Maciej Drozdowski

Scheduling multiprocessor tasks — An overview☆

Abstract Multiprocessor tasks require more than one processor at the same moment of time. This relatively new concept in scheduling theory emerged with the advent of parallel computing systems. In this work we present the state of the art for multiprocessor task scheduling. We show the rationale behind the concept of multiprocessor tasks. The standard three-field notation is extended to accommodate multiprocessor tasks. The main part of the work is presentation of the results in multiprocessor tasks scheduling both for parallel and for dedicated processors.

Scheduling for Parallel Processing

This book presents scheduling models for parallel processing, problems defined on the grounds of certain scheduling models, and algorithms solving the scheduling problems. The book also provides helpful generalizations about scheduling models. Features: Introduces the fundamental scheduling concepts; Discusses the technological aspects of scheduling for parallel processing; Presents the notions, concepts, and algorithms that are most immediately applicable in parallel processing; Examines the parallel task model; Outlines the methodology of computational complexity theory and introduces the basic metrics of parallel application performance; Explores scheduling with communication delays; Examines scheduling divisible loads in systems with limited memory, various interconnection types, and cost of usage; Includes detailed illustrations, a bibliography, and a notation section. This text will be valuable for researchers in parallel computing, operating systems, management science, and applied mathematics.

Divisible task scheduling — concept and verification

Abstract In this work the idea of a divisible task is presented. The divisible task is a computation which can be divided with arbitrary granularity into independent parts solved in parallel by distributed computers. A simple model of a communication delay and a computation time is adopted, based on which various computer architectures and communication methods are analyzed. We review the ways of applying the divisible task concept in the case of a linear array, star, bus, hypercube, and mesh of processors. Then, the results of an empirical justification of the analysis are presented.

Scheduling divisible MapReduce computations

In this paper we analyze MapReduce distributed computations as a divisible load scheduling problem. The two operations of mapping and reducing can be understood as two divisible applications with precedence constraints. A divisible load model of the computation, and two load partitioning algorithms are proposed. Performance limits of MapReduce computations are investigated. To our best knowledge this is the first time that processing applications with precedence constraints have been considered on the grounds of divisible load theory.

Experiments with Scheduling Divisible Tasks in Clusters of Workstations

We present results of a series of experiments with parallel processing divisible tasks on various cluster of workstations platforms. Divisible task is a new model of scheduling distributed computations. It is assumed that the parallel application can be divided into parts of arbitrary sizes and the parts can be processed independently on distributed computers. Though practical verification of the scheduling model was the primary goal of the experiments also an insight into the behavior and performance of cluster computing platforms has been gained.

Distributed processing of divisible jobs with communication startup costs

In this work we analyze the problem of an optimal distribution of a computational task among a set of processors. We assume that the task can be arbitrarily divided and its parts can be processed in parallel on different processors. A wide range of interconnection architectures of distributed computer systems is taken into consideration: a chain, a loop, a tree, a star of processors, a set of processors using shared buses, and a hypercube of processors. It is assumed that the communication time is equal to some startup value plus some amount proportional to the volume of transferred data. Using a uniform methodology we present a method to find the distribution of the load so that the minimum completion time is achieved for the considered data distribution scheme. The results can also be used to find such parameters of the processor network as equivalent speed, speedup and utilization. Moreover, the methodology presented here can be a model of the application roll-in time, and can be applied in load balancing in a heterogeneous multiprocessor system.

Scheduling divisible jobs on hypercubes

In this work a problem of finding an optimal distribution of a divisible computational job among a set of processors is considered. In the model of parallel computer systems two important factors must be taken into account: speeds of processors and speeds of communications links. With regard to this, we propose a deterministic approach finding an optimal distribution of the jobs load on a hypercube of processors. The method used allows also the determination of performance bounds on the hypercube architecture.

Scheduling divisible loads in a three-dimensional mesh of processors

Abstract We study distributed processing of a divisible load in a three-dimensional mesh of communicating processors. The objective is to find distribution of the load among processors which guarantees minimal processing time. We describe a family of load distribution algorithms and obtain closed-form formulae for optimal load shares allocated to processors in each algorithm. Our model takes into consideration communication delays involved in moving load shares from one processor to another. In large meshes our algorithms attain speedup limit of 1+p/ρ, where p is the number of communication ports used simultaneously by each processor in data transfer and ρ is the ratio of processing to communication transfer rate. We also show a matching upper bound on the speedup in this topology.

Scheduling multiprocessor tasks on a dynamic configuration of dedicated processors

In the classical scheduling theory, it is widely assumed that a task can be processed by only one processor at a time. With the rapid development of technology, this assumption is no longer valid. In this work we present a problem of scheduling tasks, each of which requires for its processing a set of processors simultaneously and which can be executed on several alternative sets of processors. Scheduling algorithms based on dynamic and linear programming are presented that construct minimum length non-preemptive and preemptive schedules, respectively. Results of computational experiments are also reported.

Scheduling a divisible task in a two-dimensional toroidal mesh

Abstract In this paper, a problem of scheduling an arbitrarily divisible task is considered. Taking into account both communication delays and computation time we propose a scheduling method which minimizes total execution time. We focus on two dimensional processor networks assuming a circuit-switching routing mechanism. The scheduling method uses a scattering scheme proposed in Peters and Syska (IEEE Trans. Parallel Distributed Systems 7(3) (1996) 246–255) to distribute parts of the task to processors in a minimum time. We show how to model and solve this problem with a set of algebraic equations. A solution of the latter allows one to analyze the performance of the network depending on various actual parameters of the task and the parallel machine. Though the method is defined for a particular architecture and scattering scheme it can be generalized to analyze other architectures of parallel computer systems.