This research investigates the problem of robust static resource allocation for distributed computing systems operating under imposed Quality of Service (QoS) constraints. Often, such systems are expected to function in a physical environment replete with uncertainty, which causes the amount of processing required to fluctuate substantially over time. Determining a resource allocation that accounts for this uncertainty in a way that can provide a probabilistic guarantee that a given level of QoS is achieved is an important research problem. The stochastic robustness metric proposed in this research is based on a mathematical model where the relationship between uncertainty in system parameters and its impact on system performance are described stochastically.The utility of the established metric is then exploited in the design of optimization techniques based on greedy and iterative approaches that address the problem of resource allocation in a large class of distributed systems operating on periodically updated data sets. The performance results are presented for a simulated environment that replicates a heterogeneous cluster-based radar data processing center. A mathematical performance lower bound is presented for comparison analysis of the heuristic results. The lower bound is derived based on a relaxation of the Integer Linear Programming formulation for a given resource allocation problem.

Heterogeneous computing (HC) systems composed of interconnected machines with varied computational capabilities often operate in environments where there may be inaccuracies in the estimation of task execution times. Makespan (defined as the completion time for an entire set of tasks) is often the performance feature that needs to be optimized in such systems. Resource allocation is typically performed based on estimates of the computation time of each task on each class of machines. Hence, it is important that makespan be robust against errors in computation time estimates. In this research, the problem of finding a static mapping of tasks to maximize the robustness of makespan against the errors in task execution time estimates given an overall makespan constraint is studied. Two variations of this basic problem are considered: (1) where there is a given, fixed set of machines, (2) where an HC system is to be constructed from a set of machines within a dollar cost constraint. Six heuristic techniques for each of these variations of the problem are presented and evaluated.

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Heterogeneous distributed computing systems often must operate in an environment where system parameters are subject to uncertainty. Robustness can be defined as the degree to which a system can function correctly in the presence of parameter values different from those assumed. We present a methodology for quantifying the robustness of resource allocations in a dynamic environment where task execution times are stochastic. The methodology is evaluated through measuring the robustness of three different resource allocation heuristics within the context of a stochastic dynamic environment. A Bayesian regression model is fit to the combined results of the three heuristics to demonstrate the correlation between the stochastic robustness metric and the presented performance metric. The correlation results demonstrated the significant potential of the stochastic robustness metric to predict the relative performance of the three heuristics given a common objective function.

Abstract

Heterogeneous parallel and distributed computing systems frequently must operate in environments where there is uncertainty in system parameters. Robustness can be defined as the degree to which a system can function correctly in the presence of parameter values different from those assumed. In such an environment, the execution time of any given task may fluctuate substantially due to factors such as the content of data to be processed. Determining a resource allocation that is robust against this uncertainty is an important area of research. In this study, we define a stochastic robustness measure to facilitate resource allocation decisions in a dynamic environment where tasks are subject to individual hard deadlines and each task requires some input data to start execution. In this environment, the tasks that cannot meet their deadlines are dropped (i.e., discarded). We define methods to determine the stochastic completion times of tasks in the presence of the task dropping. The stochastic task completion time is used in the definition of the stochastic robustness measure. Based on this stochastic robustness measure, we design novel resource allocation techniques that work in immediate and batch modes, with the goal of maximizing the number of tasks that meet their individual deadlines. We compare the performance of our technique against several well-known approaches taken from the literature and adapted to our environment. Simulation results of this study demonstrate the suitability of our new technique in a dynamic heterogeneous computing system.

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