Improved Mixed-Integer Programming Models for Multiprocessor Scheduling with Communication Delays

We revise existing and introduce new mixed-integer programming models for the Multiprocessor Scheduling Problem with Communication Delays. At first, we show how to provably reduce the number of product variables necessary to explicitly linearize the so-called packing formulation that contains bilinear terms. Then, we reveal that the feasible region of almost all existing formulations contains redundant solutions and formulate new constraints in order to exclude these. At the same time, by exploiting further structural properties, the models are improved concerning their size, strength, and modeling complexity. The discussion of these improvements leads to new much more compact formulations which are then experimentally compared with each other and with other formulations from the literature. We set up a realistic scenario with a preprocessing of the task graphs, delivering the gained information equally to all the tested models and evaluate not only running times but also the obtained lower and upper bounds on the makespan objective for unsolved instances of a large scale benchmark set

Task Scheduling for Multiprocessor Systems Using Queuing Theory

This research focuses on comparing different multi-processor task scheduling algorithms. Each algorithm has been simulated using one of queuing theory models in Operations Research (OR) science to evaluate its behavior and efficiency. The comparison includes an analysis of the behavior of central processing unit (CPU) when receiving number of jobs at four random job duration patterns that are; (random, ascending, descending, and volatile low-high). Microsoft Excel 2010 was used to form the data of each case, and the result shows convergence and divergence among the studied algorithms at different patterns. Also it has been found that the Fleischer algorithm is very efficient in enhancing and minimizing the waiting duration for each job at the total job queue of the CPU. Keywords: Operations Research, Queuing Theory, Multiprocessor, Scheduling Algorithms, Simulation

Supercomputer optimizations for stochastic optimal control applications

Supercomputer optimizations for a computational method of solving stochastic, multibody, dynamic programming problems are presented. The computational method is valid for a general class of optimal control problems that are nonlinear, multibody dynamical systems, perturbed by general Markov noise in continuous time, i.e., nonsmooth Gaussian as well as jump Poisson random white noise. Optimization techniques for vector multiprocessors or vectorizing supercomputers include advanced data structures, loop restructuring, loop collapsing, blocking, and compiler directives. These advanced computing techniques and superconducting hardware help alleviate Bellman's curse of dimensionality in dynamic programming computations, by permitting the solution of large multibody problems. Possible applications include lumped flight dynamics models for uncertain environments, such as large scale and background random aerospace fluctuations

Principles for problem aggregation and assignment in medium scale multiprocessors

One of the most important issues in parallel processing is the mapping of workload to processors. This paper considers a large class of problems having a high degree of potential fine grained parallelism, and execution requirements that are either not predictable, or are too costly to predict. The main issues in mapping such a problem onto medium scale multiprocessors are those of aggregation and assignment. We study a method of parameterized aggregation that makes few assumptions about the workload. The mapping of aggregate units of work onto processors is uniform, and exploits locality of workload intensity to balance the unknown workload. In general, a finer aggregate granularity leads to a better balance at the price of increased communication/synchronization costs; the aggregation parameters can be adjusted to find a reasonable granularity. The effectiveness of this scheme is demonstrated on three model problems: an adaptive one-dimensional fluid dynamics problem with message passing, a sparse triangular linear system solver on both a shared memory and a message-passing machine, and a two-dimensional time-driven battlefield simulation employing message passing. Using the model problems, the tradeoffs are studied between balanced workload and the communication/synchronization costs. Finally, an analytical model is used to explain why the method balances workload and minimizes the variance in system behavior

The cost of conservative synchronization in parallel discrete event simulations

The performance of a synchronous conservative parallel discrete-event simulation protocol is analyzed. The class of simulation models considered is oriented around a physical domain and possesses a limited ability to predict future behavior. A stochastic model is used to show that as the volume of simulation activity in the model increases relative to a fixed architecture, the complexity of the average per-event overhead due to synchronization, event list manipulation, lookahead calculations, and processor idle time approach the complexity of the average per-event overhead of a serial simulation. The method is therefore within a constant factor of optimal. The analysis demonstrates that on large problems--those for which parallel processing is ideally suited--there is often enough parallel workload so that processors are not usually idle. The viability of the method is also demonstrated empirically, showing how good performance is achieved on large problems using a thirty-two node Intel iPSC/2 distributed memory multiprocessor

A survey of offline algorithms for energy minimization under deadline constraints

Modern computers allow software to adjust power management settings like speed and sleep modes to decrease the power consumption, possibly at the price of a decreased performance. The impact of these techniques mainly depends on the schedule of the tasks. In this article, a survey on underlying theoretical results on power management, as well as offline scheduling algorithms that aim at minimizing the energy consumption under real-time constraints, is given