Analysis of SRPT Scheduling: Investigating Unfairness

The Shortest-Remaining-Processing-Time (SRPT) scheduling policy has long been known to be optimal for minimizing mean response time (sojourn time). Despite this fact, SRPT scheduling is rarely used in practice. It is believed that the performance improvements of SRPT over other scheduling policies stem from the fact that SRPT unfairly penalizes the large jobs in order to help the small jobs. This belief has led people to instead adopt "fair" scheduling policies such as Processor-Sharing (PS), which produces the same expected slowdown for jobs of all sizes.This paper investigates formally the problem of unfairness in SRPT scheduling as compared with PS scheduling. The analysis assumes an M/G/1 model, and emphasizes job size distributions with a heavy-tailed property, as are characteristic of empirical workloads. The analysis shows that the degree of unfairness under SRPT is surprisingly small.The M/G/1/SRPT and M/G/1/PS queues are also analyzed under overload and closed-form expressions for mean response time as a function of job size are proved in this setting.