Kyle Siegrist

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Let G be a probabilistic (n,m) graph in which each vertex exists independently with fixed probability p , 0 < p < 1. Pair-connected reliability of G, denoted PC,(G;p), is the expected number of connected pairs of vertices in G. An (n.m) graph G is uniformly optimally reliable i f PC,(G;p) 2 PC,(H;p) for all p, 0 < p < 1, over all (n,m) graphs H. It is shown(More)
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(More)
We consider Markov chains on partially ordered sets that generalize the success-runs and remaining life chains in reliability theory. We find conditions for recurrence and transience and give simple expressions for the invariant distributions. We study a number of special cases, including rooted trees, uniform posets, and posets associated with positive(More)