A Braching Random Walk with a Barrier
| dc.contributor.author | Biggins, J.D. | en_US |
| dc.contributor.author | Lubachevsky, Boris D. | en_US |
| dc.contributor.author | Shwartz, Adam | en_US |
| dc.contributor.author | Weiss, Alan | en_US |
| dc.contributor.department | ISR | en_US |
| dc.date.accessioned | 2007-05-23T09:47:15Z | |
| dc.date.available | 2007-05-23T09:47:15Z | |
| dc.date.issued | 1991 | en_US |
| dc.description.abstract | 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. | en_US |
| dc.format.extent | 521939 bytes | |
| dc.format.mimetype | application/pdf | |
| dc.identifier.uri | http://hdl.handle.net/1903/5055 | |
| dc.language.iso | en_US | en_US |
| dc.relation.ispartofseries | ISR; TR 1991-7 | en_US |
| dc.subject | queueing networks | en_US |
| dc.subject | parallel architectures | en_US |
| dc.subject | parallel computation | en_US |
| dc.subject | Systems Integration | en_US |
| dc.title | A Braching Random Walk with a Barrier | en_US |
| dc.type | Technical Report | en_US |
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