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February 2004 AIMD algorithms and exponential functionals
Fabrice Guillemin, Philippe Robert, Bert Zwart
Ann. Appl. Probab. 14(1): 90-117 (February 2004). DOI: 10.1214/aoap/1075828048


The behavior of a connection transmitting packets into a network according to a general additive-increase multiplicative-decrease (AIMD) algorithm is investigated. It is assumed that loss of packets occurs in clumps. When a packet is lost, a certain number of subsequent packets are also lost (correlated losses). The stationary behavior of this algorithm is analyzed when the rate of occurrence of clumps becomes arbitrarily small. From a probabilistic point of view, it is shown that exponential functionals associated to compound Poisson processes play a key role. A formula for the fractional moments and some density functions are derived. Analytically, to get the explicit expression of the distributions involved, the natural framework of this study turns out to be the $q$-calculus. Different loss models are then compared using concave ordering. Quite surprisingly, it is shown that, for a fixed loss rate, the correlated loss model has a higher throughput than an uncorrelated loss model.


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Fabrice Guillemin. Philippe Robert. Bert Zwart. "AIMD algorithms and exponential functionals." Ann. Appl. Probab. 14 (1) 90 - 117, February 2004.


Published: February 2004
First available in Project Euclid: 3 February 2004

zbMATH: 1041.60072
MathSciNet: MR2023017
Digital Object Identifier: 10.1214/aoap/1075828048

Primary: 60K30, 90B18
Secondary: 68M12

Rights: Copyright © 2004 Institute of Mathematical Statistics


Vol.14 • No. 1 • February 2004
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