Uniprocessor Systems Research Articles

A Comparison of Gauss Elimination Method for Dense Linear Systems on Hypercube and Mesh Parallel Architectures

The problem of solving a system of N linear equations Ax = b (where A is a known N x N matrix, and b and x are, respectively, the known and unknown N x 1 vectors) is frequently encountered in many fields of science and engineering. Efficient numerical methods for solving this problem on uniprocessor systems have been developed. The Gaussian elimination method which is inherently serial is one of the most popular methods for solving the system of linear algebraic equations. In this paper we compare the well-known Gaussian elimination algorithm for solving dense linear systems Ax = b on two well known architectures: Hypercube and two dimensional mesh. Our objective is to analyse the complexity of Gauss elimination algorithm on Hypercube and to present an algorithm for Gauss elimination and analyse its complexity on mesh parallel architecture.

A Scheduling Extension Scheme of the Earliest Deadline First Policy for Hard Real-Time Uniprocessor Systems Integrated on Posix Threads Based on Linux

A Scheduling Extension Scheme of the Earliest Deadline First Policy for Hard Real-Time Uniprocessor Systems Integrated on Posix Threads Based on Linux

Fault-Tolerant Scheduling of Non-preemptive Periodic Tasks using SCT of Timed DES on Uniprocessor Systems

Safety-critical systems employ fault-tolerant strategies in order to provide predictable performance despite the occurrence of faults. Majority of faults that affect such systems are transient (i.e., momentary) in nature which can easily be tolerated through the re-execution of the affected task before its deadline. However, evaluating all possible fault patterns to provide an optimal re-execution based fault-tolerant scheduling strategy for a given task set is an intractable problem, and is prohibitively expensive to be applied on-line. Hence, off-line techniques are often preferred over on-line techniques for solving such problems. This work proposes an off-line optimal fault-tolerant scheduler synthesis mechanism for non-preemptive periodic real-time tasks on uniprocessors. Practical applicability of the above scheduler synthesis procedure has been illustrated through a motor network example.

Online and offline scheduling with cache-related preemption delays

In this paper, we consider the problem of scheduling hard real-time tasks subjected to preemption delays on a uniprocessor system. While most of the existing work focus on either reducing these additional delays or improving the system predictability by bounding them, we focus in this work on the problem of taking scheduling decisions while considering preemption delays. We first study the behavior of existing online scheduling policies such as rm and edf when accounting for preemption delays. Then we prove that there exists no optimal online algorithm for the problem of scheduling sporadic tasks with preemption delays. Eventually, we propose an optimal offline solution to the problem of scheduling tasks subjected to preemption delays using mathematical programming.

Exact speedup factors for linear-time schedulability tests for fixed-priority preemptive and non-preemptive scheduling

In this paper, we investigate the quality of several linear-time schedulability tests for preemptive and non-preemptive fixed-priority scheduling of uniprocessor systems. The metric used to assess the quality of these tests is the resource augmentation bound commonly known as the processor speedup factor. The speedup factor of a schedulability test corresponds to the smallest factor by which the processing speed of a uniprocessor needs to be increased such that any task set that is feasible under an optimal preemptive (non-preemptive) work-conserving scheduling algorithm is guaranteed to be schedulable with preemptive (non-preemptive) fixed priority scheduling if this scheduling test is used, assuming an appropriate priority assignment. We show the surprising result that the exact speedup factors for Deadline Monotonic (DM) priority assignment combined with sufficient linear-time schedulability tests for implicit-, constrained-, and arbitrary-deadline task sets are the same as those obtained for optimal priority assignment policies combined with exact schedulability tests. Thus in terms of the speedup-factors required, there is no penalty in using DM priority assignment and simple linear schedulability tests.

Temporal Consistency Maintenance Upon Partitioned Multiprocessor Platforms

Maintaining timeliness and data freshness for real-time data objects has long been recognized as an important problem in real-time database research. Despite years of active research, most of the past work focuses on uniprocessor systems. In this paper, we study the workload-aware temporal consistency maintenance problem upon multiprocessor platforms. We consider the problem of how to partition a set of update transactions to $m \ge 2$ processors to maintain the temporal consistency of real-time data objects under both earliest deadline first (EDF) and deadline monotonic (DM) scheduling in each processor, while minimizing the total workload on $m$ processors. Firstly, we only consider the feasibility aspect of the problem by proposing two polynomial time partitioning schemes, Temporal Consistency Partitioning under EDF ( $\mathsf TCP_{\mathsf{EDF}}$ ) and Temporal Consistency Partitioning under DM ( $\mathsf TCP_{\mathsf{DM}}$ ), and formally showing that the resource augmentation bounds of both $\mathsf TCP_{\mathsf{EDF}}$ and $\mathsf TCP_{\mathsf{DM}}$ are $({3 - \frac{1}{m}})$ . Secondly, we address the partition problem globally by proposing a polynomial time heuristic, Density factor Balancing Fit ( $\mathsf{DBF}$ ), where density factor balancing plays a major role in producing workload-efficient partitionings. Finally, we evaluate the feasibility and workload performances of $\mathsf{DBF}$ versus other heuristics with comparable quality experimentally.

Energy-Aware Scheduling for Real-Time Systems

This article presents a survey of energy-aware scheduling algorithms proposed for real-time systems. The analysis presents the main results starting from the middle 1990s until today, showing how the proposed solutions evolved to address the evolution of the platform's features and needs. The survey first presents a taxonomy to classify the existing approaches for uniprocessor systems, distinguishing them according to the technology exploited for reducing energy consumption, that is, Dynamic Voltage and Frequency Scaling (DVFS), Dynamic Power Management (DPM), or both. Then, the survey discusses the approaches proposed in the literature to deal with the additional problems related to the evolution of computing platforms toward multicore architectures.

Exact comparison of fixed priority and EDF scheduling based on speedup factors for both pre-emptive and non-pre-emptive paradigms

This paper investigates the relative effectiveness of fixed priority (FP) scheduling in a uniprocessor system compared to earliest deadline first (EDF) scheduling. The quantitative metric used in this comparison is the processor speedup factor, defined as the factor by which processor speed needs to increase to ensure that any task set that is schedulable according to EDF can be scheduled using fixed priorities. In the pre-emptive case, exact speedup factors are known for sporadic task sets with implicit or constrained deadlines. In this paper, we derive exact speedup factors for both pre-emptive and non-pre-emptive fixed priority scheduling of arbitrary deadline sporadic task sets. We also show that the exact speedup factor for the pre-emptive case holds when tasks share resources according to the stack resource policy/deadline floor protocol.

Optimal Checkpoint Selection with Dual-Modular Redundancy Hardening

With the continuous scaling of semiconductor technology, failure rate is increasing significantly so that reliability becomes an important issue in multiprocessor system-on-chip (MPSoC) design. We propose an optimal checkpoint selection with task duplication hardening to tolerate transient faults. A target application is specified in a task graph, and the schedule/checkpoint placements are determined at design time. The proposed optimal algorithm minimizes the checkpoint overhead with a latency constraint. Experimental results show that the proposed algorithm effectively reduces the minimum end-to-end latency to perform a fault-tolerant schedule. In addition, the proposed algorithm dramatically decreases the checkpointing overhead on uniprocessor and multiprocessor systems compared with a greedy approach and an equidistant algorithm.

Energy Consumption Analysis Satisfying Time–Energy–Probability Constraints for Modern DVFS Microprocessor

ABSTRACTDynamic voltage and frequency scaling (DVFS) is a popular technique to save energy for modern microprocessor. DVFS-based energy-aware scheduling technique is a critical energy saving technology for multi-task execution on modern DVFS processor. Many DVFS-based energy-aware scheduling technologies are unsatisfying for the trade-off between optimizing scheduling length and saving energy, and most of these technologies do not consider task execution time with probability distribution in real world. In this paper, we propose an energy-aware probabilistic scheduling approach to balancing between optimizing scheduling length and saving energy in a time–energy–probability constrained multi-task uniprocessor system, and we consider that each task execution time follows a probability distribution. We first construct system models, including DVFS operating environment, task model with each task execution time following a probability distribution, and energy model. In order to balance between task scheduling length and energy consumption, we propose time–energy–probability constraints scheduling (TEPcs) problem for the DVFS processor system. To solve TEPcs problem, we use a probabilistic weighted timed automaton to model the running behaviours of the processor system. Then, we devise a polynomial time heuristic algorithm through the probabilistic weighted timed automaton to find the optimal energy path as the solution of TEPcs problem. A case study and repeated experimental analysis demonstrate that our method is feasible and effective.

Utilization-based admission control for aperiodic tasks under EDF scheduling

Utilization-based admission control policies for processors executing aperiodic tasks are often favored due to their low overhead. This paper investigates utilization-based admission control for uniprocessor systems executing aperiodic tasks following the earliest deadline first priority assignment. We first propose a new constant time utilization-based admission control policy, CTAC. We prove that CTAC is safe and will admit any task instance that can be admitted by the best existing utilization-based admission control policy, ASL, given the same processor state. We also introduce an optimal utilization-based admission control policy, OPAC. It is proved that given the same processor state, a newly arriving task instance that can be admitted by any other safe utilization-based admission control policy can also be admitted by OPAC. We also show that OPAC cannot be implemented in constant time. Simulation results show that CTAC indeed outperforms ASL with constant time complexity and achieves performance close to OPAC in terms of various metrics.

An optimal resource sharing protocol for generalized multiframe tasks

Many different task models of varying expressiveness have been proposed to capture the timing constraints of real-time workloads. However, techniques for optimal scheduling and exact feasibility analysis of systems with mutually-exclusive shared resources have been available only for relatively simple task models, such as the sporadic task model. We consider sharing of mutually-exclusive resources in task models that are more expressive in terms of the job-release patterns that can be modeled. We propose a new scheduling algorithm and show that it is optimal for scheduling generalized multiframe tasks with shared resources on uniprocessor systems. We also present an efficient feasibility test for such systems, and show that it is both sufficient and necessary.

Analysis on Scheduling Algorithms of Real-Time Hybrid Tasks

In real-time systems, periodic tasks and aperiodic tasks exist simultaneously. In a uniprocessor system, mainly there are Deferrable Server algorithm (DS) [1], Slack Stealing algorithm (SSA) [2] and their extended version for software/hardware hybrid real-time task scheduling. DS algorithm sets a high priority periodic task server to provide services for aperiodic tasks, while SSA algorithm computes tasks unoccupied time offline, and then schedule aperiodic tasks during the unoccupied period. The two algorithms are both proposed for soft real-time tasks, reducing the response time of the real-time tasks, but cannot guarantee that these aperiodic real-time tasks received can meet deadlines. In this paper, through combination of DS algorithm and EDF (Earliest Deadline First) algorithm [6], a new algorithm called DS-EDF is introduced, which can scheduling hard real-time aperiodic tasks on the DS server. This algorithm is not only suitable for uniprocessor systems, but also has the ability to extend to multiprocessor systems.

Optimal Scheduling for Real-Time Jobs in Energy Harvesting Computing Systems

In this paper, we study a scheduling problem, in which every job is associated with a release time, deadline, required computation time, and required energy. We focus on an important special case where the jobs execute on a uniprocessor system that is supplied by a renewable energy source and use a rechargeable storage unit with limited capacity. Earliest deadline first (EDF) is a class one online algorithm in the classical real-time scheduling theory where energy constraints are not considered. We propose a semi-online EDF-based scheduling algorithm theoretically optimal (i.e., processing and energy costs neglected). This algorithm relies on the notions of energy demand and slack energy, which are different from the well known notions of processor demand and slack time. We provide an exact feasibility test. There are no restrictions on this new scheduler: each job can be one instance of a periodic, aperiodic, or sporadic task with deadline.

Preempt a Job or Not in EDF Scheduling of Uniprocessor Systems

The earliest-deadline-first (EDF) policy has been widely studied for the scheduling of real-time jobs for its effectiveness and simplicity. However, since each preemption incurs an additional delay to the execution of jobs, the effectiveness of EDF is affected greatly by the underlying preemption policy that determines if and when a higher-priority job is allowed to preempt a currently executing lower-priority job. To address this problem, we propose a new and better (in meeting job deadlines) preemption policy of EDF, given a non-zero preemption delay. Specifically, we propose a controlled preemption (CP) policy that controls the condition of preempting jobs, whereas existing approaches focus on that of preempted jobs. We define cp-EDF in which the CP policy is applied to EDF, and analyze its schedulability. This schedulability analysis is then utilized to develop an algorithm that assigns the optimal control parameters of cp-EDF. Our in-depth evaluation has demonstrated that cp-EDF with the optimal parameter assignment improves EDF schedulability over existing preemption policies by up to 7.4%.

Implementation and evaluation of mixed-criticality scheduling approaches for sporadic tasks

Traditional fixed-priority scheduling analysis for periodic and sporadic task sets is based on the assumption that all tasks are equally critical to the correct operation of the system. Therefore, every task has to be schedulable under the chosen scheduling policy, and estimates of tasks' worst-case execution times must be conservative in case a task runs longer than is usual. To address the significant underutilization of a system's resources under normal operating conditions that can arise from these assumptions, several mixed-criticality scheduling approaches have been proposed. However, to date, there have been few quantitative comparisons of system schedulability or runtime overhead for the different approaches. In this article, we present a side-by-side implementation and evaluation of the known mixed-criticality scheduling approaches, for periodic and sporadic mixed-criticality tasks on uniprocessor systems, under a mixed-criticality scheduling model that is common to all these approaches. To make a fair evaluation of mixed-criticality scheduling, we also address previously open issues and propose modifications to improve particular approaches. Our empirical evaluations demonstrate that user-space implementations of mechanisms to enforce different mixed-criticality scheduling approaches can be achieved atop Linux without kernel modification, with reasonably low (but in some cases nontrivial) overhead for mixed-criticality real-time task sets.

Ec-A: A Task Allocation Algorithm for Energy Minimization in Multiprocessor Systems

With the necessity of increased processing capacity with less energy consumption; power aware multiprocessor system has gained more attention in the recent future. One of the additional challenges that is to be solved in a multi-processor system when compared to uni-processor system is job allocation. This paper presents a novel task dependent job allocation algorithm: Energy centric- Allocation (Ec-A) and Rate Monotonic (RM) scheduling to minimize energy consumption in a multiprocessor system. A simulation analysis is carried out to verify the performance increase with reduction in energy consumption and required number of processors in the system.

A review of fixed priority and EDF scheduling for hard real-time uniprocessor systems

This paper was written to accompany a talk at the ETR Summer School in Toulouse 2013. It provides a background and primer to scheduling and schedulability analysis for hard real-time single processor systems. The paper focuses on the two main scheduling algorithms used: Fixed Priority and Earliest Deadline First. The paper has two broad aims: Firstly to provide a guide to the fundamental results for these real-time scheduling algorithms. Secondly to provide a brief review of extensions aimed at (i) limiting the effects and overheads of pre-emption and (ii) accounting for the effects of pre-emptions; specifically cache related pre-emption delays. The paper also briefly looks back at success stories in real-time scheduling, and forwards at the current hot topics in this research area.

Applying dynamic priority scheduling scheme to static systems of pinwheel task model in power-aware scheduling.

Power-aware scheduling reduces CPU energy consumption in hard real-time systems through dynamic voltage scaling (DVS). In this paper, we deal with pinwheel task model which is known as static and predictable task model and could be applied to various embedded or ubiquitous systems. In pinwheel task model, each task's priority is static and its execution sequence could be predetermined. There have been many static approaches to power-aware scheduling in pinwheel task model. But, in this paper, we will show that the dynamic priority scheduling results in power-aware scheduling could be applied to pinwheel task model. This method is more effective than adopting the previous static priority scheduling methods in saving energy consumption and, for the system being still static, it is more tractable and applicable to small sized embedded or ubiquitous computing. Also, we introduce a novel power-aware scheduling algorithm which exploits all slacks under preemptive earliest-deadline first scheduling which is optimal in uniprocessor system. The dynamic priority method presented in this paper could be applied directly to static systems of pinwheel task model. The simulation results show that the proposed algorithm with the algorithmic complexity of O(n) reduces the energy consumption by 10–80% over the existing algorithms.

A memory management approach based on page coloring for multi-core systems

Most multi-core platforms currently adopt shared cache among the processor cores. Due to the problem of cache contention,it is extremely difficult to predict the w orst-case execution time of the computation tasks running on different cores. A page-coloring technique w as proposed to avoid cache contention in memory access for multi-core platforms. The advantage is that the w orst case execution time of tasks running on individual core can be estimated separately using the existing WCET analysis methods for uni-processor systems. A memory management system w as designed based on the Linux to support page coloring mechanism,w hich is evaluated using the standard benchmarks. Experimental results show n that the execution time for different processor cores becomes deterministic w hen it is executed on the same platform running in the Linux supported w ith the management system.