An Accurate Link Model and Its Application to Stability Analysis of FAST TCP

Abstract

This paper presents a link model which captures the queue dynamics when congestion windows of TCP sources change. By considering both the self-clocking and the link integrator effects, the model is a generalization of existing models and is shown to be more accurate by both open loop and closed loop packet level simulations. It reduces to the known static link model when flows' round trip delays are similar, and approximates the standard integrator link model when the heterogeneity of round trip delays is significant. We then apply this model to the stability analysis of FAST TCP. It is shown that FAST TCP flows over a single link are always linearly stable regardless of delay distribution. This result resolves the notable discrepancy between empirical observations and previous theoretical predictions. The analysis highlights the critical role of self-clocking in TCP stability and the scalability of FAST TCP with respect to delay. The proof technique is new and less conservative than the existing ones.

Parameter Conditions for Global Stability of FAST TCP

“…∆ = d + q(t). In this case, it follows from Theorem 2 that FAST TCP is globally asymptotically stable with its default parameter setting γ = 0.5, and this result agrees with the local stability results of [3], [4]. However, if each source updates its congestion window once every RTT, then the sources with the large RTT can suffer from unfairly slow update of their congestion window when they compete with the sources with the small RTT.…”

“…Remark 2: In [3], [4], it is assumed that the FAST TCP source updates its congestion window once every RTT, i.e. ∆ = d + q(t).…”

Window Flow Control: Macroscopic Properties from Microscopic Factors

“…However, due to the lack of an accurate model whose prediction can be verified by packet level simulations, there has been certain confusion in this area. Take FAST TCP as an example; existing experiments always showed it to be stable regardless of feedback delay [30] while analysis has made diverse predictions (see [24]). …”

“…This instability, which is confirmed by NS simulation, is expected not to appear in real networks with jitter as explained in Section IV-D (like the phase effect artifact [5]), but affects formal stability proofs. Consider a network (24) with N = 2 flows with equal rate, µ 1 = µ 2 = 1/2 and RTTs τ 1 = 1+δ and τ 2 = k, k = 2, 3, . .…”

“…If δ is sufficiently small, this system oscillates with a frequency near ω * ≈ 2π(1 − δ/(k + 1)), as will now be shown. Recall that the individual terms T (jωτ i ) = 1/2 + jy i (ω) lie on the line {z ∈ C|Re(z) = 1/2}, as does their convex combination in the denominator of (24). Each of these points moves vertically upwards as ω increases, at a rate depending on τ i , with all starting from 1/2 − j∞ at ω = 0.…”