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Probability calculus for silent elimination: A method for medium access controlPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2007 (English)Report (Other academic)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Umeå: Umeå universitet , 2007. , p. 20
##### 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, id: diva2:148059
#####

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Available from: 2008-01-20 Created: 2008-01-20 Last updated: 2018-03-15Bibliographically approved

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.

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