An Exact Schedulability Test for Global FP Using State Space Pruning

Presented at 23rd International Conference on Real-Time Networks and Systems (RTNS 2015). 4 to 6, Nov, 2015, Main Track. Lille, France.

Laxity dynamics and LLF schedulability analysis on multiprocessor platforms

LLF (Least Laxity First) scheduling, which assigns a higher priority to a task with a smaller laxity, has been known as an optimal preemptive scheduling algorithm on a single processor platform. However, little work has been made to illuminate its characteristics upon multiprocessor platforms. In this paper, we identify the dynamics of laxity from the system’s viewpoint and translate the dynamics into LLF multiprocessor schedulability analysis. More specifically, we first characterize laxity properties under LLF scheduling, focusing on laxity dynamics associated with a deadline miss. These laxity dynamics describe a lower bound, which leads to the deadline miss, on the number of tasks of certain laxity values at certain time instants. This lower bound is significant because it represents invariants for highly dynamic system parameters (laxity values). Since the laxity of a task is dependent of the amount of interference of higher-priority tasks, we can then derive a set of conditions to check whether a given task system can go into the laxity dynamics towards a deadline miss. This way, to the author’s best knowledge, we propose the first LLF multiprocessor schedulability test based on its own laxity properties. We also develop an improved schedulability test that exploits slack values. We mathematically prove that the proposed LLF tests dominate the state-of-the-art EDZL tests. We also present simulation results to evaluate schedulability performance of both the original and improved LLF tests in a quantitative manner.

LLF schedulability analysis on multiprocessor platforms

LLF (Least Laxity First) scheduling, which assigns a higher priority to a task with smaller laxity, has been known as an optimal preemptive scheduling algorithm on a single processor platform. However, its characteristics upon multiprocessor platforms have been little studied until now. Orthogonally, it has remained open how to efficiently schedule general task systems, including constrained deadline task systems, upon multiprocessors. Recent studies have introduced zero laxity (ZL) policy, which assigns a higher priority to a task with zero laxity, as a promising scheduling approach for such systems (e.g., EDZL). Towards understanding the importance of laxity in multiprocessor scheduling, this paper investigates the characteristics of ZL policy and presents the first ZL schedulability test for any work-conserving scheduling algorithm that employs this policy. It then investigates the characteristics of LLF scheduling, which also employs the ZL policy, and derives the first LLF-specific schedulability test on multiprocessors. It is shown that the proposed LLF test dominates the ZL test as well as the state-of-art EDZL test.

一种改进的RM可调度性判定算法

固定优先级任务可调度性判定是实时系统调度理论研究的核心问题之一.目前已有的各种判定方法可归结为两大类:多项式时间调度判定和确切性判定.多项式时间调度判定通常采用调度充分条件来进行,为此,许多理想条件下基于RM(rate monotonic)调度算法的CPU利用率最小上界被提了出来.确切性判定利用RM调度的充要条件,保证任何任务集均可被判定,并且判定结果是确切的.但是由于时间复杂度较差,确切性判定方法难以实现在线分析.提出了一种改进的RM可调度性判定方法(improved schedulability test algorithm,简称ISTA).首先介绍了任务调度空间这一概念,并提出了二叉树表示,然后进一步提出了相关的剪枝理论.在此基础上,研究了任务之间可调度性的相关性及其对判定任务集可调度性的影响,提出并证明了相关的定理.最后基于提出的定理,给出了一种改进的伪多项式时间可调度性判定算法,并与已有的判定方法进行了比较.仿真结果表明,该算法平均性能作为任务集内任务个数的函数具有显著提高.

单调速率及其扩展算法的可调度性判定

任务可调度性判定是实时系统调度理论研究的核心问题.单调速率(RM)算法是实时调度的重要算法,自其提出以来已被广泛研究.然而到目前为止,尚缺乏专题性的文章来系统而深入地探讨RM及其扩展算法的可调度性判定,以及各种现实条件和实现方式(包括任务调度的时间开销和任务同步问题等)对可调度性的影响.围绕RM算法下的可调度性判定问题,由浅入深,系统性地讨论各种不同假设和实现方式对可调度性的影响,具体分为下述3大类问题:(1)理想的RM算法下的可调度性判定的CPU利用率最小上界及可调度的充分必要条件;(2)考虑调度时间开销情况下的可调度性判定条件;(3)优先级反转协议及其对可调度性的影响.给出了具体实例来阐述上述问题,并从算法复杂度和可检测率两方面来比较各种算法的优劣.

一种静态最少优先级分配算法

随着实时系统越来越多地应用于各种快速更新系统,尤其是各种片上系统,如PDA(personal digital assistant),PSP(play station portable)等,性价比已成为系统设计者的主要关注点.实际应用中,实时系统通常仅支持较少的优先级,常出现系统优先级数小于任务数的情况(称为有限优先级),此时,需将多个任务分配到同一系统优先级,RM(rate monotonic),DM(deadline monotonic)等静态优先级分配算法不再适用.为此,静态有限优先级分配是研究在任务集合静态优先级可调度的情况下,可否以及如何用较少或最少的系统优先级保持任务集合可调度.已有静态有限优先级分配可分为两类:固定数目优先级分配和最少优先级分配.给出了任意截止期模型下任务静态有限优先级可调度的充要条件以及不同静态有限优先级分配间转换时的几个重要性质,指出了系统优先级从低到高分配策略的优越性,定义了饱和任务组与饱和分配的概念,证明了在任务集合静态优先级可调度的情况下,最少优先级分配比固定数目优先级分配更具一般性.最后提出一种最少优先级分配算法LNPA(least-number priority assignment).与现有算法相比,LNPA适用范围更广,且复杂度较低.

RM及其扩展可调度性判定算法性能分析

可调度性判定是实时调度算法的关键问题．单调速率算法RM（rate monotonic）及其扩展是应用广泛的实时调度算法，大量文献讨论了实时任务在这些算法下的可调度性判定，给出了相应的判定算法．但迄今为止，对这些判定算法的性能分析都是理论上的定性分析或者只是少数几种判定算法之间的简单比较，这不利于实时系统的开发．归纳了RM及其扩展的可调度性判定算法，通过测试平台，系统地测试和分析了各算法的性能和适用场合，讨论了各种条件和实现方式对算法性能和可调度性的影响．

Statistic Rate Monotonic Scheduling

In this paper we present Statistical Rate Monotonic Scheduling (SRMS), a generalization of the classical RMS results of Liu and Layland that allows scheduling periodic tasks with highly variable execution times and statistical QoS requirements. Similar to RMS, SRMS has two components: a feasibility test and a scheduling algorithm. The feasibility test for SRMS ensures that using SRMS' scheduling algorithms, it is possible for a given periodic task set to share a given resource (e.g. a processor, communication medium, switching device, etc.) in such a way that such sharing does not result in the violation of any of the periodic tasks QoS constraints. The SRMS scheduling algorithm incorporates a number of unique features. First, it allows for fixed priority scheduling that keeps the tasks' value (or importance) independent of their periods. Second, it allows for job admission control, which allows the rejection of jobs that are not guaranteed to finish by their deadlines as soon as they are released, thus enabling the system to take necessary compensating actions. Also, admission control allows the preservation of resources since no time is spent on jobs that will miss their deadlines anyway. Third, SRMS integrates reservation-based and best-effort resource scheduling seamlessly. Reservation-based scheduling ensures the delivery of the minimal requested QoS; best-effort scheduling ensures that unused, reserved bandwidth is not wasted, but rather used to improve QoS further. Fourth, SRMS allows a system to deal gracefully with overload conditions by ensuring a fair deterioration in QoS across all tasks---as opposed to penalizing tasks with longer periods, for example. Finally, SRMS has the added advantage that its schedulability test is simple and its scheduling algorithm has a constant overhead in the sense that the complexity of the scheduler is not dependent on the number of the tasks in the system. We have evaluated SRMS against a number of alternative scheduling algorithms suggested in the literature (e.g. RMS and slack stealing), as well as refinements thereof, which we describe in this paper. Consistently throughout our experiments, SRMS provided the best performance. In addition, to evaluate the optimality of SRMS, we have compared it to an inefficient, yet optimal scheduler for task sets with harmonic periods.

Uniprocessor EDF scheduling with mode change

Consider the problem of scheduling sporadically-arriving tasks with implicit deadlines using Earliest-Deadline-First (EDF) on a single processor. The system may undergo changes in its operational modes and therefore the characteristics of the task set may change at run-time. We consider a well-established previously published mode-change protocol and we show that if every mode utilizes at most 50% of the processing capacity then all deadlines are met. We also show that there exists a task set that misses a deadline although the utilization exceeds 50% by just an arbitrarily small amount. Finally, we present, for a relevant special case, an exact schedulability test for EDF with mode change.

Efficient schedulability tests for real-time embedded systems with urgent routines

Task scheduling is one of the key mechanisms to ensure timeliness in embedded real-time systems. Such systems have often the need to execute not only application tasks but also some urgent routines (e.g. error-detection actions, consistency checkers, interrupt handlers) with minimum latency. Although fixed-priority schedulers such as Rate-Monotonic (RM) are in line with this need, they usually make a low processor utilization available to the system. Moreover, this availability usually decreases with the number of considered tasks. If dynamic-priority schedulers such as Earliest Deadline First (EDF) are applied instead, high system utilization can be guaranteed but the minimum latency for executing urgent routines may not be ensured. In this paper we describe a scheduling model according to which urgent routines are executed at the highest priority level and all other system tasks are scheduled by EDF. We show that the guaranteed processor utilization for the assumed scheduling model is at least as high as the one provided by RM for two tasks, namely 2(2√−1). Seven polynomial time tests for checking the system timeliness are derived and proved correct. The proposed tests are compared against each other and to an exact but exponential running time test.

A Novel Range Test

In a range test, one party holds a ciphertext and needs to test whether the message encrypted in the ciphertext is within a certain interval range. In this paper, a range test protocol is proposed, where the party holding the ciphertext asks another party holding the private key of the encryption algorithm to help him. These two parties run the protocol to implement the test. The test returns TRUE if and only if the encrypted message is within the certain interval range. If the two parties do not conspire, no information about the encrypted message is revealed from the test except what can be deduced from the test result. Advantages of the new protocol over the existing related techniques are that it achieves correctness, soundness, °exibility, high e±ciency and privacy simultaneously.