Delayed stability and performance of distributed congestion control (2004) [8 citations — 3 self]

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by Yueping Zhang

Proof. Substituting x(t) = y(t) − y ∗ in (15) we get ˙x(t) = −k1 [ y ∗ + x(t) ] [ x(t − T ) + k2 x(t) ] (16) with a solution y ∗ + x(t) = [ y ∗ + x(t0) ] · e −k1 � t−T t0−T [ x(τ)+k2 x(τ+T

http://irl.cs.tamu.edu/people/dmitri/../../people/yueping/papers/sigcomm2004.pdf

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@INPROCEEDINGS{Zhang04delayedstability,
    author = {Yueping Zhang},
    title = {Delayed stability and performance of distributed congestion control},
    booktitle = {Proof. Substituting x(t) = y(t) − y ∗ in (15) we get ˙x(t) = −k1 [ y ∗ + x(t) ] [ x(t − T ) + k2 x(t) ] (16) with a solution y ∗ + x(t) = [ y ∗ + x(t0) ] · e −k1 � t−T t0−T [ x(τ)+k2 x(τ+T},
    year = {2004},
    pages = {307--318}
}

Abstract:

Recent research efforts to design better Internet transport protocols combined with scalable Active Queue Management (AQM) have led to significant advances in congestion control. One of the hottest topics in this area is the design of discrete congestion control algorithms that are asymptotically stable under heterogeneous feedback delay and whose control equations do not explicitly depend on the RTTs of end-flows. In this paper, we show that max-min fair congestion control methods with a stable symmetric Jacobian remain stable under arbitrary feedback delay (including heterogeneous directional delays) and that the stability condition of such methods does not involve any of the delays. To demonstrate the practicality of the obtained result, we change the original controller in Kelly’s work [14] to become robust under random feedback delay and fixed constants of the control equation. We call the resulting framework Maxmin Kelly Control (MKC) and show that it offers smooth sending rate, exponential convergence to efficiency, and fast convergence to fairness, all of which make it appealing for future high-speed networks.

Citations

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551	Equation-Based Congestion Control for Unicast Applications – Floyd, Handley, et al. - 2000
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165	Scalable TCP: Improving Performance in Highspeed Wide Area Networks – Kelly - 2003
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134	A duality model of TCP and queue management algorithms – Low - 2003
129	End-to-end congestion control schemes: utility functions, random losses and ECN marks – Kunniyur, Srikant - 2003
106	End-to-end congestion control for the internet: Delays and stability – Johari, Tan - 2000
78	Stability of distributed congestion control with heterogeneous feedback delays – Massoulié - 2002
71	A Time-Scale Decomposition Approach to Adaptive ECN Marking – Kunniyur, Srikant
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10	Robust congestion control for the Internet – Vinnicombe - 2002
7	Congestion Control and AQM Schemes that Achieve High Utilization in the Internet – Kunniyur, Srikant, et al. - 2003
5	Difference Equations – Kelley, Peterson - 2001
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