**On AIMD algorithms with correlated losses**

**F. Guillemin, Ph. Robert, and B. Zwart**

**Abstract:**

The behavior of 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). We analyze the
congestion window size distribution and the throughput of the
connection in the stationary regime when the occurrence of clumps
becomes arbitrarily small. From a probabilistic point of view, it is
shown that exponential integral random variables associated to
compound Poisson processes play a key role. Analytically, to derive
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 model.

**Presentation Slides**

**Based on the Papers:**

V. Dumas, F. Guillemin, and Ph. Robert,
"A Markovian analysis of AIMD algorithms"

F. Guillemin, Ph. Robert and B. Zwart,
"AIMD algorithms and exponential functionals",

Submitted to *The Annals of Applied Probability*, April 2002