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Many parallel computer systems installed in computing centers worldwide, which adopts backfilling based job scheduling policies, require that users should provide estimated job execution time when submitting a job to the system. This paper presents an approach, taking advantage of the estimated job execution time, to effectively allocating processors to jobs submitted to a heterogeneous computing grid. The proposed adaptive processor allocation approach was evaluated with simulation studies under various workload and processor speed conditions. The results indicate that the adaptive processor allocation approach can effectively improve the overall system performance, in terms of jobspsila average turnaround time, from two to four times under different conditions, compared to currently used methods.