On AIMD Congestion Control in Multiple Bottleneck Networks.

We consider a linear algebraic model of the Additive-Increase Multiplicative-Decrease congestion control algorithm and present results on average fairness and convergence for multiple bottleneck networks. Results are presented for networks of both long-lived and short-lived flows

Partitioning and Invariance of AIMD Dynamics in Synchronised Networks.

In this paper we present new results on the dynamics of networks of AIMD flows. The results reveal an invariance and partitioning property that indicates potential for the design of soundly-based adaptive AIMD strategies

Convergence of trajectories and optimal buffer sizing for MIMD congestion control

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. © 2009 Elsevier B.V. All rights reserved

Convergence of trajectories and optimal buffer sizing for AIMD congestion control

We study the interaction between the AIMD (Additive Increase Multiplicative Decrease) multi-socket congestion control and a bottleneck router with Drop Tail buffer. We consider the problem in the framework of deterministic hybrid models. First, we show that trajectories always converge to limiting cycles. We characterize the cycles. Necessary and sufficient conditions for the absence of multiple jumps in the same cycle are obtained. Then, we propose an analytical framework for the optimal choice of the router buffer size. We formulate this problem as a multi-criteria optimization problem, in which the Lagrange function corresponds to a linear combination of the average goodput and the average delay in the queue. Our analytical results are confirmed by simulations performed with MATLAB Simulink

TCP Throughput Analysis under Transmission Error and Congestion Losses

This paper analyzes the performance of a large population of long lived TCP flows experiencing random packet losses due to both random transmission errors and congestion created by the sharing of a common tail drop bottleneck router. We propose a natural and simple model for the joint throughput evolution of the set of TCP sessions under such a mix of losses. For the case of Poisson transmission errors, we show that the asymptotic model where the population tends to infinity leads to a well defined and tractable dynamical system. In particular, we get the mean value of the throughput of each session as a function of the transmission error rate and the synchronization rate in the bottleneck router. The large population asymptotic model has two interesting and non-intuitive properties: 1) there exists a positive threshold (given in closed form) on the transmission error rate above which there are no congestion losses at all in steady state; 2) below this threshold, the mean throughput of each flow is an increasing function of the transmission error rate, so that the maximum mean value is in fact achieved when the transmission error rate is equal to this threshold. The finite population model and models based on other classes of point processes are also studied. In particular, a sufficient condition is obtained for the existence of congestion times in the case of arbitrary transmission error point processes