We consider parallel, identical machine scheduling problems where the jobs are subject to precedence constraints, release dates, and the processing times of jobs are governed by independent probability distributions. The objective is to

The major goal of dynamic load balancing is not primarily to equalize the load on the nodes of a parallel computing system, but to optimize the average response time of single requests or the throughput of all applications in the system. Therefore it is often necessary not only to keep all processors busy and all processor ready queue lengths within the same range, but to avoid delays and inefficient computations caused by foreseeable but ignored data flow and precedence constraints between related tasks. We will present concepts for dynamic consideration of inter task dependencies within small groups of tasks and evaluate them observing real applications in a load balancing environment on a network of workstations. The concepts are developed from scheduling of single task graphs towards heterogeneous multi user operation scenarios. 1 Introduction The availability of parallel processing systems and computer networks offers a multiple of the processing power, which can...

In this paper, we consider the stochastic profile scheduling problem of a partially ordered set of tasks on uniform processors. The set of available processors varies in time. The running times of the tasks are independent random variables with exponential distributions. We obtain a sufficient condition under which a list policy stochastically minimizes the makespan within the class of preemptive policies. This result allows us to obtain a simple optimal policy when the partial order is an interval order, or an in-forest, or an out-forest. Keywords: Stochastic Scheduling, Profile Scheduling, Makespan, Precedence Constraint, Interval Order, In-Forest, Out-Forest, Uniform Processors, Stochastic Ordering. 1 Introduction Consider the following scheduling problem. We are given a set of tasks to be run in a system consisting of uniform processors (i.e., processors having different speeds). The executions of these tasks must satisfy some precedence constraints which are described by a dire...

: The notion of profile scheduling was first introduced by Ullman in 1975 in the complexity analysis of deterministic scheduling algorithms. In such a model, the number of processors available to a set of tasks may vary in time. Since the last decade, this model has been used to deal with systems subject to processor failures, multiprogrammed systems, or dynamically reconfigured systems. The aim of this paper is to overview optimal polynomial solutions for scheduling a set of partially ordered tasks in these systems. Particular attentions are given to a class of algorithms referred to as list scheduling algorithms. The objective of the scheduling problem is to minimize either the maximum lateness or the makespan. Results on preemptive and nonpreemptive deterministic scheduling, and on preemptive stochastic scheduling, are presented. Keywords: Deterministic Scheduling, Stochastic Scheduling, Profile Scheduling, List Schedule, Priority Schedule, Precedence Constraints, Lateness, Makespan...

In real-time systems, the basic criteria are to satisfy both timeliness and correctness of real-time solutions. The former requirement is controlled by both resource and task scheduling at operating system level whereas the latter is achieved at language level. The efficiency of a scheduling strategy depends upon several factors such as hardware configuration, type of real-time application and the complexity of real-time problem. This report presents a classification of scheduling techniques in order to help designers model their real-time systems with appropriate scheduling schemes to meet their timeliness characteristic. It also aims to explore the scheduling properties and scope of research in real-time computing. 1.0 Introduction In general, real-time systems are classified into soft and hard real-time systems. In soft real-time systems, the tasks are expected to perform as fast as possible. The response time can vary quite considerably, but at the same time can satisfy the deadl...

. The problem of scheduling a set of tasks on two parallel and identical processors is considered. The executions of tasks are constrained by precedence relations. The running times of the tasks are independent random variables with a common exponential distribution. The goal of scheduling is to minimize the makespan, i.e. the maximum task completion time. A simple optimal preemptive policy is proven to stochastically minimize the makespan when the precedence graph belongs to a class of forest-cut graphs. 1. Introduction Parallel programs are usually represented by task graphs which are directed acyclic graphs where vertices represent tasks and arcs represent precedence relations between tasks. The executions of these tasks have to satisfy these precedence constraints in such a way that a task can start execution only when all its predecessor tasks have completed execution. For any given task graph, the scheduling problem consists in assigning tasks to a set of processors in such a wa...

We consider preemptive and nonpreemptive scheduling of partially ordered tasks on parallel processors, where the precedence relations have an interval order, an in-forest, or a uniform out-forest structure. Processing times of tasks are random variables with an ILR (increasing in likelihood ratio) distribution in the nonpreemptive case and an exponential distribution in the preemptive case. We consider a general cost that is a function of time and of the uncompleted tasks and show that the Most Successors policy (MS) stochastically minimizes the cost function when it satisfies certain agreeability conditions. A consequence is that MS stochastically minimizes makespan, weighted flowtime, and weighted number of late jobs.