Speedup Curve Research Articles

An Energy Transfer-Based Bifurcation Detection Method for Nonlinear Rotating Systems: Enables Accurate Capture of Period-Doubling Bifurcation and Instability

Rotor systems are widely used in industrial power generation and propulsion. Once the nonlinear contact stiffness and oil film force are taken into account, the dynamics and stability of rotor systems become quite complex, often accompanied by super-harmonic and chaotic motions. Furthermore, conventional methods face limitations in real-time detection of the bifurcations and complex nonlinear motions. This research investigates the bifurcations and stability induced by nonlinear factors in a rotor-bearing system from an energy perspective. Dynamic equations of a rotor-bearing system considering cubic term stiffness are established, the steady responses are obtained by the fourth-order Runge–Kutta method. The relationship between the bifurcations and energy transfers is analyzed numerically, the proposed stability criterion is validated by comparing the Lyapunov exponents. The bistable phenomenon of period-3[Formula: see text] ([Formula: see text]) motion is discussed in terms of numerical results and experiments which corresponds to the asymmetric jumps of the generalized energy. It is found that bifurcations and unstable motions of the nonlinear system can be captured accurately by detecting the energy transfers, the proposed generalized energy curve exhibits more detailed information than the conventional speed-up curve. These findings provide a new perspective on studying bifurcations and stability of rotating systems, which can be further applied in the condition monitoring, stability prediction as well as the design of nonlinear energy sink, representing significant progress in converting theory into engineering applications for rotor systems.

Online scheduling of parallelizable jobs in the directed acyclic graphs and speed-up curves models

This paper considers scheduling jobs online on m identical machines such that the jobs can be parallelized across the machines. Two models of parallelizability are considered, one is the speed-up curves model, and the other is the directed-acyclic-graph (DAG) model. For both models, the objectives considered are the average, maximum, and ℓk-norms of flow time for k≥1.We establish an Ω(m) lower bound on the competitive ratio of any algorithm for optimizing average flow time in both models without resource augmentation. With resource augmentation, we give a (1+ϵ)-speed O(1ϵ2k+1)-competitive algorithm in the DAG model for the ℓk-norms of flow time. This essentially matches the best-known result in the speed-up curve model for the ℓk-norms of flow time. Finally, we show an O(1)-competitive algorithm for minimizing the maximum flow time in the speed-up curves model.

An Efficient Discontinuous Galerkin Method Using a Tetrahedral Mesh for 3D Seismic Wave Modeling

ABSTRACTThe discontinuous Galerkin (DG) method is a numerical algorithm that is widely used in various fields. It has high accuracy and low numerical dispersion with advantages of easy handling boundary conditions and good parallel performance. In this study, we develop an efficient parallel weighted Runge–Kutta discontinuous Galerkin (WRKDG) method on unstructured meshes for solving 3D seismic wave equations. The DG method we use is based on the first-order formulation of a hyperbolic system with an explicit weighted Runge–Kutta time discretization. We describe the numerical scheme and parallel implementation in detail, and analyze the stability condition and numerical dispersion and dissipation. We carry out a convergence test on unstructured meshes and investigate the parallel efficiency of the implementation of the WRKDG method. The speedup curve shows that the method has good parallel performance. Finally, we present several numerical simulation examples, including acoustic and elastic wave propagations in isotropic and anisotropic media. Numerical results further verify the effectiveness of the WRKDG method in solving 3D wave propagation problems.

The case for phase-aware scheduling of parallelizable jobs

Parallelizable jobs typically consist of multiple phases of computation, where the job is more parallelizable in some phases and less parallelizable in others. For example, in a database, a query may consist of a highly parallelizable table scan, followed by a less parallelizable table join. In the past, this phase-varying parallelizability was summarized by a single sub-linear speedup curve that measures a job’s average parallelizability over its entire lifetime. Today, however, modern systems have fine-grained knowledge of the exact phase each job is in at every moment in time. Unfortunately, these systems do not fully leverage this real-time feedback when scheduling parallelizable jobs. Theory has failed to produce practical phase-aware scheduling policies, and thus scheduling in current systems is largely heuristic.A phase-aware scheduling policy must decide, given its knowledge of each job’s current phase, how many servers or cores to allocate to each job in the system at every moment in time. This paper provides the first stochastic model of a system processing parallelizable jobs composed of phases. Using our model, we derive an optimal phase-aware scheduling policy that minimizes the mean response time across jobs. Our provably optimal policy, Inelastic-First (IF), gives strict priority to jobs that are currently in less parallelizable phases. We validate our theoretical results using a simulation of a database running queries from the Star Schema Benchmark. We compare IF to a range of policies from both systems and theory, and show that IF reduces mean response time by up to a factor of 3.

Towards Optimality in Parallel Job Scheduling

To keep pace with Moore's law, chip designers have focused on increasing the number of cores per chip. To effectively leverage these multi-core chips, one must decide how many cores to assign to each job. Given that jobs receive sublinear speedups from additional cores, there is a tradeoff: allocating more cores to an individual job reduces the job's runtime, but decreases the efficiency of the overall system. We ask how the system should assign cores to jobs so as to minimize the mean response time over a stream of incoming jobs. To answer this question, we develop an analytical model of jobs running on a multi-core machine. We prove that EQUI, a policy which continuously divides cores evenly across jobs, is optimal when all jobs follow a single speedup curve and have exponentially distributed sizes. We also consider a class of "fixed-width" policies, which choose a single level of parallelization, k, to use for all jobs. We prove that, surprisingly, fixed-width policies which use the optimal fixed level of parallelization, k*, become near-optimal as the number of cores becomes large. In the case where jobs may follow different speedup curves, finding a good scheduling policy is even more challenging. In particular, EQUI is no longer optimal, but a very simple policy, GREEDY*, performs well empirically.

Towards Optimality in Parallel Scheduling

To keep pace with Moore's law, chip designers have focused on increasing the number of cores per chip rather than single core performance. In turn, modern jobs are often designed to run on any number of cores. However, to effectively leverage these multi-core chips, one must address the question of how many cores to assign to each job. Given that jobs receive sublinear speedups from additional cores, there is an obvious tradeoff: allocating more cores to an individual job reduces the job's runtime, but in turn decreases the efficiency of the overall system. We ask how the system should schedule jobs across cores so as to minimize the mean response time over a stream of incoming jobs. To answer this question, we develop an analytical model of jobs running on a multi-core machine. We prove that EQUI, a policy which continuously divides cores evenly across jobs, is optimal when all jobs follow a single speedup curve and have exponentially distributed sizes. EQUI requires jobs to change their level of parallelization while they run. Since this is not possible for all workloads, we consider a class of "fixed-width" policies, which choose a single level of parallelization, k, to use for all jobs. We prove that, surprisingly, it is possible to achieve EQUI's performance without requiring jobs to change their levels of parallelization by using the optimal fixed level of parallelization, k*. We also show how to analytically derive the optimal k* as a function of the system load, the speedup curve, and the job size distribution. In the case where jobs may follow different speedup curves, finding a good scheduling policy is even more challenging. In particular, we find that policies like EQUI which performed well in the case of a single speedup function now perform poorly. We propose a very simple policy, GREEDY*, which performs near-optimally when compared to the numerically-derived optimal policy.

Scheduling Parallel Jobs Online with Convex and Concave Parallelizability

Online scheduling of parallelizable jobs has received a significant amount of attention recently. Scalable algorithms are known—that is, algorithms that are (1 + e)-speed O(1)-competitive for any fixed e>0. Previous research has focused on the case where each job’s parallelizability can be expressed as a concave speedup curve. However, there are cases where a job’s speedup curve can be convex. Considering convex speedup curves has received attention in the offline setting, but, to date, there are no positive results in the online model. In this work, we consider scheduling jobs with convex or concave speedup curves for the first time in the online setting. We give a new algorithm that is (1 + e)-speed O(1)-competitive. There are strong lower bounds on the competitive ratio if the algorithm is not given resource augmentation over the adversary, and thus this is essentially the best positive result one can show for this setting.

Speed-up and Speed-down Controller of Step Motor Based on SCM

In order to prevent the locked rotor, step-out and super ledge speed control of step motor, speed-up and speed-down control to the step motor should be carried out. Based on the speed -up curve analysis, using of symmetrical design, this paper has simplified the speed-up and speed-down curve. In order to achieve real-time computing exponential curve in SCM, using the method of constant duration and control pulses, speed-up and speed-down control, exponentially, are achieved, and, the connections between step motor and drive and circuit have been designed.

Maximum speedup ratio curve (MSC) in parallel computing of the binary-tree-based drainage network

Restricted computational capacity has become a key factor in limiting the development of a majority of distributed basin models. Parallel computing is one of the most effective methods for solving this problem. Although many parallel-computing methods have been employed in basin models, few studies have carried out theoretical research on parallel characteristics of river basins. In this paper, the drainage network of river basins is treated as a binary-tree structure. Using the binary-tree theory, we find that there exists a maximum speedup curve (MSC) for an arbitrary drainage network. The x-coordinate of the MSC represents the number of processors used during the computing, while the y-coordinate corresponds to the maximum speedup ratio (MSR) that can be obtained. Under several essential assumptions, the theoretical function of MSC is established. The function indicates that the MSC consists of an ascending section and a horizontal section. A parallel algorithm capable of acquiring the MSC is proposed as well. Using this algorithm, the MSC is tested at two different-resolution drainage networks of the Lhasa River Basin. A 2-year rainfall-runoff process is simulated. The results prove the existence of MSC. However, primarily influenced by the load imbalance of subbasins, the simulation values of MSR are usually smaller than the theoretical ones.

The Effect of Time Constraints on Scaled Speedup

Gustafson, Montry, and Benner introduced the concept of scaled speedup to characterize the capabilities of distributed-memory multiprocessors. They argued that, for a fixed-size problem, the behavior of the speedup of an algorithm as a function of the number of processors, the speedup curve, can be too pessimistic a measure of a multiprocessor architecture. Instead, they measured the speedup of algorithms when the size of the corresponding problem grew with the number of processors. They referred to the resulting function as the scaled speedup curve. The scaled speedup curve is a function of how the size of the problem is allowed to grow. In this paper, it is demonstrated that allowing the size of a problem to grow to fill the available memory can produce dramatically different results from allowing the size of a problem to grow subject to satisfying an upper bound on the execution time. In particular, if a constraint on the execution time is enforced, then the scaled speedup curve is often very similar to the speedup curve for a fixed-size problem. It is shown that no more than 50 processors can be used efficiently for some common problems in scientific computation when using the current generation of distributed-memory multiprocessors. For other problems, it is shown that the scaled speedup curve indicates that massively parallel computers will be useful even if the execution time is constrained. In all of the cases examined; a meaningful interpretation of the scaled speedup curve depends on a constraint on the execution time.