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.

Ämnesord

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

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

Nyckelord

Urn problem

geometric distribution

medium access control

random walk

silent period

probability generating function

recursion

exponential generating function

periodic asymptotic distribution

Publikations- och innehållstyp

vet (ämneskategori)

rap (ämneskategori)