Controlled Synthesis of Traffic Matrices

The traffic matrix (TM) is a chief input in many network design and planning applications. In this paper, we propose a model, called the spherically additive noise model (SANM). In conjunction with iterative proportional fitting (IPF), it enables fast generation of synthetic TMs around a predicted TM. We analyze SANM and IPF’s action on the model to show theoretical guarantees on asymptotic convergence, in particular, convergence to the well-known gravity model.

[1]  M. D. McKay,et al.  Creating synthetic baseline populations , 1996 .

[2]  Nick McKeown,et al.  Designing a Predictable Internet Backbone with Valiant Load-Balancing , 2005, IWQoS.

[3]  W. Deming,et al.  On a Least Squares Adjustment of a Sampled Frequency Table When the Expected Marginal Totals are Known , 1940 .

[4]  Walter Willinger,et al.  Spatio-temporal compressive sensing and internet traffic matrices , 2009, SIGCOMM '09.

[5]  Matthew Roughan,et al.  Large-scale measurement and modeling of backbone Internet traffic , 2002, SPIE ITCom.

[6]  Emilio Leonardi,et al.  How to identify and estimate the largest traffic matrix elements in a dynamic environment , 2004, SIGMETRICS '04/Performance '04.

[7]  Friedrich Pukelsheim,et al.  Biproportional scaling of matrices and the iterative proportional fitting procedure , 2014, Ann. Oper. Res..

[8]  Albert G. Greenberg,et al.  Experience in measuring backbone traffic variability: models, metrics, measurements and meaning , 2002, IMW '02.

[9]  Carsten Lund,et al.  Estimating point-to-point and point-to-multipoint traffic matrices: an information-theoretic approach , 2005, IEEE/ACM Transactions on Networking.

[10]  I. Csiszár.  $I$-Divergence Geometry of Probability Distributions and Minimization Problems , 1975 .

[11]  Matthew Roughan,et al.  Traffic Matrix Reloaded: Impact of Routing Changes , 2005, PAM.

[12]  Jon C. Dattorro,et al.  Convex Optimization & Euclidean Distance Geometry , 2004 .

[13]  S. Fienberg.  An Iterative Procedure for Estimation in Contingency Tables , 1970 .

[14]  Kavé Salamatian,et al.  Traffic matrix estimation: existing techniques and new directions , 2002, SIGCOMM '02.

[15]  Antonio Nucci,et al.  The problem of synthetically generating IP traffic matrices: initial recommendations , 2005, CCRV.

[16]  Vijay Erramilli,et al.  An independent-connection model for traffic matrices , 2006, IMC '06.

[17]  Mikkel Thorup,et al.  Traffic engineering with estimated traffic matrices , 2003, IMC '03.

[18]  Anja Feldmann,et al.  Deriving traffic demands for operational IP networks: methodology and experience , 2001, TNET.

[19]  Ilkka Norros,et al.  On the Use of Fractional Brownian Motion in the Theory of Connectionless Networks , 1995, IEEE J. Sel. Areas Commun..

[20]  Bin Yu,et al.  A fast lightweight approach to origin-destination IP traffic estimation using partial measurements , 2006, IEEE Transactions on Information Theory.

[21]  Matthew Roughan,et al.  Simplifying the synthesis of internet traffic matrices , 2005, CCRV.

[22]  Matthew Roughan,et al.  Robust Network Planning , 2010 .

[23]  Kostas N. Oikonomou,et al.  Analytical forms for most likely matrices derived from incomplete information , 2011, Int. J. Syst. Sci..

[24]  Matthew Roughan,et al.  Internet Traffic Matrices: A Primer , 2013 .

[25]  Y. Vardi,et al.  Network Tomography: Estimating Source-Destination Traffic Intensities from Link Data , 1996 .

[26]  Evgueni A. Haroutunian,et al.  Information Theory and Statistics , 2011, International Encyclopedia of Statistical Science.

[27]  Matthew Roughan,et al.  Network-design sensitivity analysis , 2014, SIGMETRICS '14.

[28]  Richard Sinkhorn,et al.  Concerning nonnegative matrices and doubly stochastic matrices , 1967 .

[29]  Albert G. Greenberg,et al.  Fast accurate computation of large-scale IP traffic matrices from link loads , 2003, SIGMETRICS '03.

[30]  M. E. Williams,et al.  TRANSIMS: TRANSPORTATION ANALYSIS AND SIMULATION SYSTEM , 1995 .

[31]  Thomas M. Cover,et al.  Elements of information theory (2. ed.) , 2006 .

[32]  Matthew Roughan,et al.  Spatiotemporal Traffic Matrix Synthesis , 2015, Comput. Commun. Rev..