Convergence of trajectories and optimal buffer sizing for MIMD congestion control

Authors:
Yi Zhang;Alexei Piunovskiy;Urtzi Ayesta;Konstantin Avrachenkov
Affiliations:
Department of Mathematical Sciences, The University of Liverpool, Liverpool L69 7ZL, UK;Department of Mathematical Sciences, The University of Liverpool, Liverpool L69 7ZL, UK;LAAS-CNRS 7 Avenue Colonel Roche, 31077 Toulouse Cedex, France and BCAM - Basque Center for Applied Mathematics, 48160 Derio, Spain;MAESTRO Team, INRIA, 2004 route des lucioles - BP 93 FR-06902 Sophia Antipolis Cedex, France
Venue:
Computer Communications
Year:
2010

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Abstract

We study the interaction between the MIMD (Multiplicative Increase Multiplicative Decrease) congestion control and a bottleneck router with Drop Tail buffer. We consider the problem in the framework of deterministic hybrid models. We study conditions under which the system trajectories converge to limiting cycles with a single jump. Following that, we consider the problem of the optimal buffer sizing in the framework of multi-criteria optimization in which the Lagrange function corresponds to a linear combination of the average throughput and the average delay in the queue. As case studies, we consider the Slow Start phase of TCP New Reno and Scalable TCP for high speed networks.