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Probability calculus for silent elimination: A method for medium access control
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
YAHM Sweden AB, SE–224 78 Lund, Sweden.
2007 (English)Report (Other academic)
Abstract [en]

A probability problem arising in the context of medium access control in wireless networks is considered. It is described as a problem with n urns, each one having one ball at time 0. Each ball leaves its urn after a geometrically distributed time. Then there is a first time T such that no departures take place at the times T +1, T +2, . . . , T +k, where k is fixed. The focus is on the probability distribution of (XT , ST , T), where XT is the number of balls that leave their urns at time T and ST is the number of balls remaining there at that time. Efficient recursion formulas are derived. Asymptotics and continuous time approximations are considered. For k = ∞, T is the maximum of n geometrically distributed variables. This case has earlier got a large literature.

Place, publisher, year, edition, pages
Umeå: Umeå universitet , 2007. , 20 p.
Series
Research report in mathematical statistics, ISSN 1653-0829 ; 2007:3
Keyword [en]
Urn problem, geometric distribution, medium access control, random walk, silent period, probability generating function, recursion, exponential generating function, periodic asymptotic distribution
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:umu:diva-8388Libris ID: 10632977OAI: oai:DiVA.org:umu-8388DiVA: diva2:148059
Available from: 2008-01-20 Created: 2008-01-20 Last updated: 2014-03-19Bibliographically approved

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CiteExportLink to record
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