Institute for Systems Research Technical Reports

Permanent URI for this collectionhttp://hdl.handle.net/1903/4376

This archive contains a collection of reports generated by the faculty and students of the Institute for Systems Research (ISR), a permanent, interdisciplinary research unit in the A. James Clark School of Engineering at the University of Maryland. ISR-based projects are conducted through partnerships with industry and government, bringing together faculty and students from multiple academic departments and colleges across the university.

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Author: search.filters.author.Lubachevsky, Boris D.Subject: search.filters.subject.parallel computation

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    A Braching Random Walk with a Barrier
    (1991) Biggins, J.D.; Lubachevsky, Boris D.; Shwartz, Adam; Weiss, Alan; ISR
    Suppose that a child is likely to be weaker than its parent, and child who is too weak will not reproduce. What is the condition for a family to survive? Let b denote the mean number of children a viable parent will have; we suppose that this is independent of strength of strength as long as strength is positive. Let F denote the distribution of the change in strength from parent to child, and define h = supq (- log U eqt dF(t))). We show that the situation is black or white: 1) If b < eh then P(family line dies) = 1, 2) If b > eh then P(family survives) > 0. Define f(x) := E(number of members in the family | initial strength x). We show that if b < eh, then there exists a positive constant C such that limx ƀ e-ax f(x) = C where a is the smaller of the (at most) two positive roots of b U est dF(t) = 1. We also find an explicit expression for f(x) when the walk is on a lattice and is skip-free to the left. This process arose in an analysis of rollback-based simulation, and these results are the foundation of that analysis.