Before revision:  We further consider the problem under Poisson arrival and general workload distribution ,\ie and show that M-SRPT is asymptotic optimal when the traffic intensity \rho approaches 1, if the job size distribution has bounded support. 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:  We further consider the problem under Poisson arrival and general workload distribution ,\ie and show that M-SRPT is asymptotic optimal when the traffic intensity \rho approaches 1, if the job size distribution has finite support. Beyond bounded job workload, the asymptotic optimality of M-SRPT also holds for unbounded job size distributions with certain probabilistic assumptions, for example, M/M/N system with upper bounded task workload. An byproduct of our analysis is a tight 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.