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.

[1]  Donald F. Towsley,et al.  Modeling TCP throughput: a simple model and its empirical validation , 1998, SIGCOMM '98.

[2]  A. Piunovskiy.  Optimal Control of Random Sequences in Problems with Constraints , 1997 .

[3]  Cheng Jin,et al.  FAST TCP: Motivation, Architecture, Algorithms, Performance , 2006, IEEE/ACM Transactions on Networking.

[4]  João Pedro Hespanha,et al.  A hybrid systems modeling framework for fast and accurate simulation of data communication networks , 2003, SIGMETRICS '03.

[5]  G. Raina,et al.  Buffer sizes for large multiplexers: TCP queueing theory and instability analysis , 2005, Next Generation Internet Networks, 2005.

[6]  Van Jacobson,et al.  Random early detection gateways for congestion avoidance , 1993, TNET.

[7]  Injong Rhee,et al.  Binary increase congestion control (BIC) for fast long-distance networks , 2004, IEEE INFOCOM 2004.

[8]  Tom Kelly,et al.  Scalable TCP: improving performance in highspeed wide area networks , 2003, CCRV.

[9]  Eitan Altman,et al.  Analysis of scalable TCP in the presence of Markovian losses , 2005 .

[10]  Yi Zhang,et al.  Fluid Model of An Internet Router Under the Mimd Control Scheme , 2008 .

[11]  Eitan Altman,et al.  Parallel TCP Sockets: Simple Model, Throughput and Validation , 2006, Proceedings IEEE INFOCOM 2006. 25TH IEEE International Conference on Computer Communications.

[12]  Jon Crowcroft,et al.  Differentiated end-to-end Internet services using a weighted proportional fair sharing TCP , 1998, CCRV.

[13]  Jonathan S. Turner,et al.  Link buffer sizing: a new look at the old problem , 2005, 10th IEEE Symposium on Computers and Communications (ISCC'05).

[14]  Nick McKeown,et al.  Part I: buffer sizes for core routers , 2005, CCRV.

[15]  Marina Thottan,et al.  Perspectives on router buffer sizing: recent results and open problems , 2009, CCRV.

[16]  V. Jacobson,et al.  Congestion avoidance and control , 1988, CCRV.

[17]  Dragan A. Savic,et al.  Neighbourhood Search for constructing Pareto sets , 2007, Math. Methods Oper. Res..

[18]  Scott Shenker,et al.  Observations on the dynamics of a congestion control algorithm: the effects of two-way traffic , 1991, SIGCOMM 1991.

[19]  Marina Thottan,et al.  Router buffer sizing revisited: the role of the output/input capacity ratio , 2007, CoNEXT '07.

[20]  João Pedro Hespanha,et al.  Hybrid Modeling of TCP Congestion Control , 2001, HSCC.

[21]  Rade Stanojevic,et al.  A critique of recently proposed buffer-sizing strategies , 2007, CCRV.

[22]  Christophe Diot,et al.  Reasons not to deploy RED , 1999, 1999 Seventh International Workshop on Quality of Service. IWQoS'99. (Cat. No.98EX354).

[23]  Sally Floyd,et al.  HighSpeed TCP for Large Congestion Windows , 2003, RFC.

[24]  Frank Kelly,et al.  Fairness and Stability of End-to-End Congestion Control , 2003, Eur. J. Control.

[25]  David Ott,et al.  Tuning RED for Web traffic , 2001, TNET.

[26]  Vern Paxson,et al.  TCP Congestion Control , 1999, RFC.

[27]  Donald F. Towsley,et al.  Part II: control theory for buffer sizing , 2005, CCRV.

[28]  Konstantin Avrachenkov,et al.  Convergence and Optimal Buffer Sizing for Window Based AIMD Congestion Control , 2007, ArXiv.

[29]  Cheng Song,et al.  High performance TCP in ANSNET , 1994, CCRV.

[30]  Robert Shorten,et al.  Adaptive tuning of drop-tail buffers for reducing queueing delays , 2006, IEEE Communications Letters.

[31]  Tim Roughgarden,et al.  Part III: routers with very small buffers , 2005, CCRV.

[32]  David L. Black,et al.  The Addition of Explicit Congestion Notification (ECN) to IP , 2001, RFC.

[33]  Robert N. Shorten,et al.  Experimental evaluation of TCP protocols for high-speed networks , 2007, TNET.

[34]  Tim Roughgarden,et al.  Routers with Very Small Buffers , 2006, Proceedings IEEE INFOCOM 2006. 25TH IEEE International Conference on Computer Communications.

[35]  K. Avrachenkov,et al.  Optimal choice of the buffer size in the Internet routers , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[36]  Guido Appenzeller,et al.  Sizing router buffers , 2004, SIGCOMM '04.

[37]  Injong Rhee,et al.  CUBIC: a new TCP-friendly high-speed TCP variant , 2008, OPSR.

[38]  Eitan Altman,et al.  Analysis of Scalable TCP , 2004, HSNMC.