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Abstract-This study considers a heterogeneous computing system and corresponding workload being investigated by the Extreme Scale Systems Center (ESSC) at Oak Ridge National Laboratory (ORNL). The ESSC is part of a collaborative effort between the Department of Energy (DOE) and the Department of Defense (DoD) to deliver research, tools, software, and technologies that can be integrated, deployed, and used in both DOE and DoD environments. The heterogeneous system and workload described here are representative of a prototypical computing environment being studied as part of this collaboration. Each task can exhibit a time-varying importance or utility to the overall enterprise. In this system, an arriving task has an associated priority and precedence. The priority is used to describe the importance of a task, and precedence is used to describe how soon the task must be executed. These two metrics are combined to create a utility function curve that indicates how valuable it is for the system to complete a task at any given moment. This research focuses on using time-utility functions to generate a metric that can be used to compare the performance of different resource schedulers in a heterogeneous computing system. The contributions of this paper are: (a) a mathematical model of a heterogeneous computing system where tasks arrive dynamically and need to be assigned based on their priority, precedence, utility characteristic class, and task execution type, (b) the use of priority and precedence to generate time-utility functions that describe the value a task has at any given time, (c) the derivation of a metric based on the total utility gained from completing tasks to measure the performance of the computing environment, and (d) a comparison of the performance of resource allocation heuristics in this environment.

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