Before revision:  In addition, we also present a characterization of the heavy traffic behavior of work-conserving algorithms in single-task job scheduling , and prove that the average flow time in GI/GI/1 system scales with \frac{1{1-\rho}}  , if the job size distribution has bounded support, which generalizes the result in [Lin, Wierman and Zwart, 2011] to  all work-conserving algorithms.
After revision:  In addition, we also present a characterization of the heavy traffic behavior of work-conserving algorithms in single-task job scheduling . We prove that the average flow time in GI/GI/1 system scales with \frac{1{1-\rho}} , if the job size distribution has bounded support, which generalizes the result in [Lin, Wierman and Zwart, 2011] to all work-conserving algorithms.