Problems in Task Scheduling in Multiprocessor System

This contemporary computer systems are multiprocessor or multicomputer machines. Their efficiency depends on good methods of administering the executed works. Fast processing of a parallel application is possible only when its parts are appropriately ordered in time and space. This calls for efficient scheduling policies in parallel computer systems. In this work deterministic problems of scheduling are considered. The classical scheduling theory assumed that the application in any moment of time is executed by only one processor. This assumption has been weakened recently, especially in the context of parallel and distributed computer systems. This monograph is devoted to problems of deterministic scheduling applications (or tasks according to the scheduling terminology) requiring more than one processor simultaneously. We name such applications multiprocessor tasks. In this work the complexity of open multiprocessor task scheduling problems has been established. Algorithms for scheduling multiprocessor tasks on parallel and dedicated processors are proposed. For a special case of applications with regular structure which allow for dividing it into parts of arbitrary size processed independently in parallel, a method of finding optimal scattering of work in a distributed computer system is proposed. The applications with such regular characteristics are called divisible tasks. The concept of a divisible task enables creation of tractable computation models in a wide class of computer architectures such as chains, stars, meshes, hypercubes, multistage networks. Divisible task method gives rise to the evaluation of computer system performance. Examples of such performance evaluation are presented. This work summarizes earlier works of the author as well as contains new original results.