Many applications in scientific and engineering domains are structured as large numbers of independent tasks with low granularity. These applications are thus amenable to straightforward parallelization, typically in master-worker fashion, provided that efficient scheduling strategies are available. Such applications have been called divisible loads because a scheduler may divide the computation among worker processes arbitrarily, both in terms of number of tasks and of task sizes. Divisible load scheduling has been an active area of research for the last fifteen years. A vast literature offers results and scheduling algorithms for various models of the underlying distributed computing platform. Broad surveys are available that report on accomplishments in the field. By contrast, in this paper we propose a unified theoretical perspective that synthesizes previously published results, several novel results, and open questions, in a view to foster novel divisible load scheduling research. Specifically, we discuss both one-round and multi-round algorithms, and we restrict our scope to the popular star and tree network topologies, which we study with both linear and affine cost models for communication and computation.

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Abstract—Conventional divisible load scheduling algorithms attempt to achieve optimal partitioning of massive loads to be distributed among processors in a distributed computing system in the presence of communication delays in the network. However, these algorithms depend strongly upon the assumption of prior knowledge of network parameters and cannot handle variations or lack of information about these parameters. In this paper, we present an adaptive strategy that estimates network parameter values using a probing technique and uses them to obtain optimal load partitioning. Three algorithms, based on the same strategy, are presented in the paper, incorporating the ability to cope with unknown network parameters. Several illustrative numerical examples are given. Finally, we implement the adaptive algorithms on an actual network of processor nodes using MPI implementation and demonstrate the feasibility of the adaptive approach. Index Terms—Scheduling and task partitioning, divisible loads, distributed applications, workstations, multiprocessor systems. 1

Divisible Load Theory (DLT) considers the scheduling of arbitrarily partitionable loads in distributed systems. The underlying assumption of DLT is that the processors are obedient (i.e., they do not “cheat ” the protocol), which is unrealistic when the processors are owned by autonomous, self-interested organizations that have no a priori motivation for cooperation and which strive to maximize their own welfare. In this scenario, they will manipulate the algorithm if it is beneficial to so. In this paper we propose a strategyproof mechanism for scheduling divisible loads in bus networks without control processors. We augment DLT with incentives so that it is to the benefit of a processor to truthfully report its processing capacity and to process its assignment at full capacity. The mechanism provide incentives to processors for reporting deviants and issue fines to deviants, resulting in abated willingness to deviate. 1.

This survey covers hard real-time scheduling algorithms and schedulability analysis techniques for homogeneous multiprocessor systems. It reviews the key results in this field from its origins in the late 1960s to the latest research published in late 2009. The survey outlines fundamental results about multiprocessor real-time scheduling that hold independent of the scheduling algorithms employed. It provides a taxonomy of the different scheduling methods, and considers the various performance metrics that can be used for comparison purposes. A detailed review is provided covering partitioned, global, and hybrid scheduling algorithms, approaches to resource sharing, and the latest results from empirical investigations. The survey identifies open issues, key research challenges, and likely productive research directions.

In this paper, we present a resource conscious dynamic scheduling strategy for handling large volume computationally intensive loads in a Grid system involving multiple sources and sinks / processing nodes. We consider a "pull-based" strategy, wherein the processing nodes request load from the sources. We employ the Incremental Balancing Strategy (IBS) algorithm proposed in the literature and propose a buffer estimation strategy to derive optimal load distribution. Here, we consider non-time critical loads that arrive at arbitrary times with time varying buffer availability at sinks and utilize buffer reclamation techniques so as to schedule the loads. We demonstrate detailed workings of the proposed algorithm with illustrative examples using real-life parameters derived from STAR experiments in BNL for scheduling large volume loads.

To date solutions for optimal finish time and job allocation in divisible load theory are largely obtained only for network topologies with a single load originating (root) processor. However in large-scale data intensive problems with geographically distributed resources, load is generated from multiple sources. This paper introduces a new divisible load scheduling strategy for tree networks with two load originating processors. Solutions for an optimal allocation of fraction of loads to nodes in single level tree networks are obtained via linear programming. Performance evaluation of a two source homogeneous single level tree network with concurrent communication strategy is presented.

Data Grid technology promises geographically distributed scientists to access and share physically distributed resources such as compute resource, networks, storage, and most importantly data collections for large-scale data intensive problems. The massive size and distributed nature of these datasets poses challenges to data intensive applications. Scheduling Data Grid applications must consider communication and computation simultaneously to achieve high performance. In many Data Grid applications, Data can be decomposed into multiple independent sub datasets and distributed for parallel execution and analysis. In this paper, we exploit this property and propose a novel Genetic Algorithm based approach that automatically decomposes data onto communication and computation resources. The proposed GA-based scheduler takes advantage of the parallelism of decomposable Data Grid applications to achieve the desired performance level. We evaluate the proposed approach comparing with other algorithms. Simulation results show that the proposed GA-based approach can be a competitive choice for scheduling large Data Grid applications in terms of both scheduling overhead and the quality of solutions as compared to other algorithms

Closed form solutions for optimal finish time and job allocation are largely obtained only for network topologies with a single load originating (root) processor. However, it often happens that load can be generated from multiple sources as in large-scale data intensive problems with geographically distributed resources. This paper introduces load scheduling strategy for tree networks with two load originating processors. A unique scheduling strategy that allows one to obtain closed form solutions for the optimal finish time and load allocation for each processor in the network is proposed.

this paper considers the energy consumption by the different reporting strategies and results are compared in terms of each processor's energy use. The organization of this paper is as follows. In Section II, the literature to date in the areas of DLT and wireless sensor networks is briefly presented. Section III discusses the system model and some notations used in this work. The analysis of the measurement and reporting time processes using divisible load theory as a starting point is presented in Section IV. The corresponding energy use models for the various measurement and data reporting strategies in single level tree networks are also presented in Section V. In Section VI, a performance evaluation of the various strategies appears. Finally the conclusion appears in Section VII. II. LITERATURE TO DATE A. Divisible Load Scheduling Theory The problem of minimizing processing time and/or energy consumption of wireless sensor networks has received significant attention over the last few years. The optimization process involves a need for efficient allocation of sensor loads to processors as well as links. Divisible load theory is used to allow tractable performance analyses of systems incorporating sensing, communication and computation aspects. In divisible load theory, an arbitrarily divisible load without precedence relations is partitioned and distributed among processors in a multi-computer system so that the entire load is processed in the shortest possible amount of time. Since the original work on algebraic solutions for divisible load scheduling models by Cheng and Robertazzi [5] in 1988, there has been an increasing amount of study on DLT. Most of these studies develop an efficient allocation of load to processors over a network by forcing all of the proces...