbitrary release offsets (or phases) have limitations for certain scenarios in constructing a schedule for testing the schedulability of a given task set. In this paper, we propose a transforming method for deriving minimal schedulability testing interval of real-time n-task sets with arbitrary release offsets under fixed priority scheduling in both the classical pre-emptive model and the Priority-based Functional Reactive Programming (P-FRP) model on uniprocessor. The complexity of our transforming method is O(n), and the validity is also proved by theoretical analysis.

Schedulability Analysis for Real-Time P-FRP Tasks under Fixed Priority Scheduling

This paper studies the schedulability of real-time tasks in the Priority-based Functional Reactive Programming (P-FRP) model under fixed priority scheduling, one of the influential scheduling policies. Since the abort-and-restart execution paradigm of the P-FRP model is different from that of the classic pre-emptive model, the schedulability analysis for P-FRP tasks under fixed priority scheduling differs widely. In P-FRP, for a synchronous n-task set under fixed priority scheduling, the least common multiple (LCM) of all n task periods is the typical length of a testing interval for an exact (necessary and sufficient) schedulability test. In this paper, we propose and prove an optimal simulation based exact schedulability test in the P-FRP model under fixed priority scheduling for a given priority order, covering scenarios from synchronous task release to asynchronous task release with the initial busy condition, and from implicit deadlines to constrained deadlines. The length of a testing interval for the exact test is the LCM of the first n-1 task periods and its optimality is proved.

P-FRP task scheduling: A survey

Functional Reactive Programming (FRP) is a declarative approach for modeling and building reactive systems. The FRP has been shown to be an expressive formalism for building graphics, robotic, and vision applications. The Priority-based FRP (P-FRP) is a formalism of FRP that allows preemption of execution and guarantees real-time response. Since functional programs cannot maintain state and mutable data, changes made by programs that are preempted have to be rolled back, and the work done by the preempted programs has to be discarded. Hence in the P-FRP model, a preempted lower priority task will have to restart after higher priority tasks have completed execution. Current real-time research mainly focuses on the classic preemptive or non-preemptive models and plenty methods have been developed to analyze the real-time guarantees of these models. Unfortunately, due to its transactional nature where preempted tasks are aborted and have to restart, the execution semantics of the P-FRP model does not fit into the standard definitions of classic preemptive or non-preemptive execution. In this survey paper, we review existing researches on the P-FRP task scheduling, and present a few research areas for future work.

Deferred Start: A Non-Work-Conserving Model for P-FRP Fixed Priority Task Scheduling

In real-time systems, FRP (Functional Reactive Programming) is playing and potentially going to play a more important role. Priority-based (preemptive) FRP (P-FRP), a variant of FRP with more real-time characteristics, demands more research in its scheduling and timing analysis. Its abort-and-restart nature indicates that reducing preemptions can be critical for improving system performance. In this paper, we present a non-work conserving scheduling model, Deferred Start, to reduce certain preemptions. Experiments show the improvement on schedulability and task response time.

Worst case response time and schedulability analysis for real-time software transactional memory-lazy conflict detection (STM-LCD)

Software transactional memory (STM) is a transactional mechanism of controlling access to shared resources in memory. This transactional mechanism is similar to the abort-and-restart execution model in a functional reactive system (FRS). Due to its abort-and-restart nature, the execution semantics of STM are different from the classic preemptive or nonpreemptive model. Some research has strong constraints for its worst case response time (WCRT) analysis. In this paper, we research on worst case response time and schedulability analysis for real-time software transactional memory-lazy conflict detection (STM-LCD). Specifically, we introduce a parameter the remainder factor m, formally derive an exact WCRT for a 2-task set on STM systems using lazy conflict detection (LCD), propose an exact schedulability test for a 2-task set. Also, we present a near-exact WCRT for an n-task set on STM-LCD, and propose a new necessary condition and a new sufficient condition to schedule an n-task set. Finally, we show that experimental results are accordant with the aforementioned analysis.

A Non-Work-Conserving Model for P-FRP Fixed Priority Scheduling

In real-time systems, Functional Reactive Programming (FRP) is already playing an important role and will potentially be more so in the future. Priority-based (preemptive) FRP (P-FRP), a variant of FRP with more real-time characteristics, demands more research in its scheduling and timing analysis. Its Abort-and-Restart (AR) nature indicates that reducing preemptions can be critical for improving system performance. In this paper, we present a new non-work-conserving scheduling model, P-FRP Deferred Start (DS) model, to reduce certain preemptions under fixed priority scheduling. We analyze some properties of the P-FRP DS model. Experiments show the domination on schedulability rate and task response time to those of the P-FRP AR model. The schedulability rate increases up to 243.1% and the portion of task sets that have response time decreased ranges from 15.49% for 3-task sets to 98.28% for 10-task sets.

Finding a Steady State Point for Fixed Priority Independent Periodic Real-Time Tasks with Arbitrary Given Release Offsets

Minimal schedulability interval is one of the important considerations of both research motivation and practice stage. In this paper, we investigate the problem of finding a starting time point of the minimal schedulability interval for fixed priority independent periodic real-time preemptive tasks with arbitrary given release offsets (phasing). A linked list-based method is proposed for solving the problem. Each node in the linked list represents a pending-less busy period. Analysis and experimental results show that the linked list-based method outperforms the current best acyclic-idle-slot-based one.

Multi-mode P-FRP Task Scheduling

Functional Reactive Programming (FRP) provides an elegant way to express computation in domains such as interactive animations, robotics, computer vision, user interfaces, and simulation. Priority-based (preemptive) FRP (P-FRP), a variant of FRP with more real-time characteristics, demands research in its scheduling and timing analysis. Different from the classic preemptive model, in a P-FRP system, when a task is preempted, all changes made by the task are discarded and after higher priority tasks complete their execution the preempted task will restart from the beginning (abort-and-restart). P-FRP is thus able to capture changes of the task in time and provides an option other than the classic preemptive model in certain scenarios. In the P-FRP model, previous studies use the largest execution time of a task for all its restarted jobs. In practice, however, when considering the changing/unchanging inputs/outputs of the task or the memory effects such as cache-hit in loading code and data, the restarted jobs likely consume less time than its largest execution time. In this paper, for the first time we present a multi-mode P-FRP task framework and two particular scenarios for the framework that are able to reflect such effects and then improve the performance of a developing commercial software platform. We show that the multi-mode task P-FRP system has significant schedulability improvements over the original P-FRP model.

Real-Time Multiprocessor Scheduling Algorithm Based on Information Theory Principles

Reducing job migrations is essential for any global multiprocessor scheduling algorithm. In this letter, we present a global, dynamic-priority, laxity-based algorithm that reduces the number of migrations on multiprocessor embedded systems by leveraging information theory principles. A simplification of the proposed scheduling theory is presented to reduce the overhead caused by using information theory. Our results show that the proposed algorithm is able to reduce the number of migrations by up to 41.21% when compared with other global, dynamic-priority, laxity-based algorithms. As the utilization per task set and the number of processors increase, simplified information-theoretic scheduling algorithm is able to improve its performance in terms of the number of migrations.

Poster Abstract: Using Linked List in Exact Schedulability Tests for Fixed Priority Scheduling

Summary form only given. In the context of fixed priority preemptive real-time systems, for n periodic/sporadic tasks that comply with a restrictive system model and that have implicit deadlines the Rate-Monotonic (RM) scheduling is optimal. When these tasks are released simultaneously the time required by the first job of each task defines its response time. It thus needs only to make response time analysis or conduct exact schedulability test within a time length no more than the maximum task period (Tn) for RM scheduling, and these tests are thus known to be pseudo-polynomial in time complexity. Although the response time computation for RM schedules of implicit-deadline task-systems has been proved to be an NPhard problem, the scale of many commercial systems is such that pseudo-polynomial exact tests can be used, and to achieve more efficient exact tests such as for online response time analysis (RTA) is one of important considerations of both research motivation and practice stage. The innovative aspect of our solution is that we use a linked list for representing the schedule in the exact response-time schedulability test, referred to as the LList-based test. A busy period in the schedule is represented by a linked list node, recording the starting time and the end time of a busy period, and the pointer to the next node. The simulation is performed task per task in the priority order (from 1 to n), and, when the starting time or the end time of a busy period is the same as that of other busy periods, then the two nodes are merged into one node to represent a longer busy period. For improving the efficiency, memory allocation and recycle for each node are also performed in the user space. The time complexity of the LList-based test is O(N) where N is the total number of jobs within the time length Tn, while the total number of nodes in the linked list is no more than N - n + 1 in the worst case. Our experiments show that the LList-based exact test is a better candidate in exact response-time tests when task periods span no more than three orders of magnitude, since it outperforms the current best exact tests in this scenario, and the needed memory space is also affordable.