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- Bondesson, Lennart, 1944-, et al.
(författare)
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Probability calculus for silent elimination : A method for medium access control
- 2007
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- 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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- Lundquist, Anders, 1978-, et al.
(författare)
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On sampling with desired inclusion probabilities of first and second order
- 2005
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- We present a new simple approximation of target probabilities pi for conditional Poisson sampling to obtain given inclusion probabilities. This approximation is based on the fact that the Sampford design gives inclusion probabilities as desired. Some alternative routines to calculate exact pi-values are presented and compared numerically. Further we derive two methods for achieving prescribed 2nd order inclusion probabilities. First we use a probability function belonging to the exponential family. The parameters of this probability function are determined by using an iterative proportional fitting algorithm. Then we modify the conditional Poisson probability function with an additional quadratic factor.
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