Forward collision resolution-a technique for random multiple-access to the adder channel

1993 ◽  
Vol 39 (5) ◽  
pp. 1671-1675 ◽  
Author(s):  
I. Bar-David ◽  
E. Plotnik ◽  
R. Rom
Keyword(s):  
Multiple Access ◽  
Collision Resolution

scholarly journals On a functional equation arising in the analysis of a protocol for a multi-access broadcast channel

1986 ◽  
Vol 18 (02) ◽  
pp. 441-472 ◽  
Author(s):  
Guy Fayolle ◽  
Philippe Flajolet ◽  
Micha Hofri
Keyword(s):  
Functional Equation ◽  
Multiple Access ◽  
Mellin Transform ◽  
Multiple Access Channel ◽  
Collision Resolution ◽  
Access Channel ◽  
Iteration Semigroup ◽  
Non Local ◽  
The Mean ◽  
Multi Access

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.

scholarly journals On a functional equation arising in the analysis of a protocol for a multi-access broadcast channel

1986 ◽  
Vol 18 (2) ◽  
pp. 441-472 ◽  
Author(s):  
Guy Fayolle ◽  
Philippe Flajolet ◽  
Micha Hofri
Keyword(s):  
Functional Equation ◽  
Multiple Access ◽  
Mellin Transform ◽  
Multiple Access Channel ◽  
Collision Resolution ◽  
Access Channel ◽  
Iteration Semigroup ◽  
Non Local ◽  
The Mean ◽  
Multi Access

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.

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