An Information Theoretic Approach for Systems with Parallel Distributions: Case Studying Internet Traffic

The principle of Minimum Relative Entropy (MRE) is applied to characterize a ‘proportionality’ relationship between the state probabilities of infinite and finite capacity queues at equilibrium and thus, establish an information theoretic interpretation for the exact global balance solution of some finite capacity queues with or without correlated arrival processes. This result serves to establish the utility of the MRE inference technique and encourage its applicability to the analysis of more complex, and thus more realistic, queuing systems. The principles of Maximum Entropy (ME) and MRE are then employed, as least-biased methods of inference, towards the analysis of a Internet link carrying realistic TCP traffic, that exhibit this ‘proportionality’ relationship between a finite and infinite buffer system, as produced by a large number of connections. The analytic approximations are validated against exhaustive simulation experiments. Despite its simplicity, the methodology captures the behavior of the system under study both in the cases of finite and infinite buffers and finally and can easily be utilized for network management and design, capacity planning, and congestion control.

[1]  Matthias Grossglauser,et al.  On the relevance of long-range dependence in network traffic , 1999, TNET.

[2]  Thomas Bonald,et al.  Statistical bandwidth sharing: a study of congestion at flow level , 2001, SIGCOMM.

[3]  A. E. Ferdinand.  A statistical mechanical approach to systems analysis , 1970 .

[4]  Walter Willinger,et al.  Experimental queueing analysis with long-range dependent packet traffic , 1996, TNET.

[5]  Stefan Savage,et al.  Modeling TCP latency , 2000, Proceedings IEEE INFOCOM 2000. Conference on Computer Communications. Nineteenth Annual Joint Conference of the IEEE Computer and Communications Societies (Cat. No.00CH37064).

[6]  V. Paxson,et al.  WHERE MATHEMATICS MEETS THE INTERNET , 1998 .

[7]  Philippe Owezarski,et al.  A flow-based model for internet backbone traffic , 2002, IMW '02.

[8]  E. Jaynes.  Information Theory and Statistical Mechanics , 1957 .

[9]  Armand M. Makowski,et al.  Positive correlations and buffer occupancy: lower bounds via supermodular ordering , 2002, Proceedings.Twenty-First Annual Joint Conference of the IEEE Computer and Communications Societies.

[10]  Demetres D. Kouvatsos,et al.  Maximum entropy and the G/G/1/N queue , 1986, Acta Informatica.

[11]  A. Mullin,et al.  Mathematical Theory of Connecting Networks and Telephone Traffic. , 1966 .

[12]  Yechiam Yemini,et al.  A Statistical Mechanics of Some Interconnection Networks , 1984, Performance.

[13]  Iraj Saniee,et al.  Performance impacts of multi-scaling in wide area TCP/IP traffic , 2000, Proceedings IEEE INFOCOM 2000. Conference on Computer Communications. Nineteenth Annual Joint Conference of the IEEE Computer and Communications Societies (Cat. No.00CH37064).

[14]  Rodney W. Johnson,et al.  Axiomatic derivation of the principle of maximum entropy and the principle of minimum cross-entropy , 1980, IEEE Trans. Inf. Theory.

[15]  Demetres D. Kouvatsos,et al.  A Maximum Entropy Analysis of the G/G/1 Queue at Equilibrium , 1988 .

[16]  Demetres D. Kouvatsos,et al.  Arbitrary open queueing networks with server vacation periods and blocking , 1998, Ann. Oper. Res..

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

[18]  Donald F. Towsley,et al.  Modeling, simulation and measurements of queuing delay under long-tail internet traffic , 2003, SIGMETRICS '03.

[19]  Anja Feldmann,et al.  Data networks as cascades: investigating the multifractal nature of Internet WAN traffic , 1998, SIGCOMM '98.

[20]  R. Johnson,et al.  Properties of cross-entropy minimization , 1981, IEEE Trans. Inf. Theory.

[21]  Richard G. Baraniuk,et al.  Multiscale queuing analysis of long-range-dependent network traffic , 2000, Proceedings IEEE INFOCOM 2000. Conference on Computer Communications. Nineteenth Annual Joint Conference of the IEEE Computer and Communications Societies (Cat. No.00CH37064).

[22]  Azer Bestavros,et al.  Self-similarity in World Wide Web traffic: evidence and possible causes , 1996, SIGMETRICS '96.