Multiprocessor scheduling with testing: improved online algorithms and numerical experiments

Spiking Neural Networks (SNNs) have gained popularity due to their high energy efficiency. Prior works have proposed various methods for training SNNs, including backpropagation-based methods. Training SNNs is computationally expensive compared to their conventional counterparts and would benefit from multiprocessor hardware acceleration. This is the first paper to propose inter-layer pipelining to accelerate training in SNNs using systolic array-based processors and multiprocessor scheduling. The impact of training using delayed gradients is observed using four networks training on different datasets, showing no degradation for small networks and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$&lt;10$</tex-math></inline-formula>% degradation for large networks. The mapping of various training tasks of the SNN onto systolic arrays is formulated, and the proposed scheduling method is evaluated on the four networks. The results are compared against standard pipelining algorithms. The results show that the proposed method achieves an average speedup of 1.7<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\times$</tex-math></inline-formula> compared to standard pipelining algorithms, with an upwards of 2<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\times$</tex-math></inline-formula> improvement in some cases. The incurred communication overhead due to the proposed method is less than <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$0.5$</tex-math></inline-formula>% of the total required communication of training in networks with convolutional layers.

The adoption of multiprocessor platforms is growing commonplace in Internet of Things (IoT) applications to handle large volumes of sensor data while maintaining real-time performance at a reasonable cost and with low power consumption. Partitioned scheduling is a competitive approach to ensure the temporal constraints of real-time sensor data processing tasks on multiprocessor platforms. However, the problem of partitioning real-time sensor data processing tasks to individual processors is strongly NP-hard, making it crucial to develop efficient partitioning heuristics to achieve high real-time performance. This paper presents an enhanced harmonic partitioned multiprocessor scheduling method for periodic real-time sensor data processing tasks to improve system utilization over the state of the art. Specifically, we introduce a general harmonic index to effectively quantify the harmonicity of a periodic real-time task set. This index is derived by analyzing the variance between the worst-case slack time and the best-case slack time for the lowest-priority task in the task set. Leveraging this harmonic index, we propose two efficient partitioned scheduling methods to optimize the system utilization via strategically allocating the workload among processors by leveraging the task harmonic relationship. Experiments with randomly synthesized task sets demonstrate that our methods significantly surpass existing approaches in terms of schedulability.

Efficient multiprocessor scheduling is pivotal in optimizing the performance of parallel computing systems. This paper leverages the power of Petri nets and the tool GPenSIM to model and simulate a variety of multiprocessor scheduling algorithms (the basic algorithms such as first come first serve, shortest job first, and round robin, and more sophisticated schedulers like multi-level feedback queue and Linux’s completely fair scheduler). This paper presents the evaluation of three crucial performance metrics in multiprocessor scheduling (such as turnaround time, response time, and throughput) under various scheduling algorithms. However, the primary focus of the paper is to develop a robust simulation platform consisting of Petri Modules to facilitate the dynamic representation of concurrent processes, enabling us to explore the real-time interactions and dependencies in a multiprocessor environment; more advanced and newer schedulers can be tested with the simulation platform presented in this paper.

Abstract To improve the performance of real‐time systems, heterogeneous asymmetric multiprocessors are proposed. Heterogeneous asymmetric multiprocessor architecture allows the system to better match computational resources to meet the needs and dynamic workload of each application. The benefits of system performance and reduced power consumption cannot be fully exploited unless proper task scheduling and task allocation methods are implemented at the operating system level.The EDZL scheduling algorithm has been shown to be a better scheduling algorithm in heterogeneous multiprocessor platforms. In this paper, the BSF‐EDZL (best speed fit for earliest deadline first until zero‐laxity) performance asymmetric multiprocessor scheduling algorithm is proposed, and an effective schedulability analysis is performed. The algorithm selects an appropriate processor for non‐zero relaxation highest priority task rather than the fastest processor when assigning tasks. Experimental results show that the proposed BSF‐EDZL scheduling algorithm can schedule a larger set of tasks than the ordinary EDZL scheduling algorithm.

Approximation Algorithms for Multiprocessor Scheduling with Testing to Minimize the Total Job Completion Time

A 5G system is an advanced solution for industrial wireless motion control. However, because the scheduling model of 5G new radio (NR) is more complicated than those of other wireless networks, existing real-time scheduling algorithms cannot be used to improve the 5G performance. This results in NR resources not being fully available for industrial systems. Supervised learning has been widely used to solve complicated problems, and its advantages have been demonstrated in multiprocessor scheduling. One of the main reasons why supervised learning has not been used for 5G NR scheduling is the lack of training datasets. Therefore, in this paper, we propose two methods based on optimization modulo theories (OMT) and satisfiability modulo theories (SMT) to generate training datasets for 5G NR scheduling. Our OMT-based method contains fewer variables than existing work so that the Z3 solver can find optimal solutions quickly. To further reduce the solution time, we transform the OMT-based method into an SMT-based method and tighten the search space of SMT based on three theorems and an algorithm. Finally, we evaluate the solution time of our proposed methods and use the generated dataset to train a supervised learning model to solve the 5G NR scheduling problem. The evaluation results indicate that our SMT-based method reduces the solution time by 74.7% compared to existing ones, and the supervised learning algorithm achieves better scheduling performance than other polynomial-time algorithms.

The Contention-Free (CF) policy has been extensively researched in the realm of real-time multi-processor scheduling due to its wide applicability and the performance enhancement benefits it provides to existing scheduling algorithms. The CF policy improves the feasibility of executing other real-time tasks by assigning the lowest priority to a task at a moment when it is guaranteed not to miss its deadline during the remaining execution time. Despite its effectiveness, existing studies on the CF policy are largely confined to preemptive scheduling, leaving the efficiency and applicability of limited preemption scheduling unexplored. Limited preemption scheduling permits a job to execute to completion with a limited number of preemptions, setting it apart from preemptive scheduling. This type of scheduling is crucial when preemption or migration overheads are either excessively large or unpredictable. In this paper, we introduce SP-CF, a single preemption scheduling approach that incorporates the CF policy. SP-CF allows a preemption only once during each job’s execution, following a priority demotion under the CF policy. We also propose a new schedulability analysis method for SP-CF to determine whether each task is executed in a timely manner and without missing its deadline. Through simulation experiments, we demonstrate that SP-CF can significantly enhance the schedulability of the traditional rate-monotonic algorithm and the earliest deadline first algorithm.

Self-adaptive CMSA for solving the multidimensional multi-way number partitioning problem

With the rapid development of high-performance computing and parallel computing technology, by virtue of its cost-effectiveness, strong scalability, and easy programming, the multiprocessor system has gradually become the mainstream computing platform. Meanwhile, a growing number of researchers pay attention to the performance of multiprocessor systems, especially the task scheduling problem, which has an important impact on the system performance. Most of the current research works on task scheduling algorithms are based on the homogeneous computing environment. On the contrary, research works focusing on more complex performance asymmetric multiprocessor environments still remain rare. In this paper, we compare the effects of three earliest deadline first algorithms under different processor allocation strategies on performance asymmetric multiprocessors. We propose an efficient schedulability analysis for an allocation strategy that assigns high-priority tasks to the slowest idle processor. Experimental results show that the strategy of allocating processors with optimum speeds for high-priority tasks can schedule more task sets than the other two allocation strategies. The strategy that prioritizes the slowest processors for high-priority tasks has the smallest number of task migrations, and the strategy has the highest effective processor utilization.

We study the computational complexity of the non-preemptive scheduling problem of a listof independent jobs on a set of identical parallel processors with a makespan minimizationobjective. We make a maiden attempt to explore the combinatorial structure showing theexhaustive solution space of the problem by defining the Scheduling Solution Space Tree(SSST) data structure. The properties of the SSST are formally defined and characterizedthrough our analytical results. We develop a unique technique to show the problemNP using the SSST and the Weighted Scheduling Solution Space Tree (WSSST) datastructures. We design the first non-deterministic polynomial-time algorithm named MagicScheduling (MS) for the problem based on the reduction framework. We also define anew variant of multiprocessor scheduling by including the user as an additional inputparameter. We formally establish the complexity class of the variant by the reductionprinciple. Finally, we conclude the article by exploring several interesting open problemsfor future research investigation.

In recent decades, genetic algorithms (GAs) have often been applied as heuristic techniques at various settings entailing production scheduling. However, early convergence is one of the problems associated with this approach. This study develops an efficient local search rule for the target-oriented rule in traditional GAs. It also addresses the problem of two-stage multiprocessor flowshop scheduling (FSP) by viewing the due window and sequence-dependent setup times as constraints faced by common flowshops with multiprocessor scheduling suites in the actual production scenario. Using the simulated data, this study verifies the effectiveness and robustness of the proposed algorithm. The results of data testing demonstrate that the proposed method may outperform other algorithms, including a significant hybrid algorithm, in addressing the problems considered.

This article has been retracted. A retraction notice can be found at https://doi.org/10.3233/JIFS-219433.

At present, most of the scheduling models for real-time periodic tasks are established based on independent fixed periodic tasks and few by considering the task model with period allowed to change and the processor model in the scheduling process. In this paper, a task model and processor model based on line tree(LT) for sporadic real-time periodic tasks are designed, and a transformation algorithm from task line tree(TLT) model to processor line tree(PLT) model is proposed. The algorithm takes the least common multiple of all real-time periodic tasks as the benchmark of layer number, and based on the complete job replacement rule, the minimum common multiple of all real-time periodic tasks is used as the reference of layer number. In order to achieve the optimal multiprocessor scheduling result, the method of replacing the empty node of non-migrating job with the node of migrating job and the condition of allowing job to publish tasks ahead of time with variable cycle are used. Experimental results show that comparing with PEDF, GEDF and RMFF, the present method not only has higher core utilization and lower time loss rate, but also reduces the number of context switching and migration.

Improved approximation algorithms for non-preemptive multiprocessor scheduling with testing

Task pipelines are common in today's embedded systems, as data moves from source to sink in sensing-processing-actuation task chains. A real-time task pipeline is constructed by connecting a series of periodic tasks with data buffers. In a time-critical system, end-to-end timing and data-transfer properties of a task pipeline must be guaranteed. A guarantee could be mathematically expressed by assigning constraints to the tasks of a pipeline. However, deriving task scheduling parameters to meet end-to-end guarantees is an NP-hard constraint optimization problem. Hence, a traditional constraint solver is not a suitable runtime solution.In this paper, we present a heuristic constraint solver algorithm, CoPi, to derive the execution times and periods of pipelined tasks that meet the end-to-end constraints and schedulability requirements. We consider two upper bound constraints on a task pipeline: end-to-end delay and loss-rate. After satisfying these constraints, CoPi schedules a pipeline as a set of asynchronous and data independent periodic tasks, under the rate-monotonic scheduling algorithm. Simulations show that CoPi has a comparable pipeline acceptance ratio and significantly better runtime than open-source MINLPsolvers. Furthermore, we use CoPi to map multiple task pipelines to a multiprocessor system. We demonstrate that a partitioned multiprocessor scheduling algorithm coupled with CoPi accommodates dynamically appearing pipelines, while attempting to minimize task migrations.

A Mixed-Criticality System (MCS) features the integration of multiple subsystems that are subject to different levels of safety certification on a shared hardware platform. In cost-sensitive application domains such as automotive E/E systems, it is important to reduce application memory footprint, since such a reduction may enable the adoption of a cheaper microprocessor in the family. Preemption Threshold Scheduling (PTS) is a well-known technique for reducing system stack usage. We consider partitioned multiprocessor scheduling, with Preemption Threshold Adaptive Mixed-Criticality (PT-AMC) as the task scheduling algorithm on each processor and address the optimization problem of finding a feasible task-to-processor mapping with minimum total system stack usage on a resource-constrained multi-processor. We present the Extended Maximal Preemption Threshold Assignment Algorithm (EMPTAA), with dual purposes of improving the taskset’s schedulability if it is not already schedulable, and minimizing system stack usage of the schedulable taskset. We present efficient heuristic algorithms for finding sub-optimal yet high-quality solutions, including Maximum Utilization Difference based Partitioning (MUDP) and MUDP with Backtrack Mapping (MUDP-BM), as well as a Branch-and-Bound (BnB) algorithm for finding the optimal solution. Performance evaluation with synthetic task sets demonstrates the effectiveness and efficiency of the proposed algorithms.

Background: Nowadays, there is an immense increase in the demand for high power computation of real-time workloads and the trend towards multi-core and multiprocessor CPUs. The realtime system needs to be implemented upon multiprocessor platforms. Introduction: The nature of processors in an embedded real-time system is changing day by day. The two most significant challenges in a multiprocessor environment are scheduling and synchronization. The popularity of real-time multi-core systems has exploded in recent years, driving the rapid development of a variety of methods for multiprocessor scheduling of essential tasks; on the other hand; these systems have constraints when it comes to maintaining synchronization in order to access shared resources. Method: This research work presents a systematic review of different existing scheduling algorithms and synchronization protocols for shared resources in a real-time multiprocessor environment. The manuscript also presents a study based on various metrics of resource scheduling and comparison among different resource scheduling techniques. Result and Conclusion: The survey classifies open issues, key challenges, and likely useful research directions. Finally, we accept that there is still a lot of capacity in developing better resource management and further maintaining the overall quality. The paper considers such a future path of research in this field.

Elucidating two-stage flow shop multiprocessor scheduling problems using a hybrid genetic algorithm

Scheduling of real-time applications modelled according to the periodic and the sporadic task model under hierarchical and compositional real-time systems has been widely studied to provide temporal isolation among independent applications running on shared resources. However, for some real-time applications which are amenable to variation in their timing behaviour, usage of these tasks models can result in pessimistic solutions. The elastic task model addresses this pessimism by allowing the timing requirements of an application’s tasks to be specified as a range of values instead of a single value. Although the scheduling of elastic applications on dedicated resources has received considerable attention, there is limited work on scheduling of such applications in hierarchical and compositional settings. In this paper, we evaluate different earliest deadline first scheduling algorithms to schedule elastic applications in a minimum parallelism supply form reservation on a multiprocessor system. Our evaluation indicates that the proposed approach provides performance comparable to the current state-of-art algorithms for scheduling elastic applications on dedicated processors in terms of schedulability.