Graphs & digraphs (2nd ed.)
Acyclic fork-join queuing networks
Journal of the ACM (JACM)
A data structure for manipulating priority queues
Communications of the ACM
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Let G = (V, ≥) be a partially ordered set such that V is countable, there exists a minimum element a ∈ V, and {u ∈ V : u ≥ v} is finite for each v ∈ V. Suppose that {Xv : v ≠ a} is a collection of independent, identically distributed, nonnegative random variables. We think of Xv as the time required to perform a job associated with v, but the job at v cannot begin until all jobs at u ≥ v are finished. The natural random variables associated with this model are the time when all jobs in a given subset of V are completed, and the set of completed jobs at a given time. These variables are studied in terms of the structure of G, and several stochastic comparison results are obtained. The common model for sequential broadcasting in trees is a special case, and in this context, we study the broadcast center of a tree.