Stochastic differential equations (3rd ed.): an introduction with applications
Stochastic differential equations (3rd ed.): an introduction with applications
End-to-end congestion control for the internet: delays and stability
IEEE/ACM Transactions on Networking (TON)
Scalable TCP: improving performance in highspeed wide area networks
ACM SIGCOMM Computer Communication Review
The Mathematics of Internet Congestion Control (Systems and Control: Foundations and Applications)
The Mathematics of Internet Congestion Control (Systems and Control: Foundations and Applications)
Part II: control theory for buffer sizing
ACM SIGCOMM Computer Communication Review
Exponential-RED: a stabilizing AQM scheme for low- and high-speed TCP protocols
IEEE/ACM Transactions on Networking (TON)
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Recent advances in the mathematical analysis of flow control have prompted the creation of the Scalable TCP (STCP) and Exponential RED (E-RED) algorithms. These are designed to be scalable under the popular deterministic delay stability modeling framework. In this article, we analyze stochastic models of STCP and STCP combined with E-RED link behavior. We find that under certain plausible network conditions, these probabilistic models also exhibit scalable behavior. In particular, we derive parameter choice schemes for which the equilibrium coefficients of variation of flow rates are bounded, however large, fast, or complex the network. Our model is shown to exhibit behavior similar to the mean field convergence that has recently been observed in TCP.