An Analytical Model for Network Flow Analysis

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Author: Chengchen, Bin Liu Publisher: International Conference on Computational Science and Engineering Presenter: Yun-Yan Chang Date: 2012/04/18 1.

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Presentation transcript:

An Analytical Model for Network Flow Analysis Ernesto Gomez, Yasha Karant, Keith Schubert Institute for Applied Supercomputing Department of Computer Science CSU San Bernardino The authors gratefully acknowledge the support of the NSF under award CISE 98-10708

Outline Networks and Flows History Statistical Mechanics Self-similar traffic Traffic creation and destruction Master Equation and traffic flow

One View of Network

Network Flows

Outline Networks and Flows History Statistical Mechanics Self-similar traffic Traffic creation and destruction Master Equation and traffic flow

Brief History Shannon-Hartley (classical channel capacity) C=B log2(1+SNR) Leland, Taqqu, Willinger, Wilson, Paxon, … Self-similar traffic Cao, Cleveland, Lin, Sun, Ramanan Poisson in limit

Stochastic vs. Analytic Stochastic best tools currently Opnet, NS Problems limiting cases Improving estimates Analytic (closed form equations) Handles problems of stochastic Insight into structure Fluid models Statistical Mechanics

Outline Networks and Flows History Statistical Mechanics Self-similar traffic Traffic creation and destruction Master Equation and traffic flow

Overview Large number of entities Bulk properties Equilibrium or non-equilibrium properties Time-dependence Conservation over ensemble averages Can handle classical and quantum flows

Density Matrix Formalism Each component Label by state n = node source and destination f = flow index c = flow characteristics t = time step

Density Matrix II Probability of a flow Element in Density Matrix is Averaged Properties

Outline Networks and Flows History Statistical Mechanics Self-similar traffic Traffic creation and destruction Master Equation and traffic flow

Poisson Distribution  is mean Thin Tail

Problem with Poisson Burst Long-range dependence Extended period above the mean Variety of timescales Long-range dependence Poisson or Markovian arrivals Characteristic burst length Smoothed by averaging over time Real distribution is self-similar or multifractal Proven for Ethernet

Real versus Poisson

Pareto Distribution Shape parameter () Location parameter (k) Smaller means heavier tail Infinite varience when 2 ≥  Infinite mean when 1 ≥  Location parameter (k) t≥k

Pareto Distribution

Outline Networks and Flows History Statistical Mechanics Self-similar traffic Traffic creation and destruction Master Equation and traffic flow

Flow Origination Unicast Multicast One source One destination Many segments Multicast Many destinations

Multicast Possibilities

Outline Networks and Flows History Statistical Mechanics Self-similar traffic Traffic creation and destruction Master Equation and traffic flow

Probability in Density Matrix Tr = eHt (H is energy function) Tr= (1+t/tns)-1 Cauchy Boundary conditions hypersurface of flow space Ill behaved Gaussian quadrature, Monte Carlo, Pade Approximation

Unicast Flow Time

Future Directions More detailed network Bulk properties Online tool