Task assignment algorithms for two-type heterogeneous multiprocessors

Consider the problem of assigning real-time tasks on a heterogeneous multiprocessor platform comprising two different types of processors — such a platform is referred to as two-type platform. We present two linearithmic timecomplexity algorithms, SA and SA-P, each providing the follow- ing guarantee. For a given two-type platform and a given task set, if there exists a feasible task-to-processor-type assignment such that tasks can be scheduled to meet deadlines by allowing them to migrate only between processors of the same type, then (i) using SA, it is guaranteed to find such a feasible task-to- processor-type assignment where the same restriction on task migration applies but given a platform in which processors are 1+α/2 times faster and (ii) SA-P succeeds in finding 2 a feasible task-to-processor assignment where tasks are not allowed to migrate between processors but given a platform in which processors are 1+α/times faster, where 0<α≤1. The parameter α is a property of the task set — it is the maximum utilization of any task which is less than or equal to 1.

Online intra-task device scheduling for hard real-time systems

A large part of power dissipation in a system is generated by I/O devices. Increasingly these devices provide power saving mechanisms, inter alia to enhance battery life. While I/O device scheduling has been studied in the past for realtime systems, the use of energy resources by these scheduling algorithms may be improved. These approaches are crafted considering a very large overhead of device transitions. Technology enhancements have allowed the hardware vendors to reduce the device transition overhead and energy consumption. We propose an intra-task device scheduling algorithm for real time systems that allows to shut-down devices while ensuring system schedulability. Our results show an energy gain of up to 90% when compared to the techniques proposed in the state-of-the-art.

Implementing slot-based task-splitting multiprocessor scheduling

Consider the problem of scheduling a set of sporadic tasks on a multiprocessor system to meet deadlines using a task-splitting scheduling algorithm. Task-splitting (also called semi-partitioning) scheduling algorithms assign most tasks to just one processor but a few tasks are assigned to two or more processors, and they are dispatched in a way that ensures that a task never executes on two or more processors simultaneously. A particular type of task-splitting algorithms, called slot-based task-splitting dispatching, is of particular interest because of its ability to schedule tasks with high processor utilizations. Unfortunately, no slot-based task-splitting algorithm has been implemented in a real operating system so far. In this paper we discuss and propose some modifications to the slot-based task-splitting algorithm driven by implementation concerns, and we report the first implementation of this family of algorithms in a real operating system running Linux kernel version 2.6.34. We have also conducted an extensive range of experiments on a 4-core multicore desktop PC running task-sets with utilizations of up to 88%. The results show that the behavior of our implementation is in line with the theoretical framework behind it.

Practical aspects of slot-based task- splitting dispatching in its schedulability analysis

Consider the problem of scheduling a set of sporadic tasks on a multiprocessor system to meet deadlines using a tasksplitting scheduling algorithm. Task-splitting (also called semipartitioning) scheduling algorithms assign most tasks to just one processor but a few tasks are assigned to two or more processors, and they are dispatched in a way that ensures that a task never executes on two or more processors simultaneously. A certain type of task-splitting algorithms, called slot-based task-splitting, is of particular interest because of its ability to schedule tasks at high processor utilizations. We present a new schedulability analysis for slot-based task-splitting scheduling algorithms that takes the overhead into account and also a new task assignment algorithm.

Scheduling arbitrary-deadline sporadic task systems on multiprocessors

A new algorithm is proposed for scheduling preemptible arbitrary-deadline sporadic task systems upon multiprocessor platforms, with interprocessor migration permitted. This algorithm is based on a task-splitting approach - while most tasks are entirely assigned to specific processors, a few tasks (fewer than the number of processors) may be split across two processors. This algorithm can be used for two distinct purposes: for actually scheduling specific sporadic task systems, and for feasibility analysis. Simulation- based evaluation indicates that this algorithm offers a significant improvement on the ability to schedule arbitrary- deadline sporadic task systems as compared to the contemporary state-of-art. With regard to feasibility analysis, the new algorithm is proved to offer superior performance guarantees in comparison to prior feasibility tests.

Task assignment algorithms for two-type heterogeneous multiprocessors

Consider the problem of assigning implicit-deadline sporadic tasks on a heterogeneous multiprocessor platform comprising two different types of processors—such a platform is referred to as two-type platform. We present two low degree polynomial time-complexity algorithms, SA and SA-P, each providing the following guarantee. For a given two-type platform and a task set, if there exists a task assignment such that tasks can be scheduled to meet deadlines by allowing them to migrate only between processors of the same type (intra-migrative), then (i) using SA, it is guaranteed to find such an assignment where the same restriction on task migration applies but given a platform in which processors are 1+α/2 times faster and (ii) SA-P succeeds in finding a task assignment where tasks are not allowed to migrate between processors (non-migrative) but given a platform in which processors are 1+α times faster. The parameter 0<α≤1 is a property of the task set; it is the maximum of all the task utilizations that are no greater than 1. We evaluate average-case performance of both the algorithms by generating task sets randomly and measuring how much faster processors the algorithms need (which is upper bounded by 1+α/2 for SA and 1+α for SA-P) in order to output a feasible task assignment (intra-migrative for SA and non-migrative for SA-P). In our evaluations, for the vast majority of task sets, these algorithms require significantly smaller processor speedup than indicated by their theoretical bounds. Finally, we consider a special case where no task utilization in the given task set can exceed one and for this case, we (re-)prove the performance guarantees of SA and SA-P. We show, for both of the algorithms, that changing the adversary from intra-migrative to a more powerful one, namely fully-migrative, in which tasks can migrate between processors of any type, does not deteriorate the performance guarantees. For this special case, we compare the average-case performance of SA-P and a state-of-the-art algorithm by generating task sets randomly. In our evaluations, SA-P outperforms the state-of-the-art by requiring much smaller processor speedup and by running orders of magnitude faster.

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.

CPMD-mindful task assignment for NPS-F

The multiprocessor scheduling scheme NPS-F for sporadic tasks has a high utilisation bound and an overall number of preemptions bounded at design time. NPS-F binpacks tasks offline to as many servers as needed. At runtime, the scheduler ensures that each server is mapped to at most one of the m processors, at any instant. When scheduled, servers use EDF to select which of their tasks to run. Yet, unlike the overall number of preemptions, the migrations per se are not tightly bounded. Moreover, we cannot know a priori which task a server will be currently executing at the instant when it migrates. This uncertainty complicates the estimation of cache-related preemption and migration costs (CPMD), potentially resulting in their overestimation. Therefore, to simplify the CPMD estimation, we propose an amended bin-packing scheme for NPS-F allowing us (i) to identify at design time, which task migrates at which instant and (ii) bound a priori the number of migrating tasks, while preserving the utilisation bound of NPS-F.

Energy-aware task mapping onto heterogeneous platforms using DVFS and sleep states

Heterogeneous multicore platforms are becoming an interesting alternative for embedded computing systems with limited power supply as they can execute specific tasks in an efficient manner. Nonetheless, one of the main challenges of such platforms consists of optimising the energy consumption in the presence of temporal constraints. This paper addresses the problem of task-to-core allocation onto heterogeneous multicore platforms such that the overall energy consumption of the system is minimised. To this end, we propose a two-phase approach that considers both dynamic and leakage energy consumption: (i) the first phase allocates tasks to the cores such that the dynamic energy consumption is reduced; (ii) the second phase refines the allocation performed in the first phase in order to achieve better sleep states by trading off the dynamic energy consumption with the reduction in leakage energy consumption. This hybrid approach considers core frequency set-points, tasks energy consumption and sleep states of the cores to reduce the energy consumption of the system. Major value has been placed on a realistic power model which increases the practical relevance of the proposed approach. Finally, extensive simulations have been carried out to demonstrate the effectiveness of the proposed algorithm. In the best-case, savings up to 18% of energy are reached over the first fit algorithm, which has shown, in previous works, to perform better than other bin-packing heuristics for the target heterogeneous multicore platform.

Influence of dual-task on sit-to-stand-to-sit postural control in Parkinson's disease

Postural control deficits are the most disabling aspects of Parkinson's disease (PD), resulting in decreased mobility and functional independence. The aim of this study was to assess the postural control stability, revealed by variables based on the centre of pressure (CoP), in individuals with PD while performing a sit-to-stand-to-sit sequence under single- and dual-task conditions. An observational, analytical and cross-sectional study was performed. The sample consisted of 9 individuals with PD and 9 healthy controls. A force platform was used to measure the CoP displacement and velocity during the sit-to-stand-to-sit sequence. The results were statistically analysed. Individuals with PD required greater durations for the sit-to-stand-to-sit sequence than the controls (p < 0.05). The anteroposterior and mediolateral CoP displacement were higher in the individuals with PD (p < 0.05). However, only the anteroposterior CoP velocity in the stand-to-sit phase (p = 0.006) was lower in the same individuals. Comparing the single- and dual-task conditions in both groups, the duration, the anteroposterior CoP displacement and velocity were higher in the dual-task condition (p < 0.05). The individuals with PD presented reduced postural control stability during the sit-to-stand-to-sit sequence, especially when under the dual-task condition. These individuals have deficits not only in motor performance, but also in cognitive performance when performing the sit-to-stand-to-sit sequence in their daily life tasks. Moreover, both deficits tend to be intensified when two tasks are performed simultaneously.

Standing balance in individuals with Parkinson's disease during single and dual-task conditions

This study aimed to examine the differences in standing balance between individuals with Parkinson's disease (PD) and subjects without PD (control group), under single and dual-task conditions. A cross-sectional study was designed using a non-probabilistic sample of 110 individuals (50 participants with PD and 60 controls) aged 50 years old and over. The individuals with PD were in the early or middle stages of the disease (characterized by Hoehn and Yahr as stages 1-3). The standing balance was assessed by measuring the centre of pressure (CoP) displacement in single-task (eyes-open/eyes-closed) and dual-task (while performing two different verbal fluency tasks). No significant differences were found between the groups regarding sociodemographic variables. In general, the standing balance of the individuals with PD was worse than the controls, as the CoP displacement across tasks was significantly higher for the individuals with PD (p<0.01), both in anteroposterior and mediolateral directions. Moreover, there were significant differences in the CoP displacement based parameters between the conditions, mainly between the eyes-open condition and the remaining conditions. However, there was no significant interaction found between group and condition, which suggests that changes in the CoP displacement between tasks were not influenced by having PD. In conclusion, this study shows that, although individuals with PD had a worse overall standing balance than individuals without the disease, the impact of performing an additional task on the CoP displacement is similar for both groups.

Effects of dual-task training on balance and executive functions in Parkinson's disease: A pilot study

The aim of this study was to analyze the efficacy of cognitive-motor dual-task training compared with single-task training on balance and executive functions in individuals with Parkinson's disease. Fifteen subjects, aged between 39 and 75 years old, were randomly assigned to the dual-task training group (n = 8) and single-task training group (n = 7). The training was run twice a week for 6 weeks. The single-task group received balance training and the dual-task group performed cognitive tasks simultaneously with the balance training. There were no significant differences between the two groups at baseline. After the intervention, the results for mediolateral sway with eyes closed were significantly better for the dual-task group and anteroposterior sway with eyes closed was significantly better for the single-task group. The results suggest superior outcomes for the dual-task training compared to the single-task training for static postural control, except in anteroposterior sway with eyes closed.