Probability calculus for silent elimination : A method for medium access control

• 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.

Subject headings

NATURVETENSKAP  -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Probability Theory and Statistics (hsv//eng)

Keyword

Urn problem

geometric distribution

medium access control

random walk

silent period

probability generating function

recursion

exponential generating function

periodic asymptotic distribution

Publication and Content Type

vet (subject category)

rap (subject category)