Before revision:  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. We prove that the average response time in GI/GI/1 scales with 1/(1-\rho), if the job size distribution has finite support, which generalizes the growth rate in Lin, Wierman and Zwart, 2011 to general arrival processes and all work-conserving algorithms .
After revision:  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 Lin, Wierman and Zwart, 2011 to general arrival processes and all work-conserving algorithms .