Steady state and scaling limit for a traffic congestion model
Ilie Grigorescu, Min Kang · ESAIM Probability and Statistics · 2008
In a general model (AIMD) of transmission control protocol (TCP) used in internet traffic congestion management, the time dependent data flow vector x(t) > 0 undergoes a biased random walk on two distinct scales. The amount of data of each component xi(t) goes up to xi(t)+a with probability 1-ζi(x) on a unit scale or down to γxi(t), 0 c+(n, γ). Additionally, a scaling limit is proved when ζi(x) and a are of order N–1 and t → Nt, in the form of a continuum model with jump rate α(x).