Packing Sporadic Real-Time Tasks on Identical Multiprocessor Systems

In real-time systems, in addition to the functional correctness recurrent tasks must fulfill timing constraints to ensure the correct behavior of the system. Partitioned scheduling is widely used in real-time systems, i.e., the tasks are statically assigned onto processors while ensuring that all timing constraints are met. The decision version of the problem, which is to check whether the deadline constraints of tasks can be satisfied on a given number of identical processors, has been known ${\cal NP}$-complete in the strong sense. Several studies on this problem are based on approximations involving resource augmentation, i.e., speeding up individual processors. This paper studies another type of resource augmentation by allocating additional processors, a topic that has not been explored until recently. We provide polynomial-time algorithms and analysis, in which the approximation factors are dependent upon the input instances. Specifically, the factors are related to the maximum ratio of the period to the relative deadline of a task in the given task set. We also show that these algorithms unfortunately cannot achieve a constant approximation factor for general cases. Furthermore, we prove that the problem does not admit any asymptotic polynomial-time approximation scheme (APTAS) unless ${\cal P}={\cal NP}$ when the task set has constrained deadlines, i.e., the relative deadline of a task is no more than the period of the task.Comment: Accepted and to appear in ISAAC 2018, Yi-Lan, Taiwa

Towards Efficient Explainability of Schedulability Properties in Real-Time Systems

The notion of efficient explainability was recently introduced in the context of hard-real-time scheduling: a claim that a real-time system is schedulable (i.e., that it will always meet all deadlines during run-time) is defined to be efficiently explainable if there is a proof of such schedulability that can be verified by a polynomial-time algorithm. We further explore this notion by (i) classifying a variety of common schedulability analysis problems according to whether they are efficiently explainable or not; and (ii) developing strategies for dealing with those determined to not be efficiently schedulable, primarily by identifying practically meaningful sub-problems that are efficiently explainable

Packing sporadic real-time tasks on identical multiprocessor systems

In real-time systems, in addition to the functional correctness recurrent tasks must fulfill timing constraints to ensure the correct behavior of the system. Partitioned scheduling is widely used in real-time systems, i.e., the tasks are statically assigned onto processors while ensuring that all timing constraints are met. The decision version of the problem, which is to check whether the deadline constraints of tasks can be satisfied on a given number of identical processors, has been known NP-complet

Packing Sporadic Real-Time Tasks on Identical Multiprocessor Systems

In real-time systems, in addition to the functional correctness recurrent tasks must fulfill timing constraints to ensure the correct behavior of the system. Partitioned scheduling is widely used in real-time systems, i.e., the tasks are statically assigned onto processors while ensuring that all timing constraints are met. The decision version of the problem, which is to check whether the deadline constraints of tasks can be satisfied on a given number of identical processors, has been known NP-complete in the strong sense. Several studies on this problem are based on approximations involving resource augmentation, i.e., speeding up individual processors. This paper studies another type of resource augmentation by allocating additional processors, a topic that has not been explored until recently. We provide polynomial-time algorithms and analysis, in which the approximation factors are dependent upon the input instances. Specifically, the factors are related to the maximum ratio of the period to the relative deadline of a task in the given task set. We also show that these algorithms unfortunately cannot achieve a constant approximation factor for general cases. Furthermore, we prove that the problem does not admit any asymptotic polynomial-time approximation scheme (APTAS) unless P=NP when the task set has constrained deadlines, i.e., the relative deadline of a task is no more than the period of the task

Many suspensions, many problems: a review of self-suspending tasks in real-time systems

In general computing systems, a job (process/task) may suspend itself whilst it is waiting for some activity to complete, e.g., an accelerator to return data. In real-time systems, such self-suspension can cause substantial performance/schedulability degradation. This observation, first made in 1988, has led to the investigation of the impact of self-suspension on timing predictability, and many relevant results have been published since. Unfortunately, as it has recently come to light, a number of the existing results are flawed. To provide a correct platform on which future research can be built, this paper reviews the state of the art in the design and analysis of scheduling algorithms and schedulability tests for self-suspending tasks in real-time systems. We provide (1) a systematic description of how self-suspending tasks can be handled in both soft and hard real-time systems; (2) an explanation of the existing misconceptions and their potential remedies; (3) an assessment of the influence of such flawed analyses on partitioned multiprocessor fixed-priority scheduling when tasks synchronize access to shared resources; and (4) a discussion of the computational complexity of analyses for different self-suspension task models

Fast and Effective Multiframe-Task Parameter Assignment Via Concave Approximations of Demand

Task parameters in traditional models, e.g., the generalized multiframe (GMF) model, are fixed after task specification time. When tasks whose parameters can be assigned within a range, such as the frame parameters in self-suspending tasks and end-to-end tasks, the optimal offline assignment towards schedulability of such parameters becomes important. The GMF-PA (GMF with parameter adaptation) model proposed in recent work allows frame parameters to be flexibly chosen (offline) in arbitrary-deadline systems. Based on the GMF-PA model, a mixed-integer linear programming (MILP)-based schedulability test was previously given under EDF scheduling for a given assignment of frame parameters in uniprocessor systems. Due to the NP-hardness of the MILP, we present a pseudo-polynomial linear programming (LP)-based heuristic algorithm guided by a concave approximation algorithm to achieve a feasible parameter assignment at a fraction of the time overhead of the MILP-based approach. The concave programming approximation algorithm closely approximates the MILP algorithm, and we prove its speed-up factor is (1+delta)^2 where delta > 0 can be arbitrarily small, with respect to the exact schedulability test of GMF-PA tasks under EDF. Extensive experiments involving self-suspending tasks (an application of the GMF-PA model) reveal that the schedulability ratio is significantly improved compared to other previously proposed polynomial-time approaches in medium and moderately highly loaded systems

Push Forward: Global Fixed-Priority Scheduling of Arbitrary-Deadline Sporadic Task Systems

The sporadic task model is often used to analyze recurrent execution of tasks in real-time systems. A sporadic task defines an infinite sequence of task instances, also called jobs, that arrive under the minimum inter-arrival time constraint. To ensure the system safety, timeliness has to be guaranteed in addition to functional correctness, i.e., all jobs of all tasks have to be finished before the job deadlines. We focus on analyzing arbitrary-deadline task sets on a homogeneous (identical) multiprocessor system under any given global fixed-priority scheduling approach and provide a series of schedulability tests with different tradeoffs between their time complexity and their accuracy. Under the arbitrary-deadline setting, the relative deadline of a task can be longer than the minimum inter-arrival time of the jobs of the task. We show that global deadline-monotonic (DM) scheduling has a speedup bound of 3-1/M against any optimal scheduling algorithms, where M is the number of identical processors, and prove that this bound is asymptotically tight

Scheduling Mixed-Criticality Real-Time Systems

This dissertation addresses the following question to the design of scheduling policies and resource allocation mechanisms in contemporary embedded systems that are implemented on integrated computing platforms: in a multitasking system where it is hard to estimate a task's worst-case execution time, how do we assign task priorities so that 1) the safety-critical tasks are asserted to be completed within a specified length of time, and 2) the non-critical tasks are also guaranteed to be completed within a predictable length of time if no task is actually consuming time at the worst case? This dissertation tries to answer this question based on the mixed-criticality real-time system model, which defines multiple worst-case execution scenarios, and demands a scheduling policy to provide provable timing guarantees to each level of critical tasks with respect to each type of scenario. Two scheduling algorithms are proposed to serve this model. The OCBP algorithm is aimed at discrete one-shot tasks with an arbitrary number of criticality levels. The EDF-VD algorithm is aimed at recurrent tasks with two criticality levels (safety-critical and non-critical). Both algorithms are proved to optimally minimize the percentage of computational resource waste within two criticality levels. More in-depth investigations to the relationship among the computational resource requirement of different criticality levels are also provided for both algorithms.Doctor of Philosoph

Efficient Allocation And Enforcement Of Interfaces In Compositional Real-Time Systems

Compositional real-time research has become one of the emerging trends in embedded and real-time systems due to the increasing scale and complexity of such systems. In this design paradigm, a large system is decomposed into smaller and simpler components, each of which abstracts their temporal requirements via interfaces. Such systems are mostly implemented by resource partitions to ensure that the components receive resources according to their interfaces. Potential implementations of a resource partition are via server-based interfaces or demand-based interfaces. In this context, our thesis in this dissertation is as follows: Currently, server-based interfaces ensure strong temporal isolation among components at the cost of resource over-provisioning whereas demand-based interfaces precisely model the resource demand of a component without the guarantee of temporal isolation. For both these models, efficient and effective resource allocation as well as strict temporal isolation among components can be achieved. Specifically, we can obtain efficient and near-optimal bandwidth allocation schemes and admission controllers for periodic resource model and arbitrary demand-based interface respectively. Furthermore, efficient slack reclamation technique can be obtained to allocate unused processing resources at runtime while still enforcing the given interface. To support our thesis, we address efficient resource allocation among components with server-based interfaces by providing fully-polynomial-time approximation schemes (FPTAS) for allocating processing resource to components scheduled by earliest-deadline-first (EDF) or fixed-priority (FP) scheduling algorithm. For enforcing temporal isolation of demand-based interfaces, we provide a parametric approximate admission control algorithm, which has polynomial-time complexity in terms of number of active jobs in the system and the approximation parameter. Finally, to address efficient reclamation of unused processing resources, we give a novel technique to optimally and efficiently determine maximum allowable runtime slack for a component with arbitrary interface, considering active jobs in the system and guaranteeing system schedulability even for worst-case future job arrival scenarios. We expect that these techniques can ultimately be used to minimize the size, weight, and power requirements of real-time and embedded systems by reducing the processing resource requirements of such systems