This paper presents new results on the problem of scheduling jobs on K≥1 parallel processors to stochastically minimize the makespan. The jobs are subject to out-forest precedence constraints, i.e., each job has at most one immediate predecessor, and job running times are independent samples from a given exponential distribution. The authors define a class of uniform out-forests in which all subtrees are are ordered by an embedding relation. They prove that an intuitive greedy policy is optimal for K=2, and that if out-forests satisfy an additional, uniform root-embedding constraint, then the greedy policy is optimal for all K≥2.
