Abstract
We consider n jobs with independent exponentially distributed processing times that are to be processed on two machines operating in parallel. The jobs are subject to precedence constraints that have the form of an intree, i.e., each job, except for the last one, has one direct successor. A job is at level l if its successor is at level l − 1 (the last job is at level 0). We assume that all jobs at level l have i.i.d. exponentially distributed processing times, with mean 1/μl. Under these assumptions, we show that the policy that schedules HLF (highest level first) minimizes the expected makespan in the class of preemptive as well as nonpreemptive schedules. This conclusion generalizes a previous result of Chandy and Reynolds.
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