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Critical Scale for a Continuous AIMD Model
Authors:Ilie Grigorescu  Min Kang
Institution:1. Department of Mathematics, University of Miami, Coral Gables, Florida, USA;2. Department of Mathematics, North Carolina State University, Raleigh, North Carolina, USA
Abstract:A scaled version of the general AIMD model of transmission control protocol (TCP) used in Internet traffic congestion management leads to a Markov process x(t) representing the time dependent data flow that moves forward with constant speed on the positive axis and jumps backward to γx(t), 0 < γ < 1 according to a Poisson clock whose rate α(x) depends on the interval swept in between jumps. We give sharp conditions for Harris recurrence and analyze the convergence to equilibrium on multiple scales (polynomial, fractional exponential, exponential) identifying the critical case xα(x) ~ β. Criticality has different behavior according to whether it occurs at the origin or infinity. In each case, we determine the transient (possibly explosive), null—and positive—recurrent regimes by comparing β to ( ? ln?γ)? 1.
Keywords:AIMD  Criticality  Geometric ergodicity  Harris recurrence  Local Doeblin condition  TCP
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