Analysis of Scheduling for Job Size Distributions with High Variance

Recent studies of Internet traffic have shown that flow size distributions often exhibit a high variability property in the sense that most of the flows are short and more than half of the total load is constituted by a small percentage of the largest flows. In the light of this observation, it is interesting to revisit scheduling policies that are known to favor small jobs in order to quantify the benefit for small and the penalty for large jobs. Among all scheduling policies that do not require knowledge of job size, the least attained service (LAS) scheduling policy is known to favor small jobs the most. We investigate the M/G/1/LAS queue for both, load and . Our analysis shows that for job size distributions with a high variability property, LAS favors short jobs with a negligible penalty to the few largest jobs, and that LAS achieves a mean response time over all jobs that is close to the mean response time achieved by SRPT. Finally, we implement LAS in the ns-2 network simulator to study its performance benefits for TCP flows. When LAS is used to schedule packets over the bottleneck link, more than 99% of the shortest flows experience smaller mean response times under LAS than under FIFO and only the largest jobs observe a negligible increase in response time. The benefit of using LAS as compared to FIFO is most pronounced at high load.