多处理器固定优先级算法的可调度性分析

针对多处理器实时调度中的固定优先级(FP)调度算法,提出了一种改进的可调度性判定方法。引入Baruah的最早截止期优先(EDF)窗口分析框架,将高优先级任务带入作业的最大数量限定为m-1(m为处理器个数),进而对任务的干涉上界进行重新界定,并由此得到一个更加紧密的可调度性判定充分条件。仿真实验结果表明,该方法增加了通过判定任务集的数量,体现出更优的可调度判定性能。     

An exact schedulability test for fixed-priority preemptive mixed-criticality real-time systems

The current literature of fixed-priority scheduling algorithms relies on sufficient tests to determine if a set of mixed-criticality sporadic tasks is schedulable on a single processor. The drawback of these safe tests is their pessimism, a matter that could be solved if an exact schedulability analysis is used. However, because of the non-deterministic behavior of tasks in the mentioned setups, exact quantification of worst-case response times, needed for the test, is a difficult problem; more precisely, such a quantification needs evaluation of enormous sequences of job executions. The core problem is thus to merge such sequences to make the analysis practical. This paper, for the first time, gives an algorithm for exact worst-case response time characterization of mixed-criticality sporadic real-time tasks executing according to a given fixed-priority scheduler. We use a set of techniques which carefully consider the task properties and their relation to the worst scenarios to prune the analysis state space. We also show an interesting result that if an exact schedulability test is used, the Audsley’s optimal priority assignment algorithm is not applicable to the mixed-criticality case. Accordingly, we need new priority assignment algorithms to work with the exact test; we give a simple task priority assignment algorithm to this aim. The performance of the proposed exact test (in terms of time complexity) is examined and the effectiveness of some heuristic priority assignment algorithms using the test (in terms of the ratio of task sets which are deemed schedulable) are compared.     

Commentary to: An exact schedulability test for fixed-priority preemptive mixed-criticality real-time systems

Real-Time Systems - In this paper we point to some errors in recent paper by Asyaban et al. in which they devise an exact schedulability test. These errors are critical for the correct operation of...     

Sensitivity analysis for fixed-priority real-time systems

At early stages in the design of real-time embedded applications, the timing attributes of the computational activities are often incompletely specified or subject to changes. Later in the development cycle, schedulability analysis can be used to check the feasibility of the task set. However, the knowledge of the worst-case response times of tasks is often not sufficient to precisely determine the actions that would correct a non-schedulable design. In these situations, sensitivity analysis provides useful information for changing the implementation, by giving a measure of those computation times that must be reduced to achieve feasibility, or those that can be increased in case of a product extension, or providing the range of feasible periods for selecting the proper task activation rates. In this work, we exploit the concept of feasibility region to propose a faster and more concise solution to the sensitivity analysis problem with respect to existing techniques based on binary search. Furthermore, we show how the formalization of other problems in the feasibility domain, such as managing overloads through elastic scheduling, can be extended to the exact analysis.     

Schedulability analysis of fixed-priority systems using timed automata

In classic scheduling theory, real-time tasks are usually assumed to be periodic, i.e. tasks are released and computed with fixed rates periodically. To relax the stringent constraints on task arrival times, we propose to use timed automata to describe task arrival patterns. In a previous work, it is shown that the general schedulability checking problem for such models is a reachability problem for a decidable class of timed automata extended with subtraction. Unfortunately, the number of clocks needed in the analysis is proportional to the maximal number of schedulable task instances associated with a model, which is in many cases huge. In this paper, we show that for fixed-priority scheduling strategy, the schedulability checking problem can be solved using standard timed automata with two   extra clocks in addition to the clocks used in the original model to describe task arrival times. The analysis can be done in a similar manner to response time analysis in classic Rate-Monotonic Analysis (RMA). The result is further extended to systems with data-dependent control, in which the release time of a task may depend on the time-point at which other tasks finish their execution. For the case when the execution times of tasks are constants, we show that the schedulability problem can be solved using n+1$n+1$ extra clocks, where n$n$ is the number of tasks. The presented analysis techniques have been implemented in the Times tool. For systems with only periodic tasks, the performance of the tool is comparable with tools implementing the classic RMA technique based on equation-solving, without suffering from the exponential explosion in the number of tasks.     

Improved multiprocessor global schedulability analysis

A new technique was recently introduced by Bonifaci et al. for the analysis of real-time systems scheduled on multiprocessor platforms by the global Earliest Deadline First (EDF) scheduling algorithm. In this paper, this technique is generalized so that it is applicable to the schedulability analysis of real-time systems scheduled on multiprocessor platforms by any work-conserving algorithm. The resulting analysis technique is applied to obtain a new sufficient global Deadline Monotonic (DM) schedulability test. It is shown that this new test is quantitatively superior to pre-existing DM schedulability analysis tests; in addition, the degree of its deviation from any hypothetical optimal scheduler (that may be clairvoyant) is quantitatively bounded. A new global EDF schedulability test is also proposed here that builds on the results of Bonifaci et al. This new test is shown to be less pessimistic and more widely applicable than the earlier result was, while retaining the strong theoretical properties of the earlier result.     

An analysis of EDF schedulability on a multiprocessor

A new schedulability test is derived for preemptive deadline scheduling of periodic or sporadic real-time tasks on a single-queue m-server system. The new test allows the task deadline to be more or less than the task period, and is based on a new analysis concept, called a /spl mu/-busy interval. This generalizes a result of Goossens et al. [2003] that a system of periodic tasks with maximum individual task utilization u/sub max/ is EDF-schedulable on m processors if the total utilization does not exceed m(1 /sup max/)+u/sub max/. The new test allows the analysis of hybrid EDF-US [x] scheduling, and the conclusion that EDF-US[1/2] is optimal, with a guaranteed worst-case schedulable utilization of (m +1)/2.     

Timing analysis for fixed-priority scheduling of hard real-timesystems

This paper presents a timing analysis for a quite general hard real-time periodic task set on a uniprocessor using fixed-priority methods. Periodic tasks are composed of serially executed subtasks, where each subtask is characterized by an execution time, a fixed priority and a deadline. A method for determining the schedulability of each task and subtask is presented along with its theoretical underpinnings. This method can be used to analyze the schedulability of any task set on a uniprocessor whose priority structure can be modeled as serially executed subtasks, which can lead to a very complex priority structure. Important examples include task sets that involve interrupts, certain synchronization protocols, certain precedence constraints, nonpreemptible sections, and some message-passing systems. The method is illustrated by a robotics example     

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.     

Unified overhead-aware schedulability analysis for slot-based task-splitting

Hard real- time multiprocessor scheduling has seen, in recent years, the flourishing of semi-partitioned scheduling algorithms. This category of scheduling schemes combines elements of partitioned and global scheduling for the purposes of achieving efficient utilization of the system’s processing resources with strong schedulability guarantees and with low dispatching overheads. The sub-class of slot-based “task-splitting” scheduling algorithms, in particular, offers very good trade-offs between schedulability guarantees (in the form of high utilization bounds) and the number of preemptions/migrations involved. However, so far there did not exist unified scheduling theory for such algorithms; each one was formulated in its own accompanying analysis. This article changes this fragmented landscape by formulating a more unified schedulability theory covering the two state-of-the-art slot-based semi-partitioned algorithms, S-EKG and NPS-F (both fixed job-priority based). This new theory is based on exact schedulability tests, thus also overcoming many sources of pessimism in existing analysis. In turn, since schedulability testing guides the task assignment under the schemes in consideration, we also formulate an improved task assignment procedure. As the other main contribution of this article, and as a response to the fact that many unrealistic assumptions, present in the original theory, tend to undermine the theoretical potential of such scheduling schemes, we identified and modelled into the new analysis all overheads incurred by the algorithms in consideration. The outcome is a new overhead-aware schedulability analysis that permits increased efficiency and reliability. The merits of this new theory are evaluated by an extensive set of experiments.     

A comparison of schedulability analysis methods using state and digraph models for the schedulability analysis of synchronous FSMs

Real-Time Systems - Synchronous reactive models are widely used in the development of embedded software and systems. The schedulability analysis of tasks obtained as the code implementation of...     

Performance analysis of hierarchical cache-consistent multiprocessors

This paper investigates the potential performance of hierachical, cache-consistent multiprocessors. We have developed a mean-value queueing model that considers bus latency, shared memory latency and bus interference as the primary sources of performance degradation in the system. A key feature of the model is its choice of high-level input parameters that can be related to application program characteristics. Another important property of the model is that it is computationally efficient. Very large systems can be analyzed in a matter of seconds.

Results of the model show that system topology has an important effect on overall performance. We find optimal two-level, three-level and four-level topologies that distribute the bus traffic uniformly across all levels in the hierarchy. We provide processing power estimates for the optimal topologies, under a particular set of workload assumptions. For example, the optimal three-level topology supports 512 processors each with a peak processing rate of 4 MIPS, and provides an effective 1400 (1700) MIPS in processing power, if the buses operate at 20 (40) MHz. This result assumes 22% of the data references are to globally shared data and that the shared data is read on the average by a significant fraction of processors between write operations. Results of our study also indicate that for reasonably low cache miss rates (3% at level 0), and 20 MHz buses, the bus subnetwork saturates with processor speeds of 6–8 MIPS, at least for topologies of five or fewer levels. Finally, we present parametric results that indicate how performance is affected by one of the parameters that characterizes data sharing in the workload.     

FPSL, FPCL and FPZL schedulability analysis

This paper presents the Fixed Priority until Static Laxity (FPSL), Fixed Priority until Critical Laxity (FPCL) and Fixed Priority until Zero Laxity (FPZL) scheduling algorithms for multiprocessor real-time systems. FPZL is similar to global fixed priority pre-emptive scheduling; however, whenever a task reaches a state of zero laxity it is given the highest priority. FPSL and FPCL are variants of FPZL that introduce no additional scheduling points beyond those present with fixed priority scheduling. FPSL, FPCL and FPZL are minimally dynamic algorithms, in that the priority of a job can change at most once during its execution, bounding the number of pre-emptions. Polynomial time and pseudo-polynomial time sufficient schedulability tests are derived for these algorithms. The tests are then improved by computing upper bounds on the amount of execution that each task can perform at the highest priority. An empirical evaluation shows that FPSL, FPCL, and FPZL are highly effective, with a significantly larger number of tasksets deemed schedulable by the tests derived in this paper, than by state-of-the-art schedulability tests for EDZL scheduling.     

Demand-based schedulability analysis for real-time multi-core scheduling

In real-time systems, schedulability analysis has been widely studied to provide offline guarantees on temporal correctness, producing many analysis methods. The demand-based schedulability analysis method has a great potential for high schedulability performance and broad applicability. However, such a potential is not yet fully realized for real-time multi-core scheduling mainly due to (i) the difficulty of calculating the resource demand under dynamic priority scheduling algorithms that are favorable to multi-cores, and (ii) the lack of understanding how to combine the analysis framework with deadline-miss conditions specialized for those scheduling algorithms. Addressing those two issues, to the best of our knowledge, this paper presents the first demand-based schedulability analysis for dynamic job-priority scheduling algorithms: EDZL (Earliest Deadline first until Zero-Laxity) and LLF (Least Laxity First), which are known to be effective for real-time multi-core scheduling. To this end, we first derive demand bound functions that compute the maximum possible amount of resource demand of jobs of each task while the priority of each job can change dynamically under EDZL and LLF. Then, we develop demand-based schedulability analyses for EDZL and LLF, by incorporating those new demand bound functions into the existing demand-based analysis framework. Finally, we combine the framework with additional deadline-miss conditions specialized for those two laxity-based dynamic job-priority scheduling algorithms, yielding tighter schedulability analyses. Via simulations, we demonstrate that the proposed schedulability analyses outperform the existing schedulability analyses for EDZL and LLF.     

Response-time analysis for fixed-priority systems with a write-back cache

This paper introduces analyses of write-back caches integrated into response-time analysis for fixed-priority preemptive and non-preemptive scheduling. For each scheduling paradigm, we derive four different approaches to computing the additional costs incurred due to write backs. We show the dominance relationships between these different approaches and note how they can be combined to form a single state-of-the-art approach in each case. The evaluation explores the relative performance of the different methods using a set of benchmarks, as well as making comparisons with no cache and a write-through cache. We also explore the effect of write buffers used to hide the latency of write-through caches. We show that depending upon the depth of the buffer used and the policies employed, such buffers can result in domino effects. Our evaluation shows that even ignoring domino effects, a substantial write buffer is needed to match the guaranteed performance of write-back caches.     

Dual BEM for crack growth analysis on distributed-memory multiprocessors

The Dual Boundary Element Method (DBEM) has been presented as an effective numerical technique for the analysis of linear elastic crack problems [Portela A, Aliabadi MH. The dual boundary element method: effective implementation for crack problems. Int J Num Meth Engng 1992;33:1269–1287]. Analysis of large structural integrity problems may need the use of large computational resources, both in terms of CPU time and memory requirements. This paper reports a message-passing implementation of the DBEM formulation dealing with the analysis of crack growth in structures. We have analyzed the construction of the system and its resolution. Different data distribution techniques have been studied with several problems. Results in terms of scalability and load balance for these two stages are presented in this paper.     

Design optimization for real-time systems with sustainable schedulability analysis

Real-Time Systems - The design of modern real-time systems not only needs to guarantee their timing correctness, but also involves other critical metrics such as control quality and energy...     

Using UML-based rate monotonic analysis to predict schedulability

Timeliness is essential in real-time systems, in which a late response is sometimes worse than no response at all because the violation of a single deadline could lead to loss of life or property. System analysts use an appropriate scheduling algorithm to ensure the predictability of such a system. The Object Management Group's adoption of the UML profile for schedulability, performance, and timeliness has increased interest in using UML and object-oriented technology to model and implement real-time systems. Rate monotonic analysis (RMA) is an extensively researched and successfully implemented technique that can be used in conjunction with the UML profile to analyze schedulability in these systems.     

Allocating fixed-priority periodic tasks on multiprocessor systems

In this paper, we study the problem of allocating a set of periodic tasks on a multiprocessor system such that tasks are scheduled to meet their deadlines on individual processors by the Rate-Monotonic scheduling algorithm. A new schedulability condition is developed for the Rate-Monotonic scheduling that allows us to develop more efficient on-line allocation algorithms. Two on-line allocation algorithms—RM-FF and RM-BF are presented, and shown that their worst-case performance, over the optimal allocation, is upper bounded by 2.33 and lower bounded by 2.28. Then RM-FF and RM-BF are further improved to form two new algorithms: Refined-RM-FF (RRM-FF) and Refined-RM-BF (RRM-BF), both of which have a worst-case performance bound of 2. We also show that when the maximum allowable utilization of a task is small, the worst-case performance of all the new algorithms can be significantly improved. The worst-case performance bounds of RRM-FF and RRM-BF are currently the best bounds in the class of on-line scheduling algorithms proposed to solve the same scheduling problem. Simulation studies show that the average-case performance of the newly proposed algorithms is significantly superior to those in the existing literature.     

A subsystem-oriented performance analysis methodology forshared-bus multiprocessors

A methodology, called Subsystem Access Time (SAT) modeling, is proposed for the performance modeling and analysis of shared-bus multiprocessors. The methodology is subsystem-oriented because it is based on a Subsystem Access Time Per Instruction (SATPI) concept, in which we treat major components other than processors (e.g., off-chip cache, bus, memory, I/O) as subsystems and model for each of them the mean access time per instruction from each processor. The SAT modeling methodology is derived from the Customized Mean Value Analysis (CMVA) technique, which is request-oriented in the sense that it models the weighted total mean delay for each type of request processed in the subsystems. The subsystem-oriented view of the proposed methodology facilitates divide-and-conquer modeling and bottleneck analysis, which is rarely addressed previously. These distinguishing features lead to a simple, general, and systematic approach to the analytical modeling and analysis of complex multiprocessor systems. To illustrate the key ideas and features that are different from CMVA, an example performance model of a particular shared-bus multiprocessor architecture is presented. The model is used to conduct performance evaluation for throughput prediction. Thereby, the SATPIs of the subsystems are directly utilized to identify the bottleneck subsystem and find the requests or subsystem components that cause the bottleneck. Furthermore, the SATPIs of the subsystems are employed to explore the impact of several performance influencing factors, including memory latency, number of processors, data bus width, as well as DMA transfer