On a functional equation arising in the analysis of a protocol for a multi-access broadcast channel
Keyword(s):
The Mean
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We analyse a stack protocol of the Capetanakis–Tsybakov–Mikhailov type for resolving collisions in a random multiple-access channel. We obtain a functional equation for the generating function of the expected collision resolution interval (CRI) durations, which is non-local with a non-commutative iteration semigroup. Using Mellin transform techniques and geometric properties of the iteration semigroup we show that for arrival rates smaller than a fixed threshold, the mean CRI duration for n initial colliders is asymptotically proportional to n. Ergodicity conditions are also demonstrated.
1979 ◽
Vol 25
(2)
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pp. 257-257
2015 ◽
Vol 33
(3)
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pp. 423-437
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Keyword(s):
2005 ◽
Vol 51
(11)
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pp. 3992-4003
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Keyword(s):