2005 International Conference on Analysis of Algorithms
Conrado Martínez (ed.)
DMTCS Conference Volume AD (2005), pp. 2738
author:  Y. Baryshnikov, E. Coffman, J. Feng and P. Momčilović 

title:  Asymptotic analysis of a nonlinear AIMD algorithm 
keywords:  AIMD analysis, congestion avoidance algorithms, fair resource allocation, differentiated service 
abstract: 
The AdditiveIncreaseMultiplicative Decrease (AIMD)
algorithm is an effective technique for controlling
competitive access to a shared resource. Let
N
be the number of users and let
x
be the amount of the resource in possession of the
i
(t)
i
th user. The allocations
x
increase linearly until the aggregate demand
i
(t)
Σ
exceeds a given nominal capacity, at which point a
user is selected at a random time and its allocation
reduced from
i
x
i
(t)
x
to
i
(t)
x
for some given parameter
i
(t)/γ,
γ>1
. In our new, generalized version of AIMD, the choice
of users to have their allocations cut is determined by a
selection rule whereby the probabilities of selection are
proportional to
x
, with
i
α
(t)/ Σ
j
x
j
α
α
a parameter of the policy. Variations of parameters
allows one to adjust fairness under AIMD (as measured for
example by the variance of
x
) as well as to provide for differentiated service.
The primary contribution here is an asymptotic, large
i
(t)
N
analysis of the above nonlinear AIMD algorithm within
a baseline mathematical model that leads to explicit
formulas for the density function governing the allocations
x
in statistical equilibrium. The analysis yields
explicit formulas for measures of fairness and several
techniques for supplying differentiated service via AIMD.
i
(t)

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reference:  Y. Baryshnikov and E. Coffman and J. Feng and P. Momčilović (2005), Asymptotic analysis of a nonlinear AIMD algorithm, in 2005 International Conference on Analysis of Algorithms, Conrado Martínez (ed.), Discrete Mathematics and Theoretical Computer Science Proceedings AD, pp. 2738 
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