Worst-case Response Time Analysis Research Articles

Schedulability Analysis in Fixed-Priority Real-Time Multicore Systems with Contention

In the scheduling of hard real-time systems on multicore platforms, significant unpredictability arises from interference caused by shared hardware resources. The objective of this paper is to offer a schedulability analysis for such systems by assuming a general model that introduces interference as a time parameter for each task. The analysis assumes constrained deadlines and is provided for fixed priorities. It is based on worst-case response time analysis, which exists in the literature for monocore systems. We demonstrate that the worst-case response time is an upper bound, and we evaluate our proposal with synthetic loads and execution on a real platform.

Deadline-Aware Online Scheduling of TSN Flows for Automotive Applications

The Time-Sensitive Networking (TSN) set of standards allows to support on the same channel the different kinds of traffic flows that are typically found in automotive scenarios. This article proposes the introduction of online Earliest Deadline First-based scheduling in TSN to provide support for event-driven real-time traffic. The proposed approach, called Deadline-TSN, is an online approach, and therefore, unlike other approaches in the literature, it does not require complex offline schedule calculations. Moreover, Deadline-TSN is able to uniformly deal with real-time periodic and event-driven traffic flows. This article presents Deadline-TSN and provides both worst-case response time analysis and simulative assessments in realistic automotive scenarios.

Improving Interference Analysis for Real-Time DAG Tasks Under Partitioned Scheduling

Real-time systems with strict timing constraints have been widely applied in many fields. The Directed acyclic graph (DAG) task model has been widely studied and applied to model real-time systems with partial parallelism and precedence constraints in each task. Our paper focuses on the worst-case response time (WCRT) analysis of DAG tasks under partitioned scheduling on multiprocessors. We investigate a parallel structure named <formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex>$Str$</tex> </formula> , which helps obtain more accurate analysis results, and propose a new offline scheduling analysis algorithm named reducing repetitive calculation (RRC). Experiments with synthetic workload are conducted to compare the results calculated by RRC and the state-of-the-art, as well as the observed average response time on a real embedded system. Results show that RRC has better performance in terms of analysis accuracy.

Determining rate monotonic schedulability of real-time periodic tasks using continued fractions

Fixed-priority scheduling algorithms are widely used for real-time systems with a single processor because of their implementation simplicity and relatively low run-time overheads. However, determining whether a task set is schedulable by a fixed-priority scheduling algorithm has been shown to be NP-hard. There are few exact schedulability test methods such as the time demand analysis or the worst-case response time analysis for Rate Monotonic scheduling, while much research has been done to find a tighter sufficient condition for the fixed-priority schedulability. In this paper, a new approach to analyze the schedulability of fixed-priority scheduling using well-known mathematical tool called continued fractions is presented. With continued fractions, a new schedulability test for Rate Monotonic algorithm is derived. The schedulability test condition is an exact condition that can be applied tasks with total utilization less than 1.

Computing exact WCRT for typed DAG tasks on heterogeneous multi-core processors

Heterogeneous multi-core architectures achieve high performance and energy efficiency in real-time domain towards various applications. Most real-time parallel applications on heterogeneous multi-cores can be modeled as a typed directed acyclic graph (DAG) task, where the workload of each vertex is only allowed to execute on a particular type of core. Traditional worst-case response time (WCRT) analysis methods for these applications modeled as DAG are very pessimistic and impractical, i.e., there is a big gap between existing WCRT bounds and the exact WCRT. In this paper, we propose a satisfiability modulo theories-based method to exactly analyze the WCRT of the typed DAG task scheduled upon heterogeneous multi-cores. Experimental results show that our method can significantly improve the precision of the WCRT, and thus, dramatically increase the acceptance rate in the schedulability analysis.

Worst-Case Response Time Analysis of Multitype DAG Tasks Based on Reconstruction

With the wide application of heterogeneous multi-core processor real-time systems, the existing analysis methods of worst-case response time (WCRT) overestimate the blocking information among tasks, resulting in a rather pessimistic estimation. To improve the accuracy of the WCRT, we propose a reconstruction-based WCRT analysis method for multi-type directed acyclic graph (DAG) tasks scheduling algorithm(RMDS). The RMDS algorithm comprises the following steps: First, we unitize all task nodes in the multi-type DAG task; Then, we use key factors as task priorities to schedule tasks and reconstruct the DAG task model into a parallel node segment model; Finally, we estimate the WCRT of multi-type DAG tasks according to the parallel node segment model to assess task schedulability. To verify the performance of our algorithm, we compared it with traditional algorithms. RDMS showed an acceptance rate 6.13% higher and its overall performance increased by 25.95% in comparison with traditional algorithms.

Beyond the limitations of real-time scheduling theory: a unified scheduling theory for the analysis of real-time systems

We investigate the mathematical properties of event bound functions as they are used in the worst-case response time analysis and utilization tests. We figure out the differences and similarities between the two approaches. Based on this analysis, we derive a more general form do describe events and event bounds. This new unified approach gives clear new insights in the investigation of real-time systems, simplifies the models and will support algebraic proofs in future work. In the end, we present a unified analysis which allows the algebraic definition of any scheduler. Introducing such functions to the real-time scheduling theory will lead two a more systematic way to integrate new concepts and applications to the theory. Last but not least, we show how the response time analysis in dynamic scheduling can be improved.

Global emergency-based job-level scheduling for weakly-hard real-time systems

Weakly-hard real-time scheduling enables to tolerate certain execution timeouts of tasks, and has been widely exploited in those intelligent embedded systems over the past two decades. In general, the current weakly-hard real-time scheduling algorithms try to rapidly raise the priorities of jobs (instances) of those tasks that have missed deadlines to guarantee their individual weakly-hard constraints, while neglecting the impacts of whole task system emergency on the schedulability results. From the perspective of increasing the schedulability ratio of weakly-hard real-time task set upon a uniprocessor platform, we develop a Global Emergency-Based Scheduling (GEBS) algorithm. First, with the goal of guaranteeing the weakly-hard timeliness of jobs, the GEBS scheme formulates a set of global job-level policies for priority allocations based on the emergency-classes of jobs. With the emergency degree of whole task system being considered, GEBS intends to fairly tune the priorities of those urgent jobs following our priority adjustment scheme to reduce the possibility of dynamic failures (i.e., deadline misses) of jobs. Moreover, for a task, the minimum arrival-interval of two jobs that have the same emergency-class is thoroughly analyzed, and then its WCRT (Worst-Case Response Time) corresponding to each emergency-class can be obtained recursively. Furthermore, the schedulability test is discussed based on the WCRT analysis, followed by the investigation of a new LCM (Least Common Multiple)-based method under weakly-hard constraints for better feasibility of task set. Finally, the extensive results from simulations and case study demonstrate that the GEBS algorithm can effectively improve the schedulability performance with regard to acceptance ratio (e.g., 50% more) with acceptable running time, when compared to the existing task-level and job-class-level scheduling. The empirical results in Linux kernel further exhibit the applicability of GEBS that can experience comparable online overhead in contrast with other schemes.

Queue assignment for fixed-priority real-time flows in time-sensitive networks: Hardness and algorithm

Abstract Time sensitive networks (TSNs) enable deterministic real-time communication over Ethernet networks. According to IEEE 802.1Qbv standards, TSN switches use gates between queues and their corresponding egress ports to facilitate timing-deterministic communications. Management of switch resources, such as queues, has a significant impact on the schedulability of real-time flows. In this paper, we look into the theoretical foundation of queue management in TSN switches. We prove that the queue assignment problem for real-time flows on time sensitive networks under static priority scheduling is NP-hard in the strong sense, even if the number of queues per port is 3. Then we formulate the problem as a satisfiability modulo theories (SMT) specification. Besides, we propose a worst case response time analysis and a fast heuristic algorithms by eliminating scheduling conflicts. Experiments with randomly generated workload demonstrate the effectiveness of our algorithms for queue assignment of real-time flows.

Carry-Out Interference Optimization in WCRT Analysis for Global Fixed-Priority Multiprocessor Scheduling

With the development of multiprocessor technology, multiple processors are increasingly used in embedded real-time systems. The parallelism of multiple processors makes the worst-case response time (WCRT) analysis of multiprocessor real-time systems complicated. In the widely used global fixed-priority (GFP) scheduling, some effective approximate WCRT analysis methods have been proposed. These methods mainly focus on optimizing overall procedure or carry-in workload and assume that the whole carry-out workload of a high-priority task cause interference on the analyzed job. However, through our careful observation of specific examples, the partial carry-out workload of a high-priority task and the analyzed job may be executed in parallel. In other words, the part of parallel carry-out workload of a high-priority task could not cause interference on the analyzed job. In this article, we propose an improved WCRT analysis method by optimizing carry-out interference estimation for GFP scheduling, resulting in a more accurate upper bound of WCRT than the recent advanced methods. Experimental results show that our proposed method is superior than the recent advanced methods in terms of the acceptance rate of the system.

Parallel Scheduling of Multiple SDF Graphs Onto Heterogeneous Processors

Parallel scheduling of multiple real-time applications onto heterogeneous processors is needed in the emerging embedded systems such as self-driving cars, smart cameras, and smartphones. Assuming that an embedded application is specified as a synchronous dataflow (SDF) graph or its extension, we propose a novel parallel scheduling methodology based on an evolutionary algorithm where the mapping of tasks onto processors is evolved to optimize a given objective function in an iterative fashion. In each iteration, we use an existing worst-case response time (WCRT) analysis tool to check if all applications satisfy their real-time requirements by translating each SDF graph into a directed acyclic graph (DAG) that is assumed in the WCRT analysis tool. Since the WCRT analysis must be performed in each iteration of evolution, we propose a clustering technique to reduce drastically the analysis time that depends on the number of nodes and their dependency. We formally prove that the proposed clustering technique does not change the estimated WCRT of each application. The effectiveness of the proposed scheduling methodology with the clustering technique is verified with extensive experiments using real-life benchmarks, randomly generated graphs, and the comparison with the existing technique.

Response time analysis of multiframe mixed-criticality systems with arbitrary deadlines

The well-known model of Vestal aims to avoid excessive pessimism in the quantification of the processing requirements of mixed-criticality systems, while still guaranteeing the timeliness of higher-criticality functions. This can bring important savings in system costs, and indirectly help meet size, weight and power constraints. This efficiency is promoted via the use of multiple worst-case execution time (WCET) estimates for the same task, with each such estimate characterized by a confidence associated with a different criticality level. However, even this approach can be very pessimistic when the WCET of successive instances of the same task can vary greatly according to a known pattern, as in MP3 and MPEG codecs or the processing of ADVB video streams. In this paper, we present a schedulability analysis for the new multiframe mixed-criticality model, which allows tasks to have multiple, periodically repeating, WCETs in the same mode of operation. Our work extends both the analysis techniques for Static Mixed-Criticality scheduling (SMC) and Adaptive Mixed-Criticality scheduling (AMC), on one hand, and the schedulability analysis for multiframe task systems on the other. A constrained-deadline model is initially targeted, and then extended to the more general, but also more complex, arbitrary-deadline scenario. The corresponding optimal priority assignment for our schedulability analysis is also identified. Our proposed worst-case response time (WCRT) analysis for multiframe mixed-criticality systems is considerably less pessimistic than applying the static and adaptive mixed-criticality scheduling tests oblivious to the WCET variation patterns. Experimental evaluation with synthetic task sets demonstrates up to 20% and 31.4% higher scheduling success ratio (in absolute terms) for constrained-deadline analyses and arbitrary-deadline analyses, respectively, when compared to the best of their corresponding frame-oblivious tests.

Algorithms for Computing the WCRT Bound of OpenMP Task Systems With Conditional Branches

Multi-cores are becoming mainstream hardware platforms for embedded and real-time systems. To fully utilize the processing capacity of multi-cores, software should be parallelized. Recently, much work has been done on real-time scheduling of parallel tasks modeled as directed acyclic graphs (DAG), motivated by the parallel task structures supported by popular parallel programming frameworks such as OpenMP. The DAG-based task models in existing real-time scheduling research assume well-nested graph structures recursively composed by single-source-single-sink parallel and conditional components. However, realistic OpenMP task systems in general have more flexible structures that do not comply with those assumptions. In this article, we model the behavior of general OpenMP task systems with non-well-nested structures. The worst-case response time analysis problem for such systems is more difficult due to the flexible graph structure. As the major technical contribution, we develop two efficient algorithms to compute the worst-case response time bounds, with different trade-offs between efficiency and precision. Evaluation with both randomly generated task graphs and realistic OpenMP programs shows good performance of our approaches in terms of both precision and efficiency.

Speeding Up the Schedulability Analysis and Priority Assignment of Sporadic Tasks Under Uniprocessor FPNS

Fixed-priority non-preemptive scheduling (FPNS) is widely used in practice because of its simplicity and predictability. This article aims to enhance the efficiency of the schedulability analysis and priority assignment of sporadic tasks under uniprocessor FPNS. To speed-up the schedulability analysis, we first improve the state-of-the-art worst-case response time analysis for uniprocessor fixed-priority non-preemptive scheduling. In addition, we present two special conditions under which the worst-case response time of a task can be analyzed from its first job, which further improves the efficiency of the analysis. To accelerate the priority assignment, we present two priority-assignment algorithms based on the improved Audsley's algorithm: improved Audsley-based longest deadline first (IA-LDF) and improved Audsley-based longest worst-case execution time first (IA-LCF). The numerical experiments show that IA-LDF and IA-LCF can lead to 31.2% and 36% decrease in runtime compared to longest deadline first (LDF) and longest worst-case execution time first (LCF), respectively.

Response Time Bounds for Typed DAG Parallel Tasks on Heterogeneous Multi-Cores

Heterogeneous multi-cores utilize the strength of different architectures for executing particular types of workload, and usually offer higher performance and energy efficiency. In this paper, we study the worst-case response time (WCRT) analysis of \emph{typed} scheduling of parallel DAG tasks on heterogeneous multi-cores, where the workload of each vertex in the DAG is only allowed to execute on a particular type of cores. The only known WCRT bound for this problem is grossly pessimistic and suffers the \emph{non-self-sustainability} problem. In this paper, we propose two new WCRT bounds. The first new bound has the same time complexity as the existing bound, but is more precise and solves its \emph{non-self-sustainability} problem. The second new bound explores more detailed task graph structure information to greatly improve the precision, but is computationally more expensive. We prove that the problem of computing the second bound is strongly NP-hard if the number of types in the system is a variable, and develop an efficient algorithm which has polynomial time complexity if the number of types is a constant. Experiments with randomly generated workload show that our proposed new methods are significantly more precise than the existing bound while having good scalability.

WCRT Analysis and Evaluation for Sporadic Message-Processing Tasks in Multicore Automotive Gateways

We study the worst case response time (WCRT) analysis and evaluation for sporadic message-processing tasks in a multicore automotive gateway of a controller area network (CAN) cluster. We first build a multicore automotive gateway on CAN clusters. Two WCRT analysis methods for message-processing tasks in the multicore gateway are subsequently presented based on global and partitioned scheduling paradigms. We evaluate the WCRT results of two analysis methods with real message sets provided by the automaker, and present the design optimization guide.

Optimization of Fault-Tolerant Mixed-Criticality Multi-Core Systems with Enhanced WCRT Analysis

This article proposes a novel optimization technique of fault-tolerant mixed-criticality multi-core systems with worst-case response time (WCRT) guarantees. Typically, in fault-tolerant multi-core systems, tasks can be replicated or re-executed in order to enhance the reliability. In addition, based on the policy of mixed-criticality scheduling, low-criticality tasks can be dropped at runtime. Such uncertainties caused by hardening and mixed-criticality scheduling make WCRT analysis very difficult. We show that previous analysis techniques are pessimistic as they consider avoidably extreme cases that can be safely ignored within the given reliability constraint. We improve the analysis in order to tighten the pessimism of WCRT estimates by considering the maximum number of faults to be tolerated. Further, we improve the mixed-criticality scheduling by allowing partial dropping of low-criticality tasks. On top of those, we explore the design space of hardening, task-to-core mapping, and quality-of-service of the multi-core mixed-criticality systems. The effectiveness of the proposed technique is verified by extensive experiments with synthetic and real-life benchmarks.

Exact WCRT Analysis for Message-Processing Tasks on Gateway-Integrated In-Vehicle CAN Clusters

A typical automotive integrated architecture is a controller area network (CAN) cluster integrated by a central gateway. This study proposes a novel and exact worst-case response time (WCRT) analysis method for message-processing tasks in the gateway. We first propose a round search method to obtain lower bound on response time (LBRT) and upper bound on response time (UBRT), respectively. We then obtain the exact WCRT belonging to the scope of the LBRT and UBRT with an effective non-exhaustive exploration. Experimental results on a real CAN message set reveal that the proposed exact analysis method can reduce 99.99999% combinations on large-scale CAN clusters.

Errata for Three Papers (2004-05) on Fixed-Priority Scheduling with Self-Suspensions

The purpose of this article is to (i) highlight the flaws in three previously published works [Audsley, 2004a; Audsley, 2004b; Bletsas, 2005] on the worst-case response time analysis for tasks with self-suspensions and (ii) provide straightforward fixes for those flaws, hence rendering the analysis safe.

A hybrid performance analysis technique for distributed real-time embedded systems

It remains a challenging problem to tightly estimate the worst-case response time of an application in a distributed embedded system, especially when there are dependencies between tasks. Recently, a holistic worst-case response time analysis approach called scheduling time bound analysis has been proposed to find a tight upper bound of the worst-case response times of applications specified by a set of task graphs. Since it assumes that the starting offsets of applications are known and fixed, it fails to make a tight estimation despite increased computation time when the starting offsets are dynamic. To overcome this problem, we propose a novel conservative performance analysis, called hybrid performance analysis, combining the response time analysis technique and the scheduling time bound analysis technique to compute a tighter bound faster. The proposed scheme is proven to be conservative formally. Through extensive experiments with real-life benchmarks and synthetic examples, the superior performance of our proposed approach compared with previous methods is confirmed.