Tools for the analysis and design of communication networks with Markovian dynamics

The stochastic properties of a class of communication networks whose dynamics are Markovian are analysed. The asymptotic behaviour of such a network in terms of the first and second moments of a stochastic process that describes the network dynamics is characterised and tools for their calculation are provided. Specifically, computation techniques for the calculation of these statistics are provided and that these algorithms converge exponentially fast is shown. Finally, how the results may be used for the design of network routers to realise networks with desired statistical properties is suggested.

[1]  Christopher V. Hollot,et al.  Nonlinear stability analysis for a class of TCP/AQM networks , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[2]  Fabian R. Wirth,et al.  A positive systems model of TCP-like congestion control: asymptotic results , 2006, IEEE/ACM Transactions on Networking.

[3]  Laurent Massoulié,et al.  Stability of distributed congestion control with heterogeneous feedback delays , 2002, IEEE Trans. Autom. Control..

[4]  Robert Shorten,et al.  Stochastic Equilibria of AIMD Communication Networks , 2006, SIAM J. Matrix Anal. Appl..

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

[6]  Liang Guo,et al.  A spectrum of TCP-friendly window-based congestion control algorithms , 2003, TNET.

[7]  Fernando Paganini,et al.  Internet congestion control , 2002 .

[8]  João Pedro Hespanha,et al.  Stochastic Hybrid Systems: Application to Communication Networks , 2004, HSCC.

[9]  Yang Richard Yang,et al.  General AIMD congestion control , 2000, Proceedings 2000 International Conference on Network Protocols.

[10]  Swaroop Darbha,et al.  A method for estimating the proportion of nonresponsive traffic at a router , 2004, IEEE/ACM Transactions on Networking.

[11]  R. Srikant,et al.  Stable, scalable, fair congestion control and AQM schemes that achieve high utilization in the Internet , 2003, IEEE Trans. Autom. Control..

[12]  Glenn Vinnicombe,et al.  ON THE STABILITY OF NETWORKS OPERATING TCP-LIKE CONGESTION CONTROL , 2002 .

[13]  George Varghese,et al.  New directions in traffic measurement and accounting , 2002, CCRV.

[14]  Van Jacobson,et al.  Congestion avoidance and control , 1988, SIGCOMM '88.

[15]  F. Baccelli,et al.  Interaction of TCP flows as billiards , 2003, IEEE INFOCOM 2003. Twenty-second Annual Joint Conference of the IEEE Computer and Communications Societies (IEEE Cat. No.03CH37428).

[16]  Saverio Mascolo,et al.  Congestion control in high-speed communication networks using the Smith principle , 1999, Autom..

[17]  Ramesh Johari,et al.  End-to-end congestion control for the internet: delays and stability , 2001, TNET.

[18]  Yin Zhang,et al.  Understanding the performance of many TCP flows , 2001, Comput. Networks.

[19]  François Baccelli,et al.  AIMD, fairness and fractal scaling of TCP traffic , 2002, Proceedings.Twenty-First Annual Joint Conference of the IEEE Computer and Communications Societies.

[20]  Frank Kelly,et al.  Mathematical Modelling of the Internet , 2001 .

[21]  D. Vere-Jones.  Markov Chains , 1972, Nature.

[22]  Vishal Misra,et al.  Dynamic analysis of congested TCP networks , 2002, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301).

[23]  François Baccelli,et al.  Interaction of TCP flows as billiards , 2005, IEEE/ACM Transactions on Networking.

[24]  L. Elsner,et al.  On the convergence of asynchronous paracontractions with application to tomographic reconstruction from incomplete data , 1990 .

[25]  Ljiljana Trajkovic,et al.  An overview and comparison of analytical TCP models , 2004, 2004 IEEE International Symposium on Circuits and Systems (IEEE Cat. No.04CH37512).

[26]  Robert J. Plemmons,et al.  Nonnegative Matrices in the Mathematical Sciences , 1979, Classics in Applied Mathematics.