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A distributed heterogeneous computing (HC) system consists of diversely capable machines harnessed together to execute a set of tasks that vary in their computational requirements. Heuristics are needed to map (match and schedule) tasks onto machines in an HC system to optimize some figure of merit.This paper characterizes a simulated HC environment by using the expected execution times of the tasks that arrive in the system onto the different machines present in the system. This information is arranged in an 驴expected time to compute驴 (ETC) matrix as a model of the given HC system, where the entry (i, j) is the expected execution time of task i on machine j.This model is needed to simulate different HC environments to allow testing of relative performance of different mapping heuristics under different circumstances. In particular, the ETC model is used to express the heterogeneity among the runtimes of the tasks to be executed and among the machines in the HC system.An existing range-based technique to generate ETC matrices is described. A coefficient-of-variation based technique to generate ETC matrices is proposed, and compared with the range-based technique. The coefficient-of-variation-based ETC generation method provides a greater control over the spread of values (i.e., heterogeneity) in any given row or column of the ETC matrix than the range-based method.