On the behavior of ECN/RED gateways under a large number of TCP flows: Limit theorems

Authors:
Peerapol Tinnakornsrisuphap;Armand M. Makowski
Affiliations:
Qualcomm Inc., San Diego 92121;Department of Electrical and Computer Engineering, and Institute for Systems Research, University of Maryland, College Park 20742
Venue:
Queueing Systems: Theory and Applications
Year:
2006

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Abstract

We consider a discrete-time stochastic model of an ECN/RED gateway where competing TCP sources share the link capacity. As the number of competing flows becomes large, the asymptotic queue behavior (normalized by the number of flows) at the gateway can be described by a simple recursion and the throughput behavior of individual TCP flows becomes asymptotically independent. A Central Limit Theorem complement is also presented, yielding a more accurate characterization of the asymptotic queue size. These results suggest a scalable yet accurate model of this complex large-scale stochastic feedback system, and crisply reveal the sources of queue fluctuations.