Open Problem—Size-Based Scheduling with Estimation Errors

For queueing systems, leveraging knowledge of job sizes to perform size-based scheduling leads to policies with attractive performance characteristics. Although there is a body of literature in this area, in the interest of space, we highlight one classical result: for a single-server system, the shortest remaining processing time (SRPT) policy (priority is given to the job closest to completion) is known to minimize the mean response time (Schrage and Miller 1966). Although this and related performance results have been known for some time, such size-based scheduling policies have not been deployed to any great extent in practice. One objection to their deployment is that the assumption that one knows job sizes exactly is problematic; the typical scenario would be that estimates of job sizes are available to make scheduling decisions. There is not a large literature on the study of queueing systems in which there are estimation errors for job sizes. In the next paragraph, we discuss some typical approaches and then conclude the section with two open problems of interest in this area.