An extension of the square root law of TCP

Abstract

Using probabilistic scaling methods, we extend the square root law of TCP to schemes which may not be of the AIMD type. Our results offer insight in the relationship between throughput and loss rate, and the time scale on which losses take place. Similar results are shown to hold in scenarios where dependencies between losses occur.

TCP and iso-stationary transformations

“…[20] proves all results conjectured in [17]: weak convergence of processes as well as of stationary distributions. [15] extends the results for Q = c to a random Q. The class M is the class of scaling limits that occurs in [15].…”

“…[15] extends the results for Q = c to a random Q. The class M is the class of scaling limits that occurs in [15].…”

“…Several research papers [11,15,17,18,20,21] deal with establishing scaling limits under a "low loss" scenario for such Markov Chains. Challenges were to establish weak convergence of processes to a limiting process, and to establish weak convergence of stationary distributions to the limiting stationary distribution.…”

Steady state and scaling limit for a traffic congestion model

“…In a general model used in internet congestion control [2,9,10,14,17,19], related to classical autoregressive models [7,18], the time dependent data flow x(t) undergoes a biased random walk with linear steps in one direction (x moves to x + a, a > 0) and on a logarithmic scale in the other (x moves to γx, where 0 < γ < 1), belonging to a class of dynamics known in the literature [14] as AIMD (additive increase multiplicative decrease). In the present paper, we concentrate on one standard model, defined rigorously as the solution to the martingale problem given by (2.3), which we shall call the γ-process.…”

“…Various orders of magnitude of the jump size are considered in recent papers [14,17,19] under constant ζ but this is the first instance to our knowledge where the rates themselves are analyzed and the natural scale and criticality are identified. This approach is particularly important and the natural one since in the main application of the model, in which ζ represents the probability of loss of packets of information x, one expects non-increasing behavior in each component of x (or, in other models, the "average" level of congestionx).…”