Size-independent versus size-dependent policies in scheduling heavy-tailed distributions

Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2008.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (p. 47-48).We study the problem of scheduling jobs on a two-machine distributed server, where the job size distribution is heavy-tailed. We focus on two distributions, for which we prove that the performance of the optimal size-independent policy is asymptotically worse than that of a simple size-dependent policy. First, we consider a simple distribution where incoming jobs can only be of two possible sizes. The motivation is that with two largely different sizes, the simple distribution captures the important aspects of a heavy tail. Second, we extend to a bounded Pareto distribution, which has an actual heavy tail. For both cases, we analyze the performance with regards to slowdown (waiting time divided by job size) for several size-independent and size-dependent policies. We see that the size-dependent policies perform better, and then go on to prove that even the best size-independent policy cannot achieve the same performance. We conclude that as we increase the variance of our job size distribution, the gap between size-independent and size-dependent policies grows.by John Nham.M.Eng