Probability calculus for silent elimination: A method for medium access control
2007 (English)Report (Other academic)
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.
Research report in mathematical statistics, ISSN 1653-0829 ; 2007:3
Urn problem, geometric distribution, medium access control, random walk, silent period, probability generating function, recursion, exponential generating function, periodic asymptotic distribution
Probability Theory and Statistics
IdentifiersURN: urn:nbn:se:umu:diva-8388OAI: oai:DiVA.org:umu-8388DiVA: diva2:148059