Capacity Augmentation Bound of Federated Scheduling for Parallel DAG Tasks

We present a novel federated scheduling approach for parallel real-time tasks under a general directed acyclic graph (DAG) model. We provide a capacity augmentation bound of 2 for hard real-time scheduling; here we use the worst-case execution time and critical-path length of tasks to determine schedulability. This is the best known capacity augmentation bound for parallel tasks. By constructing example task sets, we further show that the lower bound on capacity augmentation of federated scheduling is also 2 for any m \u3e 2. Hence, the gap is closed and bound 2 is a strict bound for federated scheduling. The federated scheduling algorithm is also a schedulability test that often admits task sets with utilization much greater than 50%m

Provably Efficient Adaptive Scheduling for Parallel Jobs

Scheduling competing jobs on multiprocessors has always been an important issue for parallel and distributed systems. The challenge is to ensure global, system-wide efficiency while offering a level of fairness to user jobs. Various degrees of successes have been achieved over the years. However, few existing schemes address both efficiency and fairness over a wide range of work loads. Moreover, in order to obtain analytical results, most of them require prior information about jobs, which may be difficult to obtain in real applications. This paper presents two novel adaptive scheduling algorithms -- GRAD for centralized scheduling, and WRAD for distributed scheduling. Both GRAD and WRAD ensure fair allocation under all levels of workload, and they offer provable efficiency without requiring prior information of job's parallelism. Moreover, they provide effective control over the scheduling overhead and ensure efficient utilization of processors. To the best of our knowledge, they are the first non-clairvoyant scheduling algorithms that offer such guarantees. We also believe that our new approach of resource request-allotment protocol deserves further exploration. Specifically, both GRAD and WRAD are O(1)-competitive with respect to mean response time for batched jobs, and O(1)-competitive with respect to makespan for non-batched jobs with arbitrary release times. The simulation results show that, for non-batched jobs, the makespan produced by GRAD is no more than 1.39 times of the optimal on average and it never exceeds 4.5 times. For batched jobs, the mean response time produced by GRAD is no more than 2.37 times of the optimal on average, and it never exceeds 5.5 times.Singapore-MIT Alliance (SMA

Energy-Efficient Multiprocessor Scheduling for Flow Time and Makespan

We consider energy-efficient scheduling on multiprocessors, where the speed of each processor can be individually scaled, and a processor consumes power $s^{\alpha}$ when running at speed $s$, for $\alpha>1$. A scheduling algorithm needs to decide at any time both processor allocations and processor speeds for a set of parallel jobs with time-varying parallelism. The objective is to minimize the sum of the total energy consumption and certain performance metric, which in this paper includes total flow time and makespan. For both objectives, we present instantaneous parallelism clairvoyant (IP-clairvoyant) algorithms that are aware of the instantaneous parallelism of the jobs at any time but not their future characteristics, such as remaining parallelism and work. For total flow time plus energy, we present an $O(1)$-competitive algorithm, which significantly improves upon the best known non-clairvoyant algorithm and is the first constant competitive result on multiprocessor speed scaling for parallel jobs. In the case of makespan plus energy, which is considered for the first time in the literature, we present an $O(\ln^{1-1/\alpha}P)$-competitive algorithm, where $P$ is the total number of processors. We show that this algorithm is asymptotically optimal by providing a matching lower bound. In addition, we also study non-clairvoyant scheduling for total flow time plus energy, and present an algorithm that achieves $O(\ln P)$-competitive for jobs with arbitrary release time and $O(\ln^{1/\alpha}P)$-competitive for jobs with identical release time. Finally, we prove an $\Omega(\ln^{1/\alpha}P)$ lower bound on the competitive ratio of any non-clairvoyant algorithm, matching the upper bound of our algorithm for jobs with identical release time

Global EDF Scheduling for Parallel Real-Time Tasks

As multicore processors become ever more prevalent, it is important for real-time programs to take advantage of intra-task parallelism in order to support computation-intensive applications with tight deadlines. In this thesis, we consider the Global Earliest Deadline First (GEDF) scheduling policy for task sets consisting of parallel tasks. Each task can be represented by a directed acyclic graph (DAG) where nodes represent computational work and edges represent dependences between nodes. In this model, we prove that GEDF provides a capacity augmentation bound of 4-2/m and a resource augmentation bound of 2-1/m. The capacity augmentation bound acts as a linear-time schedulability test since it guarantees that any task set with total utilization of at most m/(4-2/m) where each task\u27s critical-path length is at most 1/(4-2/m) of its deadline is schedulable on m cores under GEDF. In addition, we present a pseudo-polynomial time fixed-point schedulability test for GEDF; this test uses a carry-in work calculation based on the proof for the capacity bound. Finally, we present and evaluate a prototype platform --- called PGEDF --- for scheduling parallel tasks using GEDF. PGEDF is built by combining the GNU OpenMP runtime system and the LITMUS_RT operating system. This platform allows programmers to write parallel OpenMP tasks and specify real-time parameters such as deadlines for tasks. We perform two kinds of experiments to evaluate the performance of GEDF for parallel tasks. (1) We run numerical simulations for DAG tasks. (2) We execute randomly generated tasks using PGEDF. Both sets of experiments indicate that GEDF performs surprisingly well and outperforms an existing scheduling techniques that involves task decomposition

Real-Time Wireless Sensor-Actuator Networks for Cyber-Physical Systems

A cyber-physical system (CPS) employs tight integration of, and coordination between computational, networking, and physical elements. Wireless sensor-actuator networks provide a new communication technology for a broad range of CPS applications such as process control, smart manufacturing, and data center management. Sensing and control in these systems need to meet stringent real-time performance requirements on communication latency in challenging environments. There have been limited results on real-time scheduling theory for wireless sensor-actuator networks. Real-time transmission scheduling and analysis for wireless sensor-actuator networks requires new methodologies to deal with unique characteristics of wireless communication. Furthermore, the performance of a wireless control involves intricate interactions between real-time communication and control. This thesis research tackles these challenges and make a series of contributions to the theory and system for wireless CPS. (1) We establish a new real-time scheduling theory for wireless sensor-actuator networks. (2) We develop a scheduling-control co-design approach for holistic optimization of control performance in a wireless control system. (3) We design and implement a wireless sensor-actuator network for CPS in data center power management. (4) We expand our research to develop scheduling algorithms and analyses for real-time parallel computing to support computation-intensive CPS

Preemptive scheduling of parallel jobs on multiprocessors

Abstract. We study the problem of processor scheduling for n parallel jobs applying the method of competitive analysis. We prove that for jobs with a single phase of parallelism, a preemptive scheduling algorithm without information about job execution time can achieve a mean completion time within 2 − 2 2 times the optimum. In other words, we prove a competitive ratio of 2 − n+1 n+1. The result is extended to jobs with multiple phases of parallelism (which can be used to model jobs with sublinear speedup) and to interactive jobs (with phases during which the job has no CPU requirements) to derive solutions guaranteed to be within 4 − 4 times the optimum. In comparison n+1 with previous work, our assumption that job execution times are unknown prior to their completion is more realistic, our multiphased job model is more general, and our approximation ratio (for jobs with a single phase of parallelism) is tighter and cannot be improved. While this work presents theoretical results obtained using competitive analysis, we believe that the results provide insight into the performance of practical multiprocessor scheduling algorithms that operate in the absence of complete information